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1  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: September 14, 2024, 11:19:57 AM
Well, it fell into an empty slot.

Imagine that we have a game cube with 64 sides and 160 throws, more throws means repetitions will occur. Next, for each of 64 we divide by 128, that is, we take a cube with 8192 sides so that there are no repetitions.

10000000000000000000000000000000 00000000000000000000000000000000 1   pz 2  
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 3  
00000000000000000000000000000000 00000000000000000000001000000000 55  pz 4  
10000000000000000000000000000000 00000000000000000000000000000000 1   pz 5  
00000000000000000000000000000000 00100000000000000000000000000000 35  pz 6  
00000000000000000000000000000000 00000000000001000000000000000000 46  pz 7  
00000000000000000000000000100000 00000000000000000000000000000000 27  pz 8  
00000000000000000000000000000000 00000000000000000000001000000000 55  pz 9  
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 10
00100000000000000000000000000000 00000000000000000000000000000000 3   pz 11
00000000000000000000010000000000 00000000000000000000000000000000 22  pz 12
00000000000000000000000000000000 00100000000000000000000000000000 35  pz 13
00000000000000000000000000000000 10000000000000000000000000000000 33  pz 14
00000000000000000000000000000000 01000000000000000000000000000000 34  pz 15
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 16
00000000000000000000000000000000 00000000000000010000000000000000 48  pz 17
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 18
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 19
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 20
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 21
00000000000000000000000000000000 00000000000000000000010000000000 54  pz 22
00000000000000000000000000000000 00000000010000000000000000000000 42  pz 23
00000000000000000000000000000000 00000000000000000000010000000000 54  pz 24
00000000000000000000000000000000 00000000000000000000000000000010 63  pz 25
00000000000000000000000000000000 00000000000000000100000000000000 50  pz 26
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 27
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 28
00000000000000000000000000000000 00000000000100000000000000000000 44  pz 29
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 30
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 31
00000000000000000000000000000000 00000000010000000000000000000000 42  pz 32
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 33
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 34
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 35
00000000000000000000000000000100 00000000000000000000000000000000 30  pz 36
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 37
00000000000000010000000000000000 00000000000000000000000000000000 16  pz 38
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 39
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 40
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 41
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 42
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 43
00000000000000000000000000000000 00000000000000000000001000000000 55  pz 44
00000000000000000000001000000000 00000000000000000000000000000000 23  pz 45
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 46
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 47
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 48
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 49
00000000000000000100000000000000 00000000000000000000000000000000 18  pz 50
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 51
00000000000000000000000000000000 00000000000000000000000000100000 59  pz 52
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 53
00000000000000000001000000000000 00000000000000000000000000000000 20  pz 54
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 55
00000000000000000000000000000100 00000000000000000000000000000000 30  pz 56
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 57
00000000000000000000000000000000 00000010000000000000000000000000 39  pz 58
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 59
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 60
00000000000000000000000000000010 00000000000000000000000000000000 31  pz 61
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 62
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 63
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 64
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 65
00000000000000000000000000000001 00000000000000000000000000000000 32  pz 66

...............x.x.x.xx..x...xxx xxxx.xx..xxxx..xxxxxxxx.xxx.xxx.                               pz 67

00000000000000000000000000000000 00000100000000000000000000000000 38  pz 70
00000000000000000000000000000000 00000000000000000000000010000000 57  pz 75
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 80
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 85
00000000000000000000000000000000 00000000000000001000000000000000 49  pz 90
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 95
00000000000000000000000000000000 00000000000000000100000000000000 50  pz 100
00000000000000000000000000000000 00000000000000010000000000000000 48  pz 105
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 110
00000000000000000000000000000000 00000000000100000000000000000000 44  pz 115
                                                                                                              pz 120
                                                                                                             pz 125

not yet dropped free sides from 1 to 15, 17 19 21 24 25 27 28 29 37 40 41 46 47 56 60 64

for example, 43, 51, 52, 53, 58, 61 have already fallen out 4 times.

sides not yet rolled in a 64-sided die (128 each for 8192)

***

pz 64
8192, 64/2 32 8192/2 4096, 8192/64 128,
7899
(√(2^63)/8192×7899)^2+2^63; 7899/128  hex(F7051F27B09112D4
[17798765725016391680  61,7109375 dec(17799667357578236628]

pz 65
8192, 64/2 32 8192/2 4096, 8192/64 128,
6640
(√(2^64)/8192×6640)^2+2^64; 6640/128;  hex(1A838B13505B26867
[30566001039707734016  51,875  dec(30568377312064202855]

pz 66
4146  
(√(2^65)/8192×4146)^2+2^65 46343414555177123840
                                            46346217550346335726
(√(2^65)/8192×4147)^2+2^65 46347973680141697024


(√(2^65)/8192×4146)^2+2^65; 4146/128
46343414555177123840 32,390625 46346217550346335726


***

free missing sides and possible space for pz 67

1-15
(√(2^66)/8192×129)^2+2^66;  8192/128 73805273267836026880
(√(2^66)/8192×1921)^2+2^66; 8192/128 77844439183633940480

17
(√(2^66)/8192×2177)^2+2^66; 8192/128 78997923638194208768
(√(2^66)/8192×2305)^2+2^66; 8192/128 79628709061002788864

19
(√(2^66)/8192×2433)^2+2^66; 8192/128 80295523280830332928
(√(2^66)/8192×2561)^2+2^66; 8192/128 80998366297676840960

21
(√(2^66)/8192×2689)^2+2^66; 8192/128 81737238111542312960
(√(2^66)/8192×2817)^2+2^66; 8192/128 82512138722426748928

24
(√(2^66)/8192×3073)^2+2^66; 8192/128 84170026335252512768
(√(2^66)/8192×3201)^2+2^66; 8192/128 85053013337193840640

25
(√(2^66)/8192×3201)^2+2^66; 8192/128 85053013337193840640
(√(2^66)/8192×3329)^2+2^66; 8192/128 85972029136154132480

27
(√(2^66)/8192×3457)^2+2^66; 8192/128 86927073732133388288
(√(2^66)/8192×3585)^2+2^66; 8192/128 87918147125131608064

28
(√(2^66)/8192×3585)^2+2^66; 8192/128 87918147125131608064
(√(2^66)/8192×3713)^2+2^66; 8192/128 88945249315148791808

29
(√(2^66)/8192×3713)^2+2^66; 8192/128 88945249315148791808
(√(2^66)/8192×3841)^2+2^66; 8192/128 90008380302184939520

37
(√(2^66)/8192×4736)^2+2^66; 8192/128 98448687854319042560
(√(2^66)/8192×4864)^2+2^66; 8192/128 99799767742530191360  

40
(√(2^66)/8192×5120)^2+2^66; 8192/128 102610013910009380864
(√(2^66)/8192×5248)^2+2^66; 8192/128 104069180189277421568

41
(√(2^66)/8192×5248)^2+2^66; 8192/128 104069180189277421568
(√(2^66)/8192×5376)^2+2^66; 8192/128 105564375265564426240

46
(√(2^66)/8192×5888)^2+2^66; 8192/128 111905443540902084608
(√(2^66)/8192×6016)^2+2^66; 8192/128 113580782602283909120

47
(√(2^66)/8192×6016)^2+2^66; 8192/128 113580782602283909120
(√(2^66)/8192×6144)^2+2^66; 8192/128 115292150460684697600

56
(√(2^66)/8192×7168)^2+2^66; 8192/128 130280130020573708288
(√(2^66)/8192×7296)^2+2^66; 8192/128 132315757052145172480

60
(√(2^66)/8192×7680)^2+2^66; 8192/128 138638810928973348864
(√(2^66)/8192×7808)^2+2^66; 8192/128 140818553148620668928

from the standpoint of probability, this doesn’t seem to mean anything, but you can try to look where else, according to this view Cool
2  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: June 11, 2023, 08:16:10 PM
bald chupacabras method...

for example, we take the square roots of the spaces and the keys themselves

pz65

2^64 √(18446744073709551616)    4294967296
30568377312064202855-18446744073709551616 12121633238354651239
√(12121633238354651239)         3481613596,933
2^63 √(9223372036854775808)     3037000499,976
                                       
4294967296/8                    536870912      
3481613596/8                    435201699,5    
536870912×x=3481613596          x = 6,485
3481613596/536870912                6,485

---

(4294967296/64)×x=(3481613596) x = 51,880085408687591552734375 pz 65

2^64 √(18446744073709551616) 4294967296
     √(12121633238354651239) 3481613596,933                              pz65
      12121633231852051216  3481613596×3481613596
      30568377305561602832  12121633231852051216+18446744073709551616   pz65
      30568377312064202855                                              pz65



and divide into parts, by 2, by 3, by 64, 128, 1024, 2048, 4096, etc.

we catch such a divider into parts so that there are no repetitions

for 64 and 2 table

                           0                                1
            1                                0

_______________1________________|_______________2_______________     2

_______1_______|________2_______|_______3_______|_______4_______     4
 
___1____|___2___|___3___|___4___|___5___|___6___|___7___|___8___      8

|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_          64


00000000000000000000010000000000 00000000000000000000000000000000 22  pz 12   0
00000000000000000000000000000000 00100000000000000000000000000000 35  pz 13   1
00000000000000000000000000000000 10000000000000000000000000000000 33  pz 14   1
00000000000000000000000000000000 01000000000000000000000000000000 34  pz 15   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 16   1
00000000000000000000000000000000 00000000000000010000000000000000 48  pz 17   1
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 18   1
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 19   1
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 20   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 21   1
00000000000000000000000000000000 00000000000000000000010000000000 54  pz 22   1
00000000000000000000000000000000 00000000010000000000000000000000 42  pz 23   1
00000000000000000000000000000000 00000000000000000000010000000000 54  pz 24   1
00000000000000000000000000000000 00000000000000000000000000000010 63  pz 25   1
00000000000000000000000000000000 00000000000000000100000000000000 50  pz 26   1
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 27   1
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 28   1
00000000000000000000000000000000 00000000000100000000000000000000 44  pz 29   1
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 30   1
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 31   1
00000000000000000000000000000000 00000000010000000000000000000000 42  pz 32   1
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 33   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 34   1
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 35   0
00000000000000000000000000000100 00000000000000000000000000000000 30  pz 36   0
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 37   1
00000000000000010000000000000000 00000000000000000000000000000000 16  pz 38   0
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 39   0
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 40   1
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 41   1
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 42   1
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 43   1
00000000000000000000000000000000 00000000000000000000001000000000 55  pz 44   1
00000000000000000000001000000000 00000000000000000000000000000000 23  pz 45   0
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 46   1
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 47   1
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 48   1
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 49   1
00000000000000000100000000000000 00000000000000000000000000000000 18  pz 50   0
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 51   1
00000000000000000000000000000000 00000000000000000000000000100000 59  pz 52   1
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 53   1
00000000000000000001000000000000 00000000000000000000000000000000 20  pz 54   0
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 55   1
00000000000000000000000000000100 00000000000000000000000000000000 30  pz 56   0
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 57   1
00000000000000000000000000000000 00000010000000000000000000000000 39  pz 58   1
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 59   1
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 60   1
00000000000000000000000000000010 00000000000000000000000000000000 31  pz 61   0
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 62   1
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 63   1
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 64   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 65   1
                ...............x.x.x.xx..x...xx.           xxxx.xx..xxxx..xxxxxxxx.xxx.xxx.      pz 66    
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 70   1
00000000000000000000000000000000 00000000000000000000000010000000 57  pz 75   1
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 80   0
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 85   1
00000000000000000000000000000000 00000000000000001000000000000000 49  pz 90   1
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 95   1
00000000000000000000000000000000 00000000000000000100000000000000 50  pz 100  1
00000000000000000000000000000000 00000000000000010000000000000000 48  pz 105  1
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 110  1
00000000000000000000000000000000 00000000000100000000000000000000 44  pz 115  1
                                                                                                              pz 120
                                                              xxxx.xx..xxxx..xxxxxxxx.xxx.xxx.      pz 125


for example, at 1664 repetitions stop falling out

1664 , 1664/2 832 ,1664/64 26, 26×x=1348 x = 51,846 pz 65

                                                             pz20
[572,924,858,887,1326,1250,1131,1190,1001,1337,1418,1096,1411,1645,1315,1360,1388,1168,1599,1628,1104,1353,1336,687,804,1127,438,701,
1511,950,936,1376,1442,615,1129,1392,996,1120,486,1514,1554,1178,545,1359,793,1594,1035,1508,1637,809,1387,1621,1604,1348,992,1494,
688,1587,1286,1403,1320,1251,941,1158]

35935527204195940 ~2^54

3+3+3+1+4+1+3+4+4+2+0+2+2+4+4+2+3+2+0+0+0+2+3+4+3+1+3+4+0+1+3+1 72 , 84-72 12,

3     3    3     1    4    1     3     4    4   2      0       2      2       4   4    2     3     2       0    0     0        2       3   4     3      1      3     4      0       1     3   1  < maybe only 4 will drop out here

x     x    x      x    .     x     x     .   .    x       x       x       x       .   .    x     x        x      x      x      x       x      x     .    x      x     x     .       x      x      x   .
33   34  35    36  37   38   39  40  41  42     43     44     45     46  47  48   49     50    51     52    53     54    55   56  57    58    59    60    61    62    63  64

858 887 924  941      992 1035         1104 1120 1158 1178              1251 1286 1320 1337 1359  1403 1411 1442     1494 1508 1554       1587 1621 1645
                  936      996                 1096 1129 1168 1190              1250        1315 1348 1376  1387 1418                    1514              1604 1637
                  950     1001                        1127                                                   1336 1353  1392                           1511              1594 1628
                                                          1131                                                   1326 1360  1388                                                1599

                                                                                                                   1327                                  1482 1509 1534 1560 1586 1612 1638
                                                                                                                   1328                                  1483 1510 1535 1561 1588 1613 1639
                                                                                                                   1329                                  1484 1512 1536 1562 1589 1614 1640
                                                                                                                   1330                                  1485 1513 1537 1563 1590 1615 1641
                                                                                                                   1331                                  1486 1515 1538 1564 1591 1616 1642
                                                                                                                   1332                                  1487 1516 1539 1565 1592 1617 1643
                                                                                                                   1333                                  1488 1517 1540 1566 1593 1618 1644
                                                                                                                   1334                                  1489 1518 1541 1567 1595 1619 1646
                                                                                                                   1335                                  1490 1519 1542 1568 1596 1620 1647
                                                                                                                   1338                                  1491 1520 1543 1569 1597 1622 1648
                                                                                                                   1339                                  1492 1521 1544 1570 1598 1623 1649
                                                                                                                   1340                                  1493 1522 1545 1571 1600 1624 1650
                                                                                                                   1341                                  1495 1523 1546 1572 1601 1625 1651
                                                                                                                   1342                                  1496 1524 1547 1573 1602 1626 1652
                                                                                                                   1343                                  1497 1525 1548 1574 1603 1627 1653
                                                                                                                   1344                                  1498 1526 1549 1575 1605 1629 1654
                                                                                                                   1345                                  1499 1527 1550 1576 1606 1630 1655
                                                                                                                   1346                                  1500 1528 1551 1577 1607 1631 1656
                                                                                                                   1347                                  1501 1529 1552 1578 1608 1632 1657
                                                                                                                   1349                                  1502 1530 1553 1579 1609 1633 1658
                                                                                                                   1350                                  1503 1531 1555 1580 1610 1634 1659
                                                                                                                   1351                                  1504 1532 1556 1581 1611 1635 1660
                                                                                                                                                           1505 1533 1557 1582         1636 1661
                                                                                                                                                           1506 1558 1583                 1662
                                                                                                                                                           1507 1559 1584                 1663
                                                                                                                                                                          1585

in general, everything is slipping somewhere, meaning that taking large divisors, we look in the table for 64 where they will fall out and so we select the spaces for the search.

the main thing is that more drops out on the right side than on the left if the table is divided into 2 equal sides, those that have already fallen out will not fall out, but you need to determine where exactly they can fall out, for example, there are parts that have not yet fallen out of 64, for example 37 40 41 46 47 56 60

we take the ones that haven't dropped yet and fit our search spots to them in the next puzzles

37 40 41 46 47 56 60 for 1664/2 832

833-1664

26×x=1348 x = 51,846 pz 65

962 37  
963 37
964 37
965 37
966 37
967 37
968 37
969 37
970 37
971 37
972 37
973 37
974 37
975 37
976 37
977 37
978 37
979 37
980 37
981 37
982 37
983 37
984 37
985 37
986 37
987 37

1560 60
1561 60
1562 60
1563 60
1564 60
1565 60
1566 60
1567 60
1568 60
1569 60
1570 60
1571 60
1572 60
1573 60
1574 60
1575 60
1576 60
1577 60
1578 60
1579 60
1580 60
1581 60
1582 60
1583 60
1584 60
1585 60

etc

(√(2^19)/2048×1646)^2+2^19        862952,5
                                                 863317    
pz20 (√(2^19)/2048×1647)^2+2^19 863364,125

2048 , 2048/2 1024 ,2048/64 32 , 32×x=1660 x = 51,875 pz 65

                                                                  pz20
[704,1137,1056,1092,1632,1538,1392,1465,1232,1646,1746,1349,1737,2025,1619,1674,1708,1437,1969,2004,1359,1666,1645,846,989,1387,539,863,
1860,1169,1152,1694,1775,757,1390,1714,1226,1379,599,1864,1912,1450,671,1673,976,1962,1275,1856,2015,996,1707,1996,1974,1660,1221,1839,
847,1953,1583,1727,1625,1540,1158,1426]

and so we are looking for where nothing has fallen out at all

pz67
(√(2^66)/2^30×536870912)^2+2^66 92233720368547758080
(√(2^66)/2^30×536870913)^2+2^66 92233720437267234880
92233720437267234880−92233720368547758080 68719476800  ~2^36

pz68
(√(2^67)/2^30×536870912)^2+2^67 184467440737095516160
(√(2^67)/2^30×536870913)^2+2^67 184467440874534469760
184467440874534469760-184467440737095516160 137438953600 ~2^37

pz69
(√(2^68)/2^30×536870912)^2+2^68 368934881474191032320
(√(2^68)/2^30×536870913)^2+2^68 368934881749068939520
368934881749068939520-368934881474191032320 274877907200 ~2^38


pz67
(√(2^66)/2^30×(2^30/2+0))^2+2^66 92233720368547758080
(√(2^66)/2^30×(2^30/2+1))^2+2^66 92233720437267234880
92233720437267234880−92233720368547758080 68719476800  ~2^36

pz68
(√(2^67)/2^31×(2^31/2+0))^2+2^67 184467440737095516160
(√(2^67)/2^31×(2^31/2+1))^2+2^67 184467440805814992928
184467440805814992928-184467440737095516160 68719476768 ~2^36

pz69
(√(2^68)/2^32×(2^32/2+0))^2+2^68 368934881474191032320
(√(2^68)/2^32×(2^32/2+1))^2+2^68 368934881542910509072
368934881542910509072-368934881474191032320 68719476752 ~2^36


***

pz65
(√(2^64)/1664×1348)^2+2^64 30552526466155465467,455
                           30568377312064202855
(√(2^64)/1664×1349)^2+2^64 30570494229757563437,443
30570494229757563437−30552526466155465467 17967763602097970  ~2^53

pz65
(√(2^64)/2048×1660)^2+2^64 30566001039707734016
                           30568377312064202855
(√(2^64)/2048×1661)^2+2^64 30580606952171110400
30580606952171110400−30566001039707734016 14605912463376384  ~2^53


pz66
(√(2^65)/2048×1660)^2+2^65 61132002079415468032
(√(2^65)/2048×1661)^2+2^65 61161213904342220800
61161213904342220800-61132002079415468032 29211824926752768 ~2^54

pz66
(√(2^65)/1664×1348)^2+2^65 61105052932310930934,911
(√(2^65)/1664×1349)^2+2^65 61140988459515126874,887
61140988459515126874-61105052932310930934    35935527204195940 ~2^54
                                                                     18014398509481984 2^54
                                                                     36028797018963968 2^55
                                
pz66
(√(2^65)/4096×3320)^2+2^65 61132002079415468032
(√(2^65)/4096×3321)^2+2^65 61146605792855588864
61146605792855588864-61132002079415468032    14603713440120832
                                                                     18014398509481984 2^54                        

pz67                      
(√(2^66)/2048×1660)^2+2^66 122264004158830936064
(√(2^66)/2048×1661)^2+2^66 122322427808684441600
122322427808684441600-122264004158830936064    58423649853505536 ~2^56   
                                                                        36028797018963968 2^55

(√(2^66)/4096×3320)^2+2^66 122264004158830936064
(√(2^66)/4096×3321)^2+2^66 122293211585711177728
122293211585711177728-122264004158830936064    29207426880241664 ~2^54   
                                                                        36028797018963968 2^55

pz68                      
(√(2^67)/2048×1660)^2+2^67 244528008317661872128
(√(2^67)/2048×1661)^2+2^67 244644855617368883200
244644855617368883200-244528008317661872128    116847299707011072 ~2^56   
                                                                        144115188075855872 2^57
pz68                      
(√(2^67)/4096×3320)^2+2^67 244528008317661872128
(√(2^67)/4096×3321)^2+2^67 244586423171422355456
244586423171422355456-244528008317661872128   58414853760483328 ~2^56   
                                                                       144115188075855872 2^57

pz69                      
(√(2^68)/2048×1660)^2+2^68 489056016635323744256
(√(2^68)/2048×1661)^2+2^68 489289711234737766400
489289711234737766400-489056016635323744256    233694599414022144 ~2^56   
                                                                         288230376151711744  2^58
                                                                         36028797018963968     2^55

                                                                         103864266406232064       3072 48*64 ((√(2^68)/3072×1661)^2+2^68)−((√(2^68)/3072×1660)^2+2^68)
                                                                         82065593209862371,555  3456 54*64 ((√(2^68)/3456×1661)^2+2^68)−((√(2^68)/3456×1660)^2+2^68)
                                                                         58423649853505536       4096 64*64 ((√(2^68)/4096×1661)^2+2^68)−((√(2^68)/4096×1660)^2+2^68)
pz69                      
(√(2^68)/4096×3320)^2+2^68 489056016635323744256
(√(2^68)/4096×3321)^2+2^68 489172846342844710912
489172846342844710912-489056016635323744256    116829707520966656 ~2^56   
                                                                         288230376151711744 2^58

i.e. 4096/2 2048 for right side of table 64 (33-64(-1); 2049-4096) and 2048/32 64 segments of the search space of the puzzle, for 37 40 41 46 47 56 where not, fell out, coincidence.

the larger the divisor, the larger the segments for the table will be in 64, etc.

I do not know why this forum distorts the text so much, but it's tin.


3  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: May 02, 2023, 07:12:49 AM
who is fast in programming, try to make such an analysis.

for example rmd160 puzzle 66 like this

13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so 20d45a6a762535700ce9e0b216e31994335db8a5
0010000011010100010110100110101001110110001001010011010101110000000011001110100 1111000001011001000010110111000110001100110010100001100110101110110111000101001 01 160 len

"1" 73, "0" 87

according to this criterion

160!/73!/87!
50039953558241343191231898620403129563706328000

50039953558241343191231898620403129563706328000/2^65 1356335658972975302954605575

2^160/50039953558241343191231898620403129563706328000 29
2^65/29 1272189246462727697

2^65/2^20 35184372088832

2^160/2^65 39614081257132168796771975168
50039953558241343191231898620403129563706328000/39614081257132168796771975168  1263186017957493013   \
                                                                                           35184372088832×35968 1265511495291109376     > 2^60-2^61  
                                                                                                                 2^65/29 1272189246462727697   /

for every 1048576 step of puzzle 66, will fall around ~36000 "1" 73, "0" 87 and if we add fishing on the first 20 bits (for example)
001000001101010001011010011010100111011000100101001101010111000000001100111010011110000010110010000 1011011100011000110011001010000110011010111011011100010100101

then, based on the probability of dropping 20 bits, you need 1048576 outcomes

1048576/36000 29

1048576 × 30 31457280
1048576 × 29 30408704  there will be only 1 00100000110101000101 "1" 73, "0" 87
1048576 × 28 29360128

what is a full turn for example by 3

001
100
010

010
100
001

100
001
010

there may be such

100
100
001

001
001
001

etc

but in theory, when hashing, the data is simply shuffled, that is, rotated

this means that 20 bits (1048576  steps) in the first 00100000110101000101 will simply move to another place in the second (1048576  steps), third (1048576  steps), etc.

1048576×1048576 = 1099511627776 1 twist

2^65/1048576 = 35184372088832

35184372088832/1099511627776 32 twists for all puzzle 66


1048576×32 = 33554432 (there will be only 1 00100000110101000101 "1" 73, "0" 87)

2^65/33554432 = 1099511627776

all puzzle be

33554432 steps by 1099511627776 len or

1099511627776 steps by 33554432 len  

during the analysis, 1-3 drops out on such steps

we can rotate this space as we like, even take a square

6074001000
6074001000

imagine that we fill with zeros those addresses that do not suit us according to the sorting criterion and mark 1 those that do

we will get a similar picture

000001000001000100000000000000000001000000100000000000000001
001000000000000010000000000110000000000000000100000000100000
etc...

if we take another piece of 20 bits from the address, it will behave similarly

11011011100010100101

so these pieces will jump around the whole puzzle according to the random distribution and in total, as I wrote above, there will be 32 full turns

the idea is to take and randomly generate all possible collisions

select statistics from the puzzle space and try to jump by sorting the template


2^10*2^10                                                           divide to state 2^10, abbreviated example  2^65/33554432 = 1099511627776 (33554432  can be divided into 1024 parts)

001 010                                                                      000 000    <  000000000000000000000000000000000000001000000000000100000000000000  33554432 step
100 100                                                                      000 000    <  000000000000000000000000000000000000010000000000000000000000000001  33554432 step
010 001                                                                      000 000    <  000000000000000000000001000000100000000000000000000000000000000000  33554432 step
  



4  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: April 26, 2023, 07:47:57 AM

@Andzhing @Evillo I believe that the person who created this puzzle did not put much thought into it. They simply selected a random number in a very ordinary manner to create the puzzle, and we may be unnecessarily complicating it. My point is that we should also consider these aspects when attempting to solve it. below in lime green text.



I am the creator.

You are quite right, 161-256 are silly.  I honestly just did not think of this.  What is especially embarrassing, is this did not occur to me once, in two years.  By way of excuse, I was not really thinking much about the puzzle at all.

I will make up for two years of stupidity.  I will spend from 161-256 to the unsolved parts, as you suggest.  In addition, I intend to add further funds.  My aim is to boost the density by a factor of 10, from 0.001*length(key) to 0.01*length(key).  Probably in the next few weeks.  At any rate, when I next have an extended period of quiet and calm, to construct the new transaction carefully.

A few words about the puzzle.  There is no pattern.  It is just consecutive keys from a deterministic wallet (masked with leading 000...0001 to set difficulty).  It is simply a crude measuring instrument, of the cracking strength of the community.

Finally, I wish to express appreciation of the efforts of all developers of new cracking tools and technology.  The "large bitcoin collider" is especially innovative and interesting!

That's right, but we don't know what he specifically did and in what program. What entropy was used 128-256 bit. 128bit enropy 12 words, still get 256bit private key. Let's say we start iterating over the entire enropy of 128bit and, by derivation, generate 256 addresses and cut them off in front, as the creator of the puzzle did. We have to iterate over all 128bits (12 worlds, 2048^12). https://github.com/Mizogg/python-mnemonic For each of 2048 to 2048^11 etc.But the generation itself (if he did not use the words brainwallets) 128bit number was caused by some data for seed() ("some garbage" > Mersenne twister 2^19937 bit > seed() > 128bit > address), what size of "some garbage" for the swirl was used. Maybe the size of the "some garbage" was less than 128bit, maybe more. If he manually cut 256 addresses for the deep puzzle, then how did he get addresses from them.

***


https://bitcointalk.org/index.php?topic=1306983.msg58670653#msg58670653

combinatorics method, placement with repetitions, select from a set of 100 elements of 2 characters [00,01,02,03...97,98,99]

we get the number 22 characters long blablabla 00 01 02 03 04 05 06 07 08 09 99
or 9999999999999999999999 ((100; 11) 5653408585997652480000) ~2^73

9999999999999999999999/2^65 ~271 collisions, 2^73/2^65 = 256 collisions

1 collision when sampling from 100 if we do not take into account the exact number (we will rearrange it to get the right one)

we don’t care how we get the right numbers in what order we will rearrange them anyway to find the right one, blablabla 00 01 02 03 04 05 06 07 08 09 99 , 01 00 02 03 04 05 06 07 08 09 99, 02 00 01 03 04 05 06 07 08 09 99 etc...

11! 39916800

271 collisions 39916800×271 = 10817452800

this is for a seed of 2 characters, we can use any combination to create a seed Aa Ab Bb BA bA etc...

"Aa" 11! 39916800, 271 collisions 39916800×271 = 10817452800
"Ab" 11! 39916800, 271 collisions 39916800×271 = 10817452800
"BA" 11! 39916800, 271 collisions 39916800×271 = 10817452800

10817452800×1000(seed Aa Ab Bb BA bA etc...) = 10817452800000

made a selection of 50 out of 100

(100; 50) 3068518756254966037202730459529469739228459721684688959447786986982158958772355 072000000000000/2^65 (or 2^73) 83172367546103805632956336834744831338220102860894879569529077863864324986 collisions



of these 50 selected, one more sample

(50; 25)  1960781468160819415703172080467968000000/2^65 (of 2^73) 53147088188731933817 collisions

etc

(25; 11)  177925144320000/2^65 0,0000048226... collisions

ok. take (50; 25) 1960781468160819415703172080467968000000/2^65 53147088188731933817 collisions

53147088188731933817/10817452800000 = 4913087, factorial 11 must be sorted out all over 4913087×39916800=196114711161600  there is already a chance to calculate Cheesy


['75', '45', '51', '72', '06', '38', '89', '88', '16', '20', '88', '38', '12', '16', '41', '43', '12', '22', '81', '33', '38', '12', '81', '60', '20', '89', '52', '13', '88', '08']
screening out...
['88', '81', '06', '89', '16', '88', '33', '81', '13', '33', '72', '52', '60', '13', '13']
loop start...
1 5288168860138933063313 hhEEEEhhhEEEhEEEEhEEEhEhhEhEhhhEhhEhEEhEEEEhhhhEhhEhEhEhEhEhEEhhhEEEhhhEhhhE <seed, bit> 0101000110101000110110100111010000100000110100000101111011100001101101111111011 0000101111110111001011110011001100010010011100011101001000100100111001001100110 00
2 5260130613883313811689 hhEEEEhEhEEEhhEhEEhhhhhhhhEEhhEhEhEEhEEEhhEEEhEhEhhhhhhEhEEhhEhEhEEEEhhEEhEE <seed, bit> 0011111011100101011001100100000001010100101111100111001101010011101111011100100 0101000001100000101000000000011100011111101010100100001011011000110011111010001 01
3 3360133306161389815281 EhhhhhEEEhhhhhEhhEhhhEEEEhEhhEEEhhhhhEEEEhEEEhhEEEEEEhEhhEEEEEhhhhEhEhEEhhhE <seed, bit> 0101011010111011011000011101011111111101001001101011011101111000011001110101110 1001111101101111000010000001011011001100011000011000001010011001011110110100011 10
4 3388168881136013890652 EhhhhhEhhEEEhEEEhhhhEhhhhEEEhhhhhhhhEEEhhEEEhEEEhhhEEhEEEhEEEEEEEEhEEhhhEEhh <seed, bit> 0111111000101000010111001101011110011100000011101101110111110100101010000000010 0101000110011010111000101011110111000111011101011010000110100111011100100000011 10
5 681131333131660725288 EEEhhEhEhhEhEEEEhhhhEhEhEEhEhhhEhEhhhEEhhEEEhEhhhEEhEhhEEhhhEEEhEEEhEEhEhhhE <seed, bit> 0100110011101111000000010100010100011000101100101010100001010111100101100010110 1100011101100100000101100011001101100111000110100010010001000011011111110011011 10
6 3381135206603388721381 EhhhhhEhEhEEEEhhEhhhEEEhEhhEhEhEhhEEEEEhEEEhhEhhhhEhEhhhEhEEEEEEhhhEhhEEEhhE <seed, bit> 1000001100110001101010011111110101011001000011100100001110010001111011111110001 1100100110101110010101101101001010001010100001100001011101101111001011010100011 10
8 660133381888913527233 EEEhhEhEEEEEhhhhEEhhhEhhEhEEhEhhEEhhhEhhhhhhhhEEEhhEEEEhEEhEEhEEhhEEhEEEEhhh <seed, bit> 1111101101011101100011010111100100011110110011000111001100001111110100110110110 0101000011000000010001010111111101010010111011010010110111110101110101001011011 10
10 1388721381893388066013 EEhhEhEEhhEEhhhEEEhEhEhhEhEEhhhhEhhhEEhhhEEEhhEhEEEhEEEhEhhhEEEhEEhhEEhhhEhE <seed, bit> 0110011100111110101000100010000000001001000011000100101010111110000110001010010 1010010010100001100110000111111101001110100001101100110111100110010100000111100 00
11 1381168113608889728806 EEhhEhEEhEEEhEhEhEhEhhEhhEEhEhhhhEhEhhEhhEEhEEEhEEEEhhEEhhEhEhEhEhhEhEhEEhhh <seed, bit> 1001111100001000001110001110101110110000100010101101111000111111001110101010101 0101100000100001101000110100011001100111100101001110101001011101001101001001010 10
15 3388527288608106331389 EhhhhhEhhEEEhhEEEEhEhhhhhEhhEEEhEEhhhhEhhhEEEEhhhhEEhEEEEEhhEEEhEEEEhEEhhhhE <seed, bit> 0100001000011000110100000101110001111111010000110011110001011011000010110001011 0100100111010011001110010100000010100110010010001100010000000111010001101011000 00
18 1652338960880633728881 EEhhhhhEEEhEhhEhEEhhEhhhhEEEhhEEhEEEhhEhhEEEhhhEhhhEEEhEhhEEEhEEhEEhhEEhEhhE <seed, bit> 0000101010111001101000101000011011110011110111000110011110100101101100010100011 1110011110100100101001001100101101110010101001110000100111101000000000100111100 10
19 3352811389720616818860 EhhhhhEEEEhhhEhhEEhEhhhEEEhEhhhEEEhEEEhEEhhhEhEEhEhhEhEhEEEhEhEEhhhhhEhEEEhE <seed, bit> 1110010010101101001111111110100010001000110111110011111111011111100101111010001 0010010000010011011111100111101100010100010110011110110010111110110101001111111 11
20 5288810688166072891381 hhEEEEhhhEEEhhEhhhEhEhhEhhhEhEhEhhEEEhhhEEhhhhEEhEEEhhhEEEhhEEEEhEEhhEEEhhEE <seed, bit> 1000001101100001000010000001000111000001101111101000010111110100000010101011011 0111100101111001010100000111011010000111011101000000101111001010110001000000011 01
22 1313896013883316815288 EEhhEEhEEEhEEEhEhhhhhEEhhEhhhEEEhhEEhhhhhEhEEhEhhEhEEEhhEEEhhEhEhhhEhhEEEEhE <seed, bit> 0010100010111100101100011001001100001100010000110110111010110100010001010010111 1101110100111111000111100101001101110001011101001110010101001011101100111000100 00
25 3381725288131388130660 EhhhhhEhEhEEhEEEhEhEEhhhhhhEEEEEEhhEEhhEhEEEEhhhhEEhEhhhhEEEhEEEEEhEhhEhhEhh <seed, bit> 0101111011010111100110110001100000100111000001100001011100100011001101100111000 0011101111110000101111011000001100110011011000101100000000010001110001011001110 11


['32', '22', '67', '57', '86', '21', '55', '39', '48', '86', '46', '40', '41', '64', '23', '74', '85', '48', '11', '75', '94', '64', '03', '29', '86', '71', '07', '65', '46', '81']
screening out...
['67', '22', '86', '64', '48', '11', '48', '22', '71', '64', '48', '57', '94', '40', '40']
loop start...
1 4894716748644822402286 3[33[3[[3[333[[[[3333[33[3[[[3[[[[3[333333[[3[[[3[333[3[3[[[3333[[[[33[[[[33 <seed, bit> 0111001000000010100100110100100111010001110101110110000001000101101100110110101 0010000011100000000111101000011000001100110111001111001111100001000011100010100 10
2 6411574886224048946740 333[33[[3[[[33[3[[3[[[[333333[3[[[3[[3[333[[33[[33[[33[[333333[[3[33[[[[3[[[ <seed, bit> 1101001101100101100110000101010010100000111100111110010101011110101111001110000 0110001011101101000101100011110111100001001010100000001100101111100000001100011 00
3 1148228622487167649464 [[3[33[[[[[333[333[[[[33[3[3[333333[[3[33[[[[[33[33[3[[[3333[[[[3[33[333[3[[ <seed, bit> 0010100000101011000101000011100101001001010110101111000001001101111111111110011 0111011010101011001001011100000101110000000101100111110101001000101111101010110 11
4 6422718611674822404864 333[33[[3333[33[[3[3[[[[33[[[3[333[[[3[33[3[[33[3[[3[3[[33[[[33[[3[[[[[33333 <seed, bit> 0000111111101100010101010101111111000010000001011100110101011100110011101010111 0000100010110011110011001001001010010110011010011111110010011000101100001011011 00
5 4064716711484822578640 3[[3[33[33[[3[3[33[[33[3[[3[[3[[[33[[33[3[333[3[[3[3[[[3333333[[[[[[[[[33333 <seed, bit> 1100110010001111101011110101000101111111101001011111100011000000101101110000110 0100111000000101000111010110101000100111111110000010111011100111000101101010100 00
6 4840644886225722716411 3[33[[3[33[[3[3[3[[3[3[[3[[[[[[[333[3[3[[33[3[[3[333[[3333[33[333[[[[3[3333[ <seed, bit> 1001110010011010110011101110000101011000101011000100111000110001010100000110010 0100001101001111101010101011011010101111010110001000001000101010010111100000011 01
7 6764226440864848941171 33333[3[[[33[3[[[3333[[[33333[[[[3[33[[3[3[33[[[[333[[[[[3333[[[3[3[[33[[3[3 <seed, bit> 1000100111011000010110011001101010011101101111100010101101110010110010111000100 0101010001001011111011000011111011110001010001100101110010111100011101010101011 10
8 5794866748114864226448 33[3[3[33[3[33[[3[[3[333333[[[[3[33[3[[3[3[[3333[33[[[[[[[[[33[3[3[333[[33[[ <seed, bit> 0010000010001111001101111010000111001110011000010110101111001101110001000001001 1010101000110000010100011001111111011001101111111100111100100011100011001001111 01
10 6494487140228648644811 333[3333333[[3[[[33[333333[[[[[3[3[[33[[[333[3[[[3[[[[[33[33[33[[3[33[[[[3[[ <seed, bit> 1110001100101111111110001001111000001011100101110000010011111110111110011101110 0011000100100110100100100100100111101010000111111100110101111000001000011101010 00


['05', '20', '99', '07', '11', '00', '21', '92', '92', '99', '20', '92', '78', '88', '26', '25', '54', '62', '70', '37', '34', '54', '78', '59', '08', '49', '59', '64', '06', '37']
screening out...
['05', '49', '99', '78', '54', '05', '99', '34', '06', '92', '78', '54', '08', '99', '59']
loop start...
1 4906999954590592053499 1+11+1+1++1++1111+++++1111++1+111+1+++++++1+11+11+11++++1111++1+11+++1+111+1 <seed, bit> 1011100110110111100001100010010101111001100000111110111100001101000000011100010 0010111100000111011111110010001100000010100101110011101101010111010111101110101 01
7 4999345408990692055978 1+111+++1++1+++111+1+1++++++11++111+11+1+1+11+11++1++1+1+111+11+++1+1+111+1+ <seed, bit> 1101111011011110101001110001001100001000101111100101111101100001010100010101000 0000111001101111001010001111100101100001011001110001001110111011100100100001011 10
8 878345999990554065478 ++1+++1+++11+++1++111+111+1+1++1+1++1+1+1+11+1+111++11+11++111+11++11+1++1+1 <seed, bit> 0000111101110011100010110100110101111000010011101011000011000100011000011011011 0110001110111000001011110011111111110011101110000010111010110100110101011010010 00
12 899785934057854069992 ++1+++11+++++++11+++1111++111+1111111+111+11++++1++1+1+11+++11+111++++11+11+ <seed, bit> 1100010101110110101011110100010011010000100110100111110111101110010111001000001 1000001010111010100010011100000100010111110010110110011110101011011100101011010 10
13 4906929954990534995459 1+11+1+1++1++11+111+1+1++1++1++11++1+111++++1++++1+1++1++1+11+1+11111+1+1+11 <seed, bit> 1001000100101111001101111100110100011001011111010000101100111001011111000111001 0110101101001000011001000001001100010111001101111001001110011001010110000110101 00
14 678545408053499927859 +++11+1+1+111++111+++1++11111++++1+11++1111+1111111+1+++++++1+1++1+11+++1++1 <seed, bit> 1001001000000100111011110000001001111111110011011110001001101100001000010001011 0011011001110111010101001110100011110001010101000111111010001110000010111111100 10
15 699080554345449990559 +++11+11+111+++1+1+11+1+1+++1+1+1++1111+++1++1+11111+++11+++111++++1+1111++1 <seed, bit> 0100111110010110100001001111110101111010011110000110010101011111101000101110111 0100001001110111111001111100111000011010101000001101100000110000111100010101001 00
17 892065478990578594905 ++1+++1+1+111+1+1+1++++1+11+1++1++++++11+1111+111+1++11+1++11111+11+1+11+++1 <seed, bit> 0001111001111000001001101001111111110011001111010011101100001001110111110011101 1111011110100000000101000000010111001110101110001000000110010010100011011111011 00
19 878340599544959929906 ++1+++1+++11+++1++1+1+11+1++11+11111+1+11111++++11++1++++11+11+111+1+1111+++ <seed, bit> 1001110000101001001110010111101010000101010110110110011010100000001001001000000 1110000010010111000110000010101011110101100100011101101101000001000101001011000 01
21 899499954590592785405 ++1+++1+1111111+++1++1++11+++++1+111+1++1++1+111+11+1++11+11+11++11+++1111++ <seed, bit> 0100001100011011110011010011100010001101011001111010000000010100111001000001100 1100111101000001011000111011011111100100011101101111000001011011110011111110000 10
22 692499954780559780554 +++11+11++11+111+11++11+111+1+++11++++111++++++++1+1++++1111+11+11+1111+11++ <seed, bit> 0011100110010011110010010001000001110010111111111100111111101010010000111001001 0001110010010111110101011110011011110110001111100001010000000100100111010001110 11
24 4959990878995499059234 1+11+111+++1++1+1111111+1++11++1+++++11+1+1111+111+1++++++1+1+1+11+++11+++1+ <seed, bit> 0111001111011000010011011111011100001111011101111110110111101111110110001100101 1010110100000001010100101100111101110111011100011010111001111110010100111010010 10
26 5405990649780599085992 11+++1111+11++1+1+1111+1111+++1+++11++11++1++11+11+1++++111++1+11++++1++11++ <seed, bit> 1110100001110111010111100101100011011011001100111011000101111110001110111001111 0101111100000101111000111011111101111110011101100100100101110111101001000001111 00
28 5999089206493454547899 11+111+1++11+111+++1+1+1++11++1+1111+1+1111+++111+1+1+11+++++++1++1++11+++1+ <seed, bit> 1100010110011000111011101101010000010000000000111100010000101111010010111100111 1000001000011101100010100101001011011110101110100011001001100100110000000100011 11
30 3405065454499278990599 +111111+++11+1+1+111+111++1++11++1+1+++1++11++1++++++111+11+++111+++11+111++ <seed, bit> 0111111001001010100100110100011100101010111011111101111001100010101100100101010 1001010000101010111101110000110000000100011110011000000101101011110111011010100 11
31 5478590806789205999999 11++1+1++1+1++++++11++1+1+1++1++++1+1++1111111+1+11+++1+1++1111+++1+1+111111 <seed, bit> 0101000100000010101111101011110010110010101101110011110000000110100010110011011 0001100110111011001000000011110010010110101010101000100100000000110101000101100 11
5  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: April 25, 2023, 08:04:11 PM
zahid888 He also wrote that he used a "It is just consecutive keys from a deterministic wallet (masked with leading 000...0001 to set difficulty)" this means that he could use anything, but most likely a regular random 2^256 address. He could create the keys a month before filling, or a week. And one time is not enough to shove all the devilry there, the clock counters... all this nonsense has a range "Mersenne twister 2^19937 bit (624·32 (2^32 = 4294967296) — 31)".

***

test

it took to open the first 3 puzzles through seed()

        a = random.seed(1,15000000)

        a1 = random.randrange(512,1024)
        if a1 == 514:

            a2 = random.randrange(256,512)
            if a2 == 467:                

                a3 = random.randrange(128,256)
                if a3 == 224:

14429208 seed-steps, 514, 467, 224

for 4 it's been a long time to search 1,1000000000...

because when finding the first one, it is necessary to iterate over all the first ones until it suits the second one, etc.

1024×1024×1024 =          1073741824        for 3pz
2048×2048×2048×2048 = 17592186044416  for 4pz
etc...

probably needed for the whole puzzle 160-66=94, (2^160)^94 ~ 2^15040

2^15040 all pz
2^19937 twister

Cheesy
6  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: April 23, 2023, 01:42:45 AM
https://towardsdatascience.com/random-seeds-and-reproducibility-933da79446e3

And how does this random.seed() work?

set some value and then Mersenne twister...

Mersenne twister 19937 bit (624·32 (2^32 = 4294967296) — 31)

for example, we take 3 random

random.seed(blablabla)
random.randrange(1,10)
random.randrange(1,10)
random.randrange(1,10)

we get for each of the 3 in order from the vortex of the first three?

                                 1— 31
random.randrange(1,10) 1,4294967296 (624·2)
random.randrange(1,10) 1,4294967296 (624·3)
random.randrange(1,10) 1,4294967296 (624·4)

and if we take 624 random.randrange(1,10) period ends and a new one begins again

                                 1— 31            next period
random.randrange(1,10) 1,4294967296 (625)624·2
random.randrange(1,10) 1,4294967296 (626)624·3
random.randrange(1,10) 1,4294967296 (627)624·4

and if we have a large sample of random.randrange(36893488147419103232,73786976294838206464) he spends 1 period for 1 sample or 624 and a new one (then why are they not repeated 2^32?)

or he these 19937 bit takes it all at once

in other words, to complete all puzzles with 1 seed() we need to iterate over this seed() to iterate over all variations of this 2^19937 bit ((2^32)^624)?

and seed() itself doesn’t matter (with brute force) you don’t need old computers to run it randomly in order to pick up the date and time, etc. to create the same bitcoin address.


random.seed(1, 2^19937) and all pz

random.randrange(36893488147419103232,73786976294838206464) 66
...
random.randrange(21267647932558653966460912964485513216,42535295865117307932921825928971026432) 125
...
random.randrange(730750818665451459101842416358141509827966271488,1461501637330902918203684832716283019655932542976) 160

and the puzzles themselves need to be multiplied 2^160×2^159×2^158...×2^66

and if it turns out that there may be collisions here , If 2^19937 the most options to open all the puzzles at once through 1 seed()

7  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: April 19, 2023, 12:20:24 PM
Well, for 6-7 years, all possible options have already been sorted out, or combinatorics to sort out (shuffle 111112233... 222221133.. 332222211... etc) or to be smart about something with collisions.

for example, we can choose from a random house any number of times


random.seed(36893488147419103232,73786976294838206464)
random.randrange(36893488147419103232,73786976294838206464,1)

etc

36893488147419103232×36893488147419103232 = 1361129467683753853853498429727072845824

random.seed(36893488147419103232,1361129467683753853853498429727072845824)
random.randrange(36893488147419103232,73786976294838206464,1)

etc

in other words, there 1361129467683753853853498429727072845824 are so many collisions 36893488147419103232

now we take this number and we need to fish out the collisions we need

random.seed(36893488147419103232,73786976294838206464)
random.randrange(1,1361129467683753853853498429727072845824 ,1)

to

random.seed(random.randrange(1,1361129467683753853853498429727072845824 ,1))
random.seed(36893488147419103232,73786976294838206464)


1361129467683753853853498429727072845824×1361129467683753853853498429727072845824 = 1852673427797059126777135760139006525652319754650249024631321344126610074238976

there will be such sections in this number where the first step by step will be collisions (36893488147419103232×36893488147419103232 = 1361129467683753853853498429727072845824)

36893488147419103232×36893488147419103232 = 1361129467683753853853498429727072845824
****************** ___________________      ****************** ___________________

there will be areas

****************** ___________________

**********___________________*********

_______*******_______********_________

*_*_*_*_*_*_*_*_**__**__**__***___***

etc...

well, according to the law of uniform distribution, somehow jump there, random means uniform distribution over space.

Quote
from os import system
system("title "+__file__)
import random
import time
#from bit import Key
#from combi import *

import gmpy2
import secp256k1 as ice


list2 = ["13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so"]

F1="01"

aa1=F1[0]*70
aa2=F1[1]*70

def find_permutation(lst,K,numberbit1,numberbit0):

    l = lst

    N = numberbit0
    M = numberbit1

    if N == len(l):
        return F1[1] * N
   
    if M == len(l):
        return F1[1] * M

    result = ''   

    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)

        if (K < K0):
            result += F1[0]
            l.remove (F1[0])
        else:
            result += F1[1]
            l.remove (F1[1])
            M -=1
            K = K - K0

    result += l[0]

    return result

#count = 0
#5444517870735015415413993718908291383296  2^66×2^66
#93820969697840041204785894580506297666600 140!/70!/70!

while True:
   
    random.seed()
    sssakkki = random.randrange(1,73786976294838206464,1)
    saki = 73786976294838206464 * sssakkki
   
    print("")
    print("")
    print("")
    print(sssakkki,saki,"step",5444517870735015415413993718908291383296//saki)
    #time.sleep(random.randrange(1,10,1))

   
    X2=0 #X=10
    while X2 <= 5444517870735015415413993718908291383296:

        X=X2 #X=10
        while X <= X2: #+1000
                   
            a3 = list(aa1+aa2)
            K = X #perm_int
            numberbit1 = len(aa1)
            numberbit0 = len(aa2)

            aa = find_permutation(a3,K,numberbit1,numberbit0)
            random.seed(aa)

            b = random.randrange(36893488147419103232,73786976294838206464,1)

           
            if b >= 36893488147419103232:
                   
                    #key = Key.from_int(b)
                addr = ice.privatekey_to_address(0, True, b) #key.address
                           
                if addr in list2:
                               
                    print ("found!!!",b,addr)
                    s1 = str(b)
                    s2 = addr
                    f=open("a.txt","a")
                    f.write(s1)
                    f.write(s2)       
                    f.close()
                    pass
                else:
                    #pass
                    print(b,addr) #print(X,r1,b,addr)

               
            X=X+1


        X2=X2+saki
       
        #print("")
        #print(X2)
        #print("")

 
8  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: April 17, 2023, 10:26:11 PM
Quote
2-the creator used a deterministic portfolio (it is another pattern but more complex).

He could use programming languages, python, c++... (2015 year, what were the random generators and what hardware did he use) or, if possible, hardware wallets Leger etc... in this case, if possible, you need to work in this direction with the processor of the Leger itself or emulate its processor (and through seed selection). Moreover, we do not know where these funds (+10x) come from, they can be stolen from the exchange, etc., but the author did not appear.



9  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: January 23, 2023, 07:47:32 PM
@Andzhig And if we increase one more character of address 16jY7qLJn & 'x' then most binaries are started from '111'

few examples -

16jY7qLJnxLQQRYPX5BLuCtcBs6tvXz8BE   1110000000100110101001101101010100100011010011001000100000110110000   7013536A91A6441B0
16jY7qLJnX9uchnyf26t3QJnsUf78Xdikb   1110010000101000111010000001111110010000001011001101111011100000   E428E81F902CDEE0
16jY7qLJnX9eX8j612s8fnbn6uzR48xjua   1110100000001101111010110011001110101001011001111010000010001111   E80DEB33A967A08F
16jY7qLJnx2EZZumnYFke3GutCrRnHKs1M   111010110100110101001101101010111010101000110011101011001010110000   3AD3536AEA8CEB2B0
16jY7qLJnx2ixrxCnTLSraerkgyB3YYAiT   1110110111111001110011010110000000110101011011011100110000011001   EDF9CD60356DCC19
16jY7qLJnxHBp3dqwV2kzYq1LucfZzgxsH   1110111010111001101010110011001101001101111100100111011100001101   EEB9AB334DF2770D
16jY7qLJnX2cZXJ78wV1ef42e7cLAZJ1Vn   1111111000101000011001011100011011011011111111101100001110000011   FE2865C6DBFEC383
16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN   1111011100000101000111110010011110110000100100010001001011010100 F7051F27B09112D4


Could this also be some logic?

can you shed more light on this issue

you still don't understand the meaning sense of the hash function? "more light" > what is random? you take a coin and flip it 1 time, it may come up heads or tails. what happens if you flip a coin 10 times in a row, according to the theory of probability, either 10 heads or 10 tails can fall out. if you want to get 5 heads and 5 tails (in any order) you will need to flip a coin in series of 10, 2^10 = 1024 (1024 by 10). to drop all possible combinations from 10 heads in a row to 10 tails in a row, for all tosses in a row 1024 by 10, you need to flip a coin, 1024^1024=... when we start looking at the numbers generated when creating a bitcoin address (any or the address itself or its private key or its 160 hash in any form, hex, dec, bin) we get some parts of this huge number 2^10 = 1024 (1024 by 10) <> 1024^1024=... if you take 3 bits, 2^3=8, 8^8=16777216, then we start looking from 1 to 2^160 what we have in rmd160 hash in hex or dec

someting blablabla
...

1111101110010000010011001101000011011011000101101111100110000011100011011110010 1101011011011101111100000100100110000001010101110011001000000111000100000111101
1111101110010000010011011101010001011110010001010101111001100100101001001001000 1010001010111001000001111010110110000110010101010100001100011111100000110111111
1111101110010000010000101000101001011101000101100110011001100110111110110010000 0011000111101001111110011101100110100010110011110100110011111010000101000000010
1111101110010000010011110100011011001001011101100011111101001110111010000111011 0001001100010000010011000110111010111010110010011001001111010010100000010100001
1111101110010000010011111001001101010000001111001001110001101011110000111011011 0111000010010000111110000100000111010010001000110010111010110111000110000011111
1111101110010000010011000111010011111010010100001000011000001100110010010110001 1010100111011011111111001101001111100000101000101000000110011010110110110111000
1111101110010000010000000110100101101111101110001100000111111001100110111011111 0010000010110100011110101010101010101000100110101100010001111000000000111110001
1111101110010000010000011010010110100011111111100110001101001111001000110101011 0010100010010101100111100010000000110101000001101101111001011101010100101010101


the principle is preserved that vertically and horizontally > 2^3=8, 8^8=16777216


11111011
11111011
11111011
111
111
111
111
111


how many such sections will fit into 2:160 > 1461501637330902918203684832716283019655932542976 / 16777216 = 87112285931760246646623899502532662132736

we will split our 160 bits by 3 bits into sections


111 110 111 001...
111 110 111 001...
111 110 111 001...
111 110 111 001...
111 110 111 001...
111 110 111 001...
111 110 111 001...
111 110 111 001...




11111011 10010000 01001100...
11111011 10010000 01001101...
11111011 10010000 01000010...

11111011 10010000 01001111...
11111011 10010000 01001111...
11111011 10010000 01001100...



of course we can't look further from where they fall from for each row > 16777216^16777216=...

with a horizontal representation, we get 160hesh/8bits = 20 parts.

8 bit 2^8 = 256, 256/20 = 12,8

2^1
1461501637330902918203684832716283019655932542976/12,8 = 114179815416476790484662877555959610910619729920 steps
2^160

256^256=... huge number 3231700607131100730071487668866995196044410266971548403213034542752465513886789 0893197201411522913463688717960921898019494119559150490921095088152386448283120 6308773673009960917501977503896521067960576383840675682767922186426197561618380 9433847617047058164585203630504288757589154106580860755239912393038552191433338 9668342420684974786564569494856176035326322058077805659331026192708460314150258 5928641771167259436037184618573575983511523016459044036976132332872312271256847 1082020972515710172693132346967854258065669793504599726835299863821552516638943 7335543602135433229604645318478604952148193555853611059596230656


16777216/12,8 =  1310720 steps, 2^1 to 2^160, 1461501637330902918203684832716283019655932542976 / 1310720 = 1115037259926531157076785913632418075299020,8

256^256=... huge number / 1115037259926531157076785913632418075299020,8

3231700607131100730071487668866995196044410266971548403213034542752465513886789 0893197201411522913463688717960921898019494119559150490921095088152386448283120 6308773673009960917501977503896521067960576383840675682767922186426197561618380 9433847617047058164585203630504288757589154106580860755239912393038552191433338 9668342420684974786564569494856176035326322058077805659331026192708460314150258 5928641771167259436037184618573575983511523016459044036976132332872312271256847 1082020972515710172693132346967854258065669793504599726835299863821552516638943 7335543602135433229604645318478604952148193555853611059596230656 / 1115037259926531157076785913632418075299020,8 =~

2898289342675449871993098867672270812704240074863894775739976204579701715524344 5980591244385169006487474859731523184059403721470360895667790293862650383583527 8052308371150131655537851476057700318587873331791124614866020470257907019747447 1073288393330068706379548507509145858817458460347497468230852750261100385960260 0438313585964807278885206604007966494048122967982378718514987992376064111499830 2154324000491294951584421374564447449664912755949011836586456519390866498333142 8684237600062725568520340756025511278116285953620110095472786524359663371614992 7614893228693106196480

in general our 2^3=8, 8^8=16777216 fall into their position from the general 256^256=... huge number...

in the first column, theirs fall out all over, in the second one, etc. when presented vertically and similarly when recalculating and converting in horizontal...

instead of constantly flipping a coin, we initiate with Mersenne twister and hash functions (256,160hashs) by initiating the creation of a bitcoin address using a number, we get a fixed result instead of randomly generating a constantly new one (but it randomly takes it from a large number), but this number itself 2^160 or 2^256 is still fixed and falls out of the total huge number that goes into infinity 2^3=8, 8^8=16777216, 16777216^16777216... etc

in general, everyone is picking something and looking for their own ways))

https://youtu.be/AYWoDqQmm1o?t=128
10  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: April 26, 2022, 02:37:06 PM
import random
from combi import *
import gmpy2

list2 = ["1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum"] # pz 20 > dec 863317 bit 11010010110001010101


F1="01"

aa1=F1[0]*50
aa2=F1[1]*50

def find_permutation(lst,K,numberbit1,numberbit0):

    l = lst

    N = numberbit0
    M = numberbit1

    if N == len(l):
        return F1[1] * N
    
    if M == len(l):
        return F1[1] * M

    result = ''    

    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)

        if (K < K0):
            result += F1[0]
            l.remove (F1[0])
        else:
            result += F1[1]
            l.remove (F1[1])
            M -=1
            K = K - K0

    result += l[0]

    return result



#ccount0 = 0

#a1 = "0"*22
#a2 = "1"*22
#a3 = a1+a2

#perm_space = PermSpace(a3)

#print(perm_space.length)
#print(perm_space.index(a4))
#( 44!/22!/22!)/2^20 2006625,140876770019531 collision
# 2104098963720 (44!/22!/22!)

#1048576×1048576 = 1099511627776
#1099511627776×1099511627776 = 1208925819614629174706176
#100!/50!/50!             100891344545564193334812497256                          
#44!/22!/22!       2104098963720


#aa = perm_space[2]
#aaa = "".join(aa)
        
#print(aaa)

pzbit = "11010010110001010101" #"11010010110001010101"
                                                                                
for XXX in range(1000000,1048576,1):

    ccount0 = 0
    
    random.seed()
    gnoy= XXX #random.randrange(1000000,1048576,1) #1048576
    saki = 1099511627776 * gnoy #random.randrange(1,1048576,1) #2^256×2^256
    
    #print(gnoy,"1208925819614629174706176 //",saki,1208925819614629174706176//saki)
    #print("")

    X2=0 #X=10
    while X2 <= 100891344545564193334812497256-1:

        if X2 >= 1208925819614629174706176:
            break
        else:
            pass
        
        #count0 = 0
        
        X=X2 #X=10
        while X <= X2: #+100


            ccount0 += 1

            if ccount0 >= 1048576: #1048576 3000
                break
            
            
        
            #aa = perm_space[X]
            #aaa = "".join(aa)    
            #count0 += 1

            a3 = list(aa1+aa2)
            K = X #perm_int
            numberbit1 = len(aa1)
            numberbit0 = len(aa2)
            aa = find_permutation(a3,K,numberbit1,numberbit0)

            random.seed(aa)

            Nn = "0","1"

            RRR = [] #func()

            for RR in range(20): # "bit" set log2(x)=20 2^20 = 1048576, 1048576/20 = 52428,8
                DDD = random.choice(Nn)
                RRR.append(DDD)

            d = ''.join(RRR)
                #print(d,count0,aa,X)
            #print(bin(X)[2:],XXX,saki,"loop count","step",d,aa,X2,ccount0)
                #break

            if pzbit in d:
                print(bin(X)[2:],gnoy,"1099511627776 *",saki,"step",d,aa,X,X2,ccount0,XXX)
                #print("")
                #print("")
                break

            X=X+1


        X2=X2+saki
            
            #print("")
            #print(X2)
            #print("")


                
print("pz end")
input() #"pause"



***


import random
from combi import *
import gmpy2
import time

list2 = ["1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum"] # pz 20 > dec 863317 bit 11010010110001010101


F1="01"

aa1=F1[0]*50
aa2=F1[1]*50

def find_permutation(lst,K,numberbit1,numberbit0):

    l = lst

    N = numberbit0
    M = numberbit1

    if N == len(l):
        return F1[1] * N
    
    if M == len(l):
        return F1[1] * M

    result = ''    

    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)

        if (K < K0):
            result += F1[0]
            l.remove (F1[0])
        else:
            result += F1[1]
            l.remove (F1[1])
            M -=1
            K = K - K0

    result += l[0]

    return result



#ccount0 = 0

#a1 = "0"*22
#a2 = "1"*22
#a3 = a1+a2

#perm_space = PermSpace(a3)

#print(perm_space.length)
#print(perm_space.index(a4))
#( 44!/22!/22!)/2^20 2006625,140876770019531 collision
# 2104098963720 (44!/22!/22!)

#1048576×1048576 = 1099511627776
#1099511627776×1099511627776 = 1208925819614629174706176
#100!/50!/50!             100891344545564193334812497256                          
#44!/22!/22!       2104098963720


#aa = perm_space[2]
#aaa = "".join(aa)
        
#print(aaa)

ccount20 = 0

pzbit = "11010010110001010101" #"11010010110001010101"
                                                                                
for XXX in range(1,1208925819614629174706176,1):

    #print("loop start",ccount20)
    #print("")

    ccount0 = 0
    
    #random.seed()
    #gnoy= XXX #random.randrange(1000000,1048576,1) #1048576
    #saki = 1099511627776 * gnoy #random.randrange(1,1048576,1) #2^256×2^256
    
    #print(gnoy,"1208925819614629174706176 //",saki,1208925819614629174706176//saki)
    #print("")

    #X2=0 #X=10
    #while X2 <= 100891344545564193334812497256-1:

        #if X2 >= 1208925819614629174706176:
            #break
        #else:
            #pass
        
        #count0 = 0
        
        #X=X2 #X=10
        #while X <= X2: #+100


    #ccount0 += 1

            #if ccount0 >= 1048576:
                #break
    

    for S1 in range(20,40,1):
        for S2 in range(1):


            random.seed()
            
            Nn1 = "1","0","0","0","0","0"

            RRR1 = [] #func()

            for RR1 in range(S1): # bit len   1000000000000000000000000000000000000000000000000000000000000000000000000000000 00 1048576×1099511627776×1048576 = 1208925819614629174706176
                DDD1 = random.choice(Nn1)
                RRR1.append(DDD1)

            d1 = ''.join(RRR1)

            llen = bin(1208925819614629174706176)[2:]
            llen2 = len(llen)
          
            
            

            d0 = "0"
            d2 = "1"+d1 # bit len   1000000000000000000000000000000000000000000000000000000000000000000000000000000 00 1048576×1099511627776×1048576 = 1208925819614629174706176
            llen3 = llen2-len(d2)
            d3 = d2+d0*llen3
            

            f1=len(d3)
            while f1 >= len(d2):
              
                
                f2 = d3[0:f1]
                d4 = int(f2,2)
                
                ccount0 += 1
                ccount20 += 1

                if d4 <= 1208925819614629174706176:
                    #ccount0 += 1
                            #print(d3,d2)

                                #aa = perm_space[X]
                                #aaa = "".join(aa)    
                                #count0 += 1

                    a3 = list(aa1+aa2)
                    K = d4 #perm_int
                    numberbit1 = len(aa1)
                    numberbit0 = len(aa2)
                    aa = find_permutation(a3,K,numberbit1,numberbit0)

                    random.seed(aa)

                    Nn = "0","1"

                    RRR = [] #func()

                    for RR in range(20): # "bit" set log2(x)=20 2^20 = 1048576, 1048576/20 = 52428,8
                        DDD = random.choice(Nn)
                        RRR.append(DDD)

                    d = ''.join(RRR)
                                        #print(d,count0,aa,X)
                                    #print(bin(X)[2:],XXX,saki,"loop count","step",d,aa,X2,ccount0)
                                        #break

                            
                            #print(FD,d2,d3,aa,d,pzbit)
                    #print(S1,S2,"",ccount0,f2,d4,d,pzbit)

                    if pzbit in d:
                        print(S1,S2,"",ccount0,f2,d4,d,aa,d,pzbit,ccount20)
                        print("")
                        print("")
                        pass
                        #time.sleep(10.0)

                                    #X=X+1


                                #X2=X2+saki
                                    
                                    #print("")
                                    #print(X2)
                                    #print("")

                f1=f1-1

                        
print("pz end")
input() #"pause"



*** random search


from os import system
system("title "+__file__)
import random
import time
import gmpy2
import secp256k1 as ice

list2 = ["16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN","13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so","1BY8GQbnueYofwSuFAT3USAhGjPrkxDdW9",
        "1MVDYgVaSN6iKKEsbzRUAYFrYJadLYZvvZ","19vkiEajfhuZ8bs8Zu2jgmC6oqZbWqhxhG","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF",
        "1PWo3JeB9jrGwfHDNpdGK54CRas7fsVzXU","1JTK7s9YVYywfm5XUH7RNhHJH1LshCaRFR","12VVRNPi4SJqUTsp6FmqDqY5sGosDtysn4",
        "1FWGcVDK3JGzCC3WtkYetULPszMaK2Jksv","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF","1Bxk4CQdqL9p22JEtDfdXMsng1XacifUtE",
        "15qF6X51huDjqTmF9BJgxXdt1xcj46Jmhb","1ARk8HWJMn8js8tQmGUJeQHjSE7KRkn2t8","15qsCm78whspNQFydGJQk5rexzxTQopnHZ",
        "13zYrYhhJxp6Ui1VV7pqa5WDhNWM45ARAC","14MdEb4eFcT3MVG5sPFG4jGLuHJSnt1Dk2","1CMq3SvFcVEcpLMuuH8PUcNiqsK1oicG2D",
        "1K3x5L6G57Y494fDqBfrojD28UJv4s5JcK","1PxH3K1Shdjb7gSEoTX7UPDZ6SH4qGPrvq","16AbnZjZZipwHMkYKBSfswGWKDmXHjEpSf",
        "19QciEHbGVNY4hrhfKXmcBBCrJSBZ6TaVt","1EzVHtmbN4fs4MiNk3ppEnKKhsmXYJ4s74","1AE8NzzgKE7Yhz7BWtAcAAxiFMbPo82NB5",
        "17Q7tuG2JwFFU9rXVj3uZqRtioH3mx2Jad","1K6xGMUbs6ZTXBnhw1pippqwK6wjBWtNpL","15ANYzzCp5BFHcCnVFzXqyibpzgPLWaD8b",
        "18ywPwj39nGjqBrQJSzZVq2izR12MDpDr8","1CaBVPrwUxbQYYswu32w7Mj4HR4maNoJSX","1JWnE6p6UN7ZJBN7TtcbNDoRcjFtuDWoNL",
        "1CKCVdbDJasYmhswB6HKZHEAnNaDpK7W4n","1PXv28YxmYMaB8zxrKeZBW8dt2HK7RkRPX","1AcAmB6jmtU6AiEcXkmiNE9TNVPsj9DULf",
        "1EQJvpsmhazYCcKX5Au6AZmZKRnzarMVZu","18KsfuHuzQaBTNLASyj15hy4LuqPUo1FNB","15EJFC5ZTs9nhsdvSUeBXjLAuYq3SWaxTc",
        "1HB1iKUqeffnVsvQsbpC6dNi1XKbyNuqao","1GvgAXVCbA8FBjXfWiAms4ytFeJcKsoyhL","12JzYkkN76xkwvcPT6AWKZtGX6w2LAgsJg",
        "1824ZJQ7nKJ9QFTRBqn7z7dHV5EGpzUpH3","18A7NA9FTsnJxWgkoFfPAFbQzuQxpRtCos","1NeGn21dUDDeqFQ63xb2SpgUuXuBLA4WT4",
        "1NLbHuJebVwUZ1XqDjsAyfTRUPwDQbemfv","1MnJ6hdhvK37VLmqcdEwqC3iFxyWH2PHUV","1KNRfGWw7Q9Rmwsc6NT5zsdvEb9M2Wkj5Z",
        "1PJZPzvGX19a7twf5HyD2VvNiPdHLzm9F6","1GuBBhf61rnvRe4K8zu8vdQB3kHzwFqSy7","17s2b9ksz5y7abUm92cHwG8jEPCzK3dLnT",
        "1GDSuiThEV64c166LUFC9uDcVdGjqkxKyh","1Me3ASYt5JCTAK2XaC32RMeH34PdprrfDx","1CdufMQL892A69KXgv6UNBD17ywWqYpKut",
        "1BkkGsX9ZM6iwL3zbqs7HWBV7SvosR6m8N","1PXAyUB8ZoH3WD8n5zoAthYjN15yN5CVq5","1AWCLZAjKbV1P7AHvaPNCKiB7ZWVDMxFiz",
        "1G6EFyBRU86sThN3SSt3GrHu1sA7w7nzi4","1MZ2L1gFrCtkkn6DnTT2e4PFUTHw9gNwaj","1Hz3uv3nNZzBVMXLGadCucgjiCs5W9vaGz",
        "1Fo65aKq8s8iquMt6weF1rku1moWVEd5Ua","16zRPnT8znwq42q7XeMkZUhb1bKqgRogyy","1KrU4dHE5WrW8rhWDsTRjR21r8t3dsrS3R",
        "17uDfp5r4n441xkgLFmhNoSW1KWp6xVLD","13A3JrvXmvg5w9XGvyyR4JEJqiLz8ZySY3","16RGFo6hjq9ym6Pj7N5H7L1NR1rVPJyw2v",
        "1UDHPdovvR985NrWSkdWQDEQ1xuRiTALq","15nf31J46iLuK1ZkTnqHo7WgN5cARFK3RA","1Ab4vzG6wEQBDNQM1B2bvUz4fqXXdFk2WT",
        "1Fz63c775VV9fNyj25d9Xfw3YHE6sKCxbt","1QKBaU6WAeycb3DbKbLBkX7vJiaS8r42Xo","1CD91Vm97mLQvXhrnoMChhJx4TP9MaQkJo",
        "15MnK2jXPqTMURX4xC3h4mAZxyCcaWWEDD","13N66gCzWWHEZBxhVxG18P8wyjEWF9Yoi1","1NevxKDYuDcCh1ZMMi6ftmWwGrZKC6j7Ux",
        "19GpszRNUej5yYqxXoLnbZWKew3KdVLkXg","1M7ipcdYHey2Y5RZM34MBbpugghmjaV89P","18aNhurEAJsw6BAgtANpexk5ob1aGTwSeL",
        "1FwZXt6EpRT7Fkndzv6K4b4DFoT4trbMrV","1CXvTzR6qv8wJ7eprzUKeWxyGcHwDYP1i2","1MUJSJYtGPVGkBCTqGspnxyHahpt5Te8jy",
        "13Q84TNNvgcL3HJiqQPvyBb9m4hxjS3jkV","1LuUHyrQr8PKSvbcY1v1PiuGuqFjWpDumN","18192XpzzdDi2K11QVHR7td2HcPS6Qs5vg",
        "1NgVmsCCJaKLzGyKLFJfVequnFW9ZvnMLN","1AoeP37TmHdFh8uN72fu9AqgtLrUwcv2wJ","1FTpAbQa4h8trvhQXjXnmNhqdiGBd1oraE",
        "14JHoRAdmJg3XR4RjMDh6Wed6ft6hzbQe9","19z6waranEf8CcP8FqNgdwUe1QRxvUNKBG","14u4nA5sugaswb6SZgn5av2vuChdMnD9E5",
        "174SNxfqpdMGYy5YQcfLbSTK3MRNZEePoy", "1NBC8uXJy1GiJ6drkiZa1WuKn51ps7EPTv"]

#262!/131!/131! 364950428295639250777230977182937950631063637653015344224357416878384793565048
#               1461501637330902918203684832716283019655932542976 2^160
#               115792089237316195423570985008687907853269984665640564039457584007913129639936 2^256 (340282366920938463463374607431768211456*340282366920938463463374607431768211456 = 2^256)

F1="01"

aa1=F1[0]*131
aa2=F1[1]*131

def find_permutation(lst,K,numberbit1,numberbit0):

    l = lst

    N = numberbit0
    M = numberbit1

    if N == len(l):
        return F1[1] * N
    
    if M == len(l):
        return F1[1] * M

    result = ''    

    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)

        if (K < K0):
            result += F1[0]
            l.remove (F1[0])
        else:
            result += F1[1]
            l.remove (F1[1])
            M -=1
            K = K - K0

    result += l[0]

    return result


#ccount0 = 0

for XXX in range(1,1000000000000,1): # loop step

    llen = bin(115792089237316195423570985008687907853269984665640564039457584007913129639936)[2:]
    llen2 = len(llen)
    d0 = "0"
    
    ccount0 = 0
    
    for S1 in range(2,128,1):   # half bit len for collision to dec set
        for S2 in range(1):    # random loop for ^ "half bit len for collision to dec set"

            random.seed()
            
            Nn1 = "0","1"  # ours dropout "1","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"

            RRR1 = []

            for RR1 in range(S1):
                DDD1 = random.choice(Nn1)
                RRR1.append(DDD1)

            d1 = ''.join(RRR1)

            #llen = bin(115792089237316195423570985008687907853269984665640564039457584007913129639936)[2:]
            #llen2 = len(llen)
            #d0 = "0"
            
            d2 = "1"+d1 # bit len for collision to dec set , 18446744073709551616 * 18446744073709551616 = 340282366920938463463374607431768211456 , 18446744073709551616 * 340282366920938463463374607431768211456 * 18446744073709551616 = 115792089237316195423570985008687907853269984665640564039457584007913129639936

            llen3 = llen2-len(d2) # num zeros +

            d3 = d2+d0*llen3
            
            print(S1,S2,"",ccount0,d3)
            
            f1=len(d3)
            while f1 >= len(d2):
              
                f2 = d3[0:f1]
                d4 = int(f2,2)
                            
                if d4 <= 115792089237316195423570985008687907853269984665640564039457584007913129639936:
                    ccount0 += 1
                    a3 = list(aa1+aa2)
                    K = d4 #perm_int
                    numberbit1 = len(aa1)
                    numberbit0 = len(aa2)
                    aa = find_permutation(a3,K,numberbit1,numberbit0)

                    random.seed(aa) # init collision seed

                    Nn = "0","1"

                    RRR = [] #func()

                    for RR in range(160): # bit collision seeded len
                        DDD = random.choice(Nn)
                        RRR.append(DDD)

                    d = ''.join(RRR)

                    #print(S1,S2,"",ccount0,f2,d4,d,aa)

                    ii = 64
                    while ii <= 160:
                        dd = (d)[0:ii]
                        b = int(dd,2)
                        if b >= 9223372036854775807:
                            
                            #key = Key.from_int(b)
                            addr = ice.privatekey_to_address(0, True, b) #key.address
                                    
                            if addr in list2:
                                        
                                print ("found!!!",b,addr)
                                s1 = str(b)
                                s2 = addr
                                f=open("a.txt","a")
                                f.write(s1)
                                f.write(s2)      
                                f.close()
                                pass
                            else:
                                
                                #print(S1,S2,"",ccount0,f2,d4,d,aa,addr)
                                pass
                        ii=ii+1


                f1=f1-1

                        
print("pz end")
input() #"pause"



*** step by step, just insert a string 128 long (128+128 for 64 pz...)

1000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000

0000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000001
0000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000011
0000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000111
...


from os import system
system("title "+__file__)
import random
import time
import gmpy2
import secp256k1 as ice

list2 = ["16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN","13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so","1BY8GQbnueYofwSuFAT3USAhGjPrkxDdW9",
        "1MVDYgVaSN6iKKEsbzRUAYFrYJadLYZvvZ","19vkiEajfhuZ8bs8Zu2jgmC6oqZbWqhxhG","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF",
        "1PWo3JeB9jrGwfHDNpdGK54CRas7fsVzXU","1JTK7s9YVYywfm5XUH7RNhHJH1LshCaRFR","12VVRNPi4SJqUTsp6FmqDqY5sGosDtysn4",
        "1FWGcVDK3JGzCC3WtkYetULPszMaK2Jksv","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF","1Bxk4CQdqL9p22JEtDfdXMsng1XacifUtE",
        "15qF6X51huDjqTmF9BJgxXdt1xcj46Jmhb","1ARk8HWJMn8js8tQmGUJeQHjSE7KRkn2t8","15qsCm78whspNQFydGJQk5rexzxTQopnHZ",
        "13zYrYhhJxp6Ui1VV7pqa5WDhNWM45ARAC","14MdEb4eFcT3MVG5sPFG4jGLuHJSnt1Dk2","1CMq3SvFcVEcpLMuuH8PUcNiqsK1oicG2D",
        "1K3x5L6G57Y494fDqBfrojD28UJv4s5JcK","1PxH3K1Shdjb7gSEoTX7UPDZ6SH4qGPrvq","16AbnZjZZipwHMkYKBSfswGWKDmXHjEpSf",
        "19QciEHbGVNY4hrhfKXmcBBCrJSBZ6TaVt","1EzVHtmbN4fs4MiNk3ppEnKKhsmXYJ4s74","1AE8NzzgKE7Yhz7BWtAcAAxiFMbPo82NB5",
        "17Q7tuG2JwFFU9rXVj3uZqRtioH3mx2Jad","1K6xGMUbs6ZTXBnhw1pippqwK6wjBWtNpL","15ANYzzCp5BFHcCnVFzXqyibpzgPLWaD8b",
        "18ywPwj39nGjqBrQJSzZVq2izR12MDpDr8","1CaBVPrwUxbQYYswu32w7Mj4HR4maNoJSX","1JWnE6p6UN7ZJBN7TtcbNDoRcjFtuDWoNL",
        "1CKCVdbDJasYmhswB6HKZHEAnNaDpK7W4n","1PXv28YxmYMaB8zxrKeZBW8dt2HK7RkRPX","1AcAmB6jmtU6AiEcXkmiNE9TNVPsj9DULf",
        "1EQJvpsmhazYCcKX5Au6AZmZKRnzarMVZu","18KsfuHuzQaBTNLASyj15hy4LuqPUo1FNB","15EJFC5ZTs9nhsdvSUeBXjLAuYq3SWaxTc",
        "1HB1iKUqeffnVsvQsbpC6dNi1XKbyNuqao","1GvgAXVCbA8FBjXfWiAms4ytFeJcKsoyhL","12JzYkkN76xkwvcPT6AWKZtGX6w2LAgsJg",
        "1824ZJQ7nKJ9QFTRBqn7z7dHV5EGpzUpH3","18A7NA9FTsnJxWgkoFfPAFbQzuQxpRtCos","1NeGn21dUDDeqFQ63xb2SpgUuXuBLA4WT4",
        "1NLbHuJebVwUZ1XqDjsAyfTRUPwDQbemfv","1MnJ6hdhvK37VLmqcdEwqC3iFxyWH2PHUV","1KNRfGWw7Q9Rmwsc6NT5zsdvEb9M2Wkj5Z",
        "1PJZPzvGX19a7twf5HyD2VvNiPdHLzm9F6","1GuBBhf61rnvRe4K8zu8vdQB3kHzwFqSy7","17s2b9ksz5y7abUm92cHwG8jEPCzK3dLnT",
        "1GDSuiThEV64c166LUFC9uDcVdGjqkxKyh","1Me3ASYt5JCTAK2XaC32RMeH34PdprrfDx","1CdufMQL892A69KXgv6UNBD17ywWqYpKut",
        "1BkkGsX9ZM6iwL3zbqs7HWBV7SvosR6m8N","1PXAyUB8ZoH3WD8n5zoAthYjN15yN5CVq5","1AWCLZAjKbV1P7AHvaPNCKiB7ZWVDMxFiz",
        "1G6EFyBRU86sThN3SSt3GrHu1sA7w7nzi4","1MZ2L1gFrCtkkn6DnTT2e4PFUTHw9gNwaj","1Hz3uv3nNZzBVMXLGadCucgjiCs5W9vaGz",
        "1Fo65aKq8s8iquMt6weF1rku1moWVEd5Ua","16zRPnT8znwq42q7XeMkZUhb1bKqgRogyy","1KrU4dHE5WrW8rhWDsTRjR21r8t3dsrS3R",
        "17uDfp5r4n441xkgLFmhNoSW1KWp6xVLD","13A3JrvXmvg5w9XGvyyR4JEJqiLz8ZySY3","16RGFo6hjq9ym6Pj7N5H7L1NR1rVPJyw2v",
        "1UDHPdovvR985NrWSkdWQDEQ1xuRiTALq","15nf31J46iLuK1ZkTnqHo7WgN5cARFK3RA","1Ab4vzG6wEQBDNQM1B2bvUz4fqXXdFk2WT",
        "1Fz63c775VV9fNyj25d9Xfw3YHE6sKCxbt","1QKBaU6WAeycb3DbKbLBkX7vJiaS8r42Xo","1CD91Vm97mLQvXhrnoMChhJx4TP9MaQkJo",
        "15MnK2jXPqTMURX4xC3h4mAZxyCcaWWEDD","13N66gCzWWHEZBxhVxG18P8wyjEWF9Yoi1","1NevxKDYuDcCh1ZMMi6ftmWwGrZKC6j7Ux",
        "19GpszRNUej5yYqxXoLnbZWKew3KdVLkXg","1M7ipcdYHey2Y5RZM34MBbpugghmjaV89P","18aNhurEAJsw6BAgtANpexk5ob1aGTwSeL",
        "1FwZXt6EpRT7Fkndzv6K4b4DFoT4trbMrV","1CXvTzR6qv8wJ7eprzUKeWxyGcHwDYP1i2","1MUJSJYtGPVGkBCTqGspnxyHahpt5Te8jy",
        "13Q84TNNvgcL3HJiqQPvyBb9m4hxjS3jkV","1LuUHyrQr8PKSvbcY1v1PiuGuqFjWpDumN","18192XpzzdDi2K11QVHR7td2HcPS6Qs5vg",
        "1NgVmsCCJaKLzGyKLFJfVequnFW9ZvnMLN","1AoeP37TmHdFh8uN72fu9AqgtLrUwcv2wJ","1FTpAbQa4h8trvhQXjXnmNhqdiGBd1oraE",
        "14JHoRAdmJg3XR4RjMDh6Wed6ft6hzbQe9","19z6waranEf8CcP8FqNgdwUe1QRxvUNKBG","14u4nA5sugaswb6SZgn5av2vuChdMnD9E5",
        "174SNxfqpdMGYy5YQcfLbSTK3MRNZEePoy", "1NBC8uXJy1GiJ6drkiZa1WuKn51ps7EPTv"]

#262!/131!/131! 364950428295639250777230977182937950631063637653015344224357416878384793565048
#               1461501637330902918203684832716283019655932542976 2^160
#               115792089237316195423570985008687907853269984665640564039457584007913129639936 2^256 (340282366920938463463374607431768211456*340282366920938463463374607431768211456 = 2^256)

F1="01"

aa1=F1[0]*131
aa2=F1[1]*131

def find_permutation(lst,K,numberbit1,numberbit0):

    l = lst

    N = numberbit0
    M = numberbit1

    if N == len(l):
        return F1[1] * N
    
    if M == len(l):
        return F1[1] * M

    result = ''    

    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)

        if (K < K0):
            result += F1[0]
            l.remove (F1[0])
        else:
            result += F1[1]
            l.remove (F1[1])
            M -=1
            K = K - K0

    result += l[0]

    return result



def lexico_permute_string(s):
    a = list(s)
    n = len(a) - 1
    while True:
        yield ''.join(a)
        for j in range(n-1, -1, -1):
            if a[j] < a[j + 1]:
                break
        else:
            return
        v = a[j]
        for k in range(n, j, -1):
            if v < a[k]:
                break
        a[j], a[k] = a[k], a[j]
        a[j+1:] = a[j+1:][::-1]

        
s = "0000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000011" #128!/126!/2!  8128
sv = lexico_permute_string(s)
ccount0 = 0

for XXX in sv: # loop step

    llen = bin(115792089237316195423570985008687907853269984665640564039457584007913129639936)[2:]
    llen2 = len(llen)
    d0 = "0"
    
    ccount0 += 1
    
    

    d1 = XXX #''.join(RRR1)

    #llen = bin(115792089237316195423570985008687907853269984665640564039457584007913129639936)[2:]
    #llen2 = len(llen)
    #d0 = "0"
            
    d2 = "1"+d1 # bit len for collision to dec set , 18446744073709551616 * 18446744073709551616 = 340282366920938463463374607431768211456 , 18446744073709551616 * 340282366920938463463374607431768211456 * 18446744073709551616 = 115792089237316195423570985008687907853269984665640564039457584007913129639936

    llen3 = llen2-len(d2) # num zeros +

    d3 = d2+d0*llen3
            
    print(XXX,"",ccount0,d3)
            
    f1=len(d3)
    while f1 >= len(d2):
              
        f2 = d3[0:f1]
        d4 = int(f2,2)
                            
        if d4 <= 115792089237316195423570985008687907853269984665640564039457584007913129639936:
            #ccount0 += 1
            a3 = list(aa1+aa2)
            K = d4 #perm_int
            numberbit1 = len(aa1)
            numberbit0 = len(aa2)
            aa = find_permutation(a3,K,numberbit1,numberbit0)

            random.seed(aa) # init collision seed

            Nn = "0","1"

            RRR = [] #func()

            for RR in range(160): # bit collision seeded len
                DDD = random.choice(Nn)
                RRR.append(DDD)

            d = ''.join(RRR)

            #print(d3,"",ccount0,f2,d4,d,aa)

            ii = 64
            while ii <= 160:
                dd = (d)[0:ii]
                b = int(dd,2)
                if b >= 9223372036854775807:
                            
                    #key = Key.from_int(b)
                    addr = ice.privatekey_to_address(0, True, b) #key.address
                                    
                    if addr in list2:
                                        
                        print ("found!!!",b,addr)
                        s1 = str(b)
                        s2 = addr
                        f=open("a.txt","a")
                        f.write(s1)
                        f.write(s2)      
                        f.close()
                        pass
                    else:
                                
                        #print(d3,"",ccount0,f2,d4,d,aa,addr)
                        pass
                ii=ii+1


        f1=f1-1

                        
print("pz end")
input() #"pause"

11  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: April 26, 2022, 02:24:21 PM
https://bitcointalk.org/index.php?topic=1306983.msg59102356#msg59102356 continuing the flight...

1048576×1048576 = 1099511627776
1099511627776×1099511627776 = 1208925819614629174706176

for 64 will be

18446744073709551616×18446744073709551616 = 340282366920938463463374607431768211456
340282366920938463463374607431768211456×340282366920938463463374607431768211456=115792089237316195423570985008687907853269984665640564039457584007913129639936

for 160, 256 bit likewise...

and select the size of "collisions" for them...

or the same

1048576×1099511627776×1048576 = 1208925819614629174706176

i.e. the 20th puzzle jumps within 1^2-2^20 blablabla

532368669374487342350336 484187 ×1099511627776×1000001
181088827760010590158848 164700 ×1099511627776×1000002
619892701383498689150976 563789 ×1099511627776×1000002
644019977303000002592768 585732 ×1099511627776×1000003
1120137428268770255699968 1018757 ×1099511627776×1000003
280959330078426262405120 255531 ×1099511627776×1000004
352372895955598358609920 320481 ×1099511627776×1000004
15992476587985050009600 14546 ×1099511627776×1000005
147981810864471083581440 134589 ×1099511627776×1000005
849455045036521008660480 772572 ×1099511627776×1000005
1092999181290656105496576 994072 ×1099511627776×1000006
142265848123988914470912 129390 ×1099511627776×1000008
520451395515858448023552 473345 ×1099511627776×1000008
852452687023533572751360 775296×1099511627776× 1000008
181419951836283866710016 165000 ×1099511627776×1000009
697292360654493845553152 634179 ×1099511627776×1000009
722959214526753365032960 657522×1099511627776× 1000010
...

in some it pops up several times

11011000101111010000110010010101010000000000000000000000000000000000000000         11010010110001010101 0000000000000000000110100111010101010100110111011111111001111110010001110011100 011011110001010111101  15992476587985050009600  14546 ×1099511627776× 1000005
11111010101100001110000101011101011000000000000000000000000000000000000000000      11010010110001010101 0000000000000000011111111011000011100000111110011001010110000101001111111101111 011001101010101011110  147981810864471083581440 134589 ×1099511627776×1000005
1011001111100001000011001101111000000111000000000000000000000000000000000000000 0   11010010110001010101 0000000000000001111101000000111100110111011100100001110000110000001111111111011 111101101011001111001  849455045036521008660480 772572 ×1099511627776×1000005

1000000000000000000000000000000000000000000000000000000000000000000000000000000 00      1208925819614629174706176 2^81-1
10000011001010111110101110111100110000000000000000000000000000000000000000             9678753217407715639296
10111011010111111110111010111111010000000000000000000000000000000000000000             13825815258173381017600
10010111001010110000000101001111000000000000000000000000000000000000000000             11154228800040674000896
10111110101100110011101011100000000000000000000000000000000000000000000                1758898127588428873728
11011000101111010000110010010101010000000000000000000000000000000000000000             15992476587985050009600
10110110000100000010110100011101100000000000000000000000000000000000000000             13433892166917160960000
10000111010010110111010111000001010000000000000000000000000000000000000000             9982991658226125111296
111011110101001111100011100100000000000000000000000000000000000000000000               4414816667071118573568
100001010011010001011111010101100000000000000000000000000000000000000000000            19657526330993040949248
10110110010000110111011111000100000000000000000000000000000000000000000000             13448675964968748711936
11110011011110011110111110111101010000000000000000000000000000000000000000             17965381037568078905344
1110111100000110010011001111000000000000000000000000000000000000000000000              8818451670323662159872
1000011000011011000000001000101100000000000000000000000000000000000000000              4947618827496440463360
100100111110101101001101011000000000000000000000000000000000000000000000               2728626692560540139520
11000100100110101011111100111100100000000000000000000000000000000000000000             14506850144679672938496
101001011000001000110101011100000000000000000000000000000000000000000000               3053095300706074624000
10010111100011000101000001101000000000000000000000000000000000000000000                1397784525321399173120
100100101010101100001111011010000000000000000000000000000000000000000000000            21644406558527521292288
10010011001100100110000001100100000000000000000000000000000000000000000000             10861205560344509939712
111010101001010001011011111100000000000000000000000000000000000000000000               4327228515271319748608
1100010100010110010101011011010100000000000000000000000000000000000000000              7271235947948482232320
1100010110011001000110101001110000000000000000000000000000000000000000000              7290081768563586105344
10011011010110100110101111001000000000000000000000000000000000000000000000             11463043410452910440448
11100100010110110011101101100110000000000000000000000000000000000000000                2106215804518520586240
1001000001011110000110111110101110000000000000000000000000000000000000000              5326224838426200375296
10011101011001011101011101111110110000000000000000000000000000000000000000             11613909172213287747584
100011001010110010110101111100100000000000000000000000000000000000000000000            20759914316371675054080
101011001001011100110101111111000000000000000000000000000000000000000000               3183735872628465860608
11010000101000001100111000100110100000000000000000000000000000000000000000             15394040034216221081600
100010111110000101001110001110011000000000000000000000000000000000000000000            20642659225394107908096
1011000110011010001111110011011110000000000000000000000000000000000000000              6552376728949719302144
11111111111011100001010100111000100000000000000000000000000000000000000000             18884301677095521615872
100000010100111110101011100111111000000000000000000000000000000000000000000            19082966744245204942848
11000001111011000000110000100100000000000000000000000000000000000000000000             14308922462804134330368
11010011100100001010100000001110100000000000000000000000000000000000000000             15610746387332732026880
111010111110110100001110001100010000000000000000000000000000000000000000               4352066501634477260800
100011100000001010111011111001101110000000000000000000000000000000000000000            20957077306601793126400
10110001010010011101100101011111000000000000000000000000000000000000000000             13081580359739640905728
1011110100011001100001010010011010000000000000000000000000000000000000000              6976547096570307280896
111110011011101000101011000001010000000000000000000000000000000000000000               4606654095766289645568
1011001000100111010000110010000000000000000000000000000000000000000000000              6572699170591182159872
1100001011101010111110000010001110000000000000000000000000000000000000000              7191199344262830358528
100101010011000100110110001111111100000000000000000000000000000000000000000            22016887670665522446336
11001111001000111101011000100100000000000000000000000000000000000000000000             15284233257106557370368
1101000000001101101100110110101000000000000000000000000000000000000000000              7675820033246287101952
11000010101101100101001001001000000000000000000000000000000000000000000                1795902996263741685760
1110000001110001100000010010110000000000000000000000000000000000000000000              8280499078575465431040
10100001010010101110011000011000000000000000000000000000000000000000000000             11901291293835867979776
11000100011110111001001101011111000000000000000000000000000000000000000000             14497865615155673432064
11101001011000111111011010011010000000000000000000000000000000000000000000             17221177932612567564288
10000111100011111110100111101001000000000000000000000000000000000000000000             10002722103015984070656
1001001001001001101101000011100000000000000000000000000000000000000000000              5397071132389644697600
100100011100100101011100000001010000000000000000000000000000000000000000               2689287368284924018688
1110111000101100110010100111101000000000000000000000000000000000000000000              8787105231532512509952
110010001100100111011100000000000000000000000000000000000000000000000000               3703894315638410182656
11110100011011110111011001111010100000000000000000000000000000000000000000             18036149182643067420672
11110010101111111001110011010000000000000000000000000000000000000000000000             17911676820374964666368
1111010000000000000110000011010000000000000000000000000000000000000000000              9002024733118352588800
10000111110011001000101110110101010000000000000000000000000000000000000000             10020198093771088330752
10011111110000001000001111100001000000000000000000000000000000000000000000             11787617945548664864768
1010001110110011110000010011101110000000000000000000000000000000000000000              6039543966877786046464
101110100100101111111101100001010000000000000000000000000000000000000000               3436570076666975485952
1010110000001110111111101100001100000000000000000000000000000000000000000              6347840992086851584000
1100010101101100111001010101010000000000000000000000000000000000000000000              7283710705611042717696
101011010101100010001101001000000000000000000000000000000000000000000                  399708439522897297408
10101000011100000110000001011100000000000000000000000000000000000000000000             12428602310673146314752
10101110011010111011001010111101110000000000000000000000000000000000000000             12869975770262824550400
100000011110011101111001101001000000000000000000000000000000000000000000000            19170476228187059650560
11011110110001010110110001110101000000000000000000000000000000000000000000             16437612233317349851136
100010101100000011110011000011000000000000000000000000000000000000000000000            20476433214725444075520
100010100000100110000000010010010100000000000000000000000000000000000000000            20370682478836041383936
100100001011101101010011110110001000000000000000000000000000000000000000000            21358636137332818837504
11010000000100110010011010001001010000000000000000000000000000000000000000             15353210834301573136384
11000110111110000010011010001100000000000000000000000000000000000000000                1835168229948320120832
10001000001101001010010111010000000000000000000000000000000000000000000000             10050203443936188432384
1011110010011110111101010000000100000000000000000000000000000000000000000              6958883896368388112384
11001110111110111110101010010110100000000000000000000000000000000000000000             15272727063634951274496
10000000001010101111011001011010010000000000000000000000000000000000000000             9457116009838443233280
110000010101011101101100000110110000000000000000000000000000000000000000               3566521045891541893120
10100000110100110011100101110011000000000000000000000000000000000000000000             11866797498612163018752
100010101110110110000001011001111000000000000000000000000000000000000000000            20502118048242849546240
1100001000101100001110000100001010000000000000000000000000000000000000000              7163709440307081773056
10101011111010101101011111101111000000000000000000000000000000000000000000             12685261974049921171456
11110011000110111001101001101110000000000000000000000000000000000000000000             17938191332172550373376
10110100001010001010100110010001100000000000000000000000000000000000000000             13293375865116969402368
11110000101110111110100100010000000000000000000000000000000000000000000000             17763035796148578156544
1001011100000100000001010101000000000000000000000000000000000000000000                 696437020210526945280
101101000000010110101000011000000000000000000000000000000000000000000000               3320821614587112587264
10101000001010011100111101010110000000000000000000000000000000000000000                1551032862808469405696
10100000111111001111000110010010000000000000000000000000000000000000000000             11878822245956684087296
10101111001111101110010100100111000000000000000000000000000000000000000000             12930849137520573153280
10110011111100111000001110100101100000000000000000000000000000000000000000             13278056958945398882304
100001011011001101011101100101100000000000000000000000000000000000000000000            19730732905885901783040
1101000001111011010110001101111000000000000000000000000000000000000000000              7691621730575567552512
110011001111001111001011001100000000000000000000000000000000000000000000               3780702978584795414528
111000011000010000010101110001100000000000000000000000000000000000000000               4160035147675468824576
1111101110001110011100100000110000000000000000000000000000000000000000                 1160099260548991942656
1110000101101100110110011111000000000000000000000000000000000000000000                 1039590245173370552320
10101000011010100101110000100100000000000000000000000000000000000000000000             12426868178526004051968
11111010111111011000010101010010000000000000000000000000000000000000000                2314977058025419833344
100100000010100011100110000100100000000000000000000000000000000000000000000            21274225675292362407936
110001111000010110010011110101100000000000000000000000000000000000000000               3680527342792309997568
110100110101010111001001110000000000000000000000000000000000000000000                  487305585327811330048
100011101001000001011000011101000000000000000000000000000000000000000000               2629838849349517312000
10000101000110111000011001100101000000000000000000000000000000000000000000             9821601382159792209920
10110000111010001100100001110000000000000000000000000000000000000000000                1631700368465162403840
100011100001011010110110101001100100000000000000000000000000000000000000000            20968594694201281609728
10001000111110100010000110001110000000000000000000000000000000000000000000             10107124149355454398464

1100000110000100101111100111101010000000000000000000000000000000000000000000000        456932713417561520209920
10010001101110110111011101011111110000000000000000000000000000000000000000             10753145046293777743872
100100001011010011001010011011001011110000000000000000000000000000000000000000         170838943426624490569728
111010100110110000000001100001111010010000000000000000000000000000000000000000         276756528897123353100288
1001111001011100110110010011101000000100000000000000000000000000000000000000000 0       747846657576038148603904
1101010111001010100011111010011110011100000000000000000000000000000000000000000 0       1009600654567916108251136

1110000101110111100001101101101110110100000000000000000000000000000000000000000        532368669374487342350336
100110010110001101100001010011011101100000000000000000000000000000000000000000         181088827760010590158848
1000001101000100011100110101111110011000000000000000000000000000000000000000000 0       619892701383498689150976
1000100001100000011001001001011011001001000000000000000000000000000000000000000 0       644019977303000002592768
1110110100110010110001011000101110001100000000000000000000000000000000000000000 0       1120137428268770255699968
111011011111101101010111110111001010000000000000000000000000000000000000000000         280959330078426262405120
1001010100111100010110001000111100000000000000000000000000000000000000000000000        352372895955598358609920
11011000101111010000110010010101010000000000000000000000000000000000000000             15992476587985050009600
11111010101100001110000101011101011000000000000000000000000000000000000000000          147981810864471083581440
1011001111100001000011001101111000000111000000000000000000000000000000000000000 0       849455045036521008660480

1011111111111110011001000000000000000000000000000000000000000000000                    110676840451932160000         100661×1099511627776×1000
1110000001100000001111110010000000000000000000000000000000000000000000                 1034751492411621376000        941102×1099511627776×1000
10001100010010001001010111110000000000000000000000000000000000000000                   161735907546524286976         146952×1099511627776×1001
1000000111110101111110111000110000000000000000000000000000000000000000                 599338725049651691520         543466×1099511627776×1003
1010111010110111000001100000000000000000000000000000000000000000000000                 805730424346065764352         729889×1099511627776×1004
1101111111110000011000000010000000000000000000000000000000000000000000                 1032736201947117256704        935527×1099511627776×1004
110010110111111010100000011000000000000000000000000000000000000000000                  469226680670150983680         424637×1099511627776×1005
1110010010110010000110001000110000000000000000000000000000000000000000                 1054672702468899471360        954448×1099511627776×1005

10000000000000000000000000000000000000000                                              1099511627776
1000000000000000000000000000000000000000000000000000000000000000000000000000000 00      1208925819614629174706176

1000000111110101111110111000110000000000000000000000000000000000000000
1110010010110010000110001000110000000000000000000000000000000000000000
1__00_0_1_110______110__100011

10000000000000000000000000000000000000000                                              1×1099511627776×1
100000000000000000000000000000000000000000                                             1×1099511627776×2
110000000000000000000000000000000000000000                                             1×1099511627776×3
1000000000000000000000000000000000000000000                                            1×1099511627776×4
1010000000000000000000000000000000000000000                                            1×1099511627776×5
100000000000000000000000000000000000000000                                             2×1099511627776×1
110000000000000000000000000000000000000000                                             3×1099511627776×1
1000000000000000000000000000000000000000000                                            4×1099511627776×1
1010000000000000000000000000000000000000000                                            5×1099511627776×1
1100100000000000000000000000000000000000000000                                         50×1099511627776×1
1111101000000000000000000000000000000000000000000                                      500×1099511627776×1
1111101010000000000000000000000000000000000000000                                      501×1099511627776×1
11111010100000000000000000000000000000000000000000                                     501×1099511627776×2
1001110010010000000000000000000000000000000000000000                                   501×1099511627776×5
1111111100000000000000000000000000000000000000000                                      510×1099511627776×1
111111110             510
10011100010000000000000000000000000000000000000000000                                  5000×1099511627776×1
1001110001000         5000
11000011010100000000000000000000000000000000000000000000                               50000×1099511627776×1
1100001101010000      50000
110000110101000000000000000000000000000000000000000000000                              50000×1099511627776×2
11011011101110100000000000000000000000000000000000000000000                            50000×1099511627776×9
11110100001001000000000000000000000000000000000000000000000                            50000×1099511627776×10
11110100001001000000000000000000000000000000000000000000000                            500000×1099511627776×1
1111010000100100000   500000
101010101110011000000000000000000000000000000000000000000000                           700000×1099511627776×1
110110111011101000000000000000000000000000000000000000000000                           900000×1099511627776×1
111101000010010000000000000000000000000000000000000000000000                           1000000×1099511627776×1
11110100001001000000  1000000
1000000000000000000000000000000000000000000000000000000000000                          1048576×1099511627776×1
100000000000000000000 1048576
111111111111111111110000000000000000000000000000000000000000                           1048575×1099511627776×1
11111111111111111111  1048575
1111111111111111111100000000000000000000000000000000000000000000000000000000000 000000000000000000000 1048575×1208925819614629174706176×1
1011111010111100001000000000000000000000000000000000000000000000000                    1000000×1099511627776×100
1111000110000100100111010000000000000000000000000000000000000000000000                 1000000×1099511627776×1013
100110101001001001010000000000000000000000000000000000000000000                        5000×1099511627776×1013


1099511627776×1099511627776 1208925819614629174706176
1208925819614629174706176×1208925819614629174706176 1461501637330902918203684832716283019655932542976

1011111010111100001000000000000000000000000000000000000000000000000                                          1000000×1099511627776×100
1011111010111100001000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000  1000000×1208925819614629174706176×100
1011111010111100001000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000 1000000×1461501637330902918203684832716283019655932542976×100

262!/131!/131! 364950428295639250777230977182937950631063637653015344224357416878384793565048
1048575×1208925819614629174706176×1048575 1329225460484924342264618696048640000  1208925819614629174706176×1099511627776 1329227995784915872903807060280344576
80!/40!/40!                               107507208733336176461620
100!/50!/50!                              100891344545564193334812497256
140!/70!/70!                              93820969697840041204785894580506297666600
120!/60!/60!                              96614908840363322603893139521372656
130!/65!/65!                              95067625827960698145584333020095113100



here it turns out so zeros are added for 20 puzzles, this is 40 + 40 zeros


1000000000000000000000000000000000000000000000000000000000000000000000000000000 00      1208925819614629174706176
1111111111111111111111111111111111111111111111111111111111111111111111111111111 1       1208925819614629174706176(-1)

10000011000100100000100001000000101000000000000000                                     576453884411904             11010010110001010101 0000000000000000000000000000000000111011111111101010111110111101010101110111011 011110111101101111011 1450500
1000011000100111000001000000000000000000000000000000000                                18880272506290176           11010010110001010101 0000000000000000000000000000000101110101101100111110101011110100011001011111111 111101111111111011101 1700914
10000000000011010000011100000000000000000000                                           8799590023168               11010010110001010101 0000000000000000000000000000000000000111111101101111110111011111111111011111110 111000101111111010011 3402713
100101000000000010010000000000001000000000000000000000000000000000000000000            21841269246843326300160     11010010110001010101 0000000000000000000111110110110000111100110111001010100011010011110100011111100 110101011110111110011 231490
100000001111000100000100000000000000000000000000000000000000                           580700744018034688          11010010110001010101 0000000000000000000000000000100011111111111111011011011111110110010111111000110 111101100101111001010 258790
1000000000000010010000101100000000001000000000000000000000000000                       9224008379343568896         11010010110001010101 0000000000000000000000000010111110111111101101010111000110110111110110101100110 111111100110111010010 3224774
1010000100000100000000000000000001000000000                                            5532454748672               11010010110001010101 0000000000000000000000000000000000000111010001110111111110111111100111111110110 111111111011001111111 3464692
10001010000110000000100100000000000000000000000000                                     607343339372544             11010010110001010101 0000000000000000000000000000000000111101011101010110111010111100111101111001111 110111010111111111111 845038
101000000000100111001000000010000000000000000000000000000000000                        5765984128772079616         11010010110001010101 0000000000000000000000000010000111010111110011011100110111111001000110111110111 000111101111111111011 531959
1011100000000010011010001100100110000000000000000                                      404640974962688             11010010110001010101 0000000000000000000000000000000000110101011111110110111111111111111111110010100 001001101111111101111 624928
10101000100000100100000101000000000000000000000                                        92638696964096              11010010110001010101 0000000000000000000000000000000000011010011111011110111111111001111111110111100 011101010111011111111 1363131
100000000000000101001010010010000000000                                                274888729600                11010010110001010101 0000000000000000000000000000000000000001111101001111001110111101111111110111111 101111111111110110111 2584878
1000001000100000000111000000010000000000000                                            4471075643392               11010010110001010101 0000000000000000000000000000000000000110110101111111110111011111110111011011111 111111111011011000111 460364
10000000000000001000010000100100100101000000000000000000000000000000000                1180610218174911086592      11010010110001010101 0000000000000000000000111111100111001101111110111000101011111101111100101100101 010101001001101101011 639556
10000101100101100100000001000000000000                                                 143437860864                11010010110001010101 0000000000000000000000000000000000000001100111101111111111011111101011111011010 111111111011011111111 306764
10000111100100000000110000001001100000000000000000000000000000000                      19536641653416656896        11010010110001010101 0000000000000000000000000100101111101101100010111101100111111011100001111111111 011100110110011100111 545697
1100000000001000000001001001010000010000000000                                         52785167270912              11010010110001010101 0000000000000000000000000000000000010011101111101111100111101100100111111101101 111110111111110111111 521087
1110000001000000100010001000000001000000000000000000000000                             252485399178379264          11010010110001010101 0000000000000000000000000000010111101010101111111001110111110011110110111000011 001110111100111111111 2088597
10000100001000000010000010100100000000000000000                                        72636760719360              11010010110001010101 0000000000000000000000000000000000010111100111111111111110010110101110101111110 111111111111100111100 2993930
10000010000000000000000000000011000100000000000000000000000000000000000                1199038366474748035072      11010010110001010101 0000000000000000000000111111110101010110010110101110111111111111100111001010100 011100110101000110110 3188671
1101000000010000000000000000010011                                                     13962838035                 11010010110001010101 0000000000000000000000000000000000000000100111111111110011111111101111111111110 010111111111101111011 3544993
1001000000110000000000100100000000000000000000000000000000000000000000000000000        340453189689176777293824    11010010110001010101 0000000000000000111101110001111111111011101011011110101101001110000011000001001 101110100111111100000 3706349
10100101000000001010010110010100010000000000000000000000000000000000                   190234961158489505792       11010010110001010101 0000000000000000000000010100011000011100111111110111101111111001011100101101111 100101111101111000110 9665405

11101111101111011101010101111111011111000000000                                        131799304879616             11010010110001010101 0000000000000000000000000000000000011101111101101111101011111110111111011111101 011100111111111110000 171916
111111101101111101011111111111111111100000000000000000000000000000000000000000         300900407024389665587200    11010010110001010101 0000000000000000111001011011001101100100111001011111011001111101111100110110011 011000110100110011010 912410
11111111101111011110110111111010111100000000000000000000000000000000000000000          150963379505513073999872    11010010110001010101 0000000000000000100000110111101111001111110000111001100011110001111100111000011 110011001111110101011 66735
11111111111111010111001111010111111111100000000000000000                               72054793048031232           11010010110001010101 0000000000000000000000000000001011110101100100111011010000111111101100101111111 011111111111111101110 1285381
11110111111111110111111101011111000000000                                              2130286919168               11010010110001010101 0000000000000000000000000000000000000011111111111111110111111101000111101111101 011111011110101101111 2017397
1110111110111111111011111101110111101111000000000                                      527215284182528             11010010110001010101 0000000000000000000000000000000000111010111111110011111011111111111011011010101 100101111101111001111 2074411
111111100111110101111101111111100111110000000000000000000000000000000                  586814457269698166784       11010010110001010101 0000000000000000000000101011011110111011111101000001111110101111110111011101100 101001100101111000101 865171
11110110110111011011110111001111100000000000000000000000000000000                      35577165604173381632        11010010110001010101 0000000000000000000000000110111011011110111001011101101000110111011111110110011 110110110010100111011 1969013
10111101110111111111111111101101111000000000000000000000000000                         3420483897526321152         11010010110001010101 0000000000000000000000000001101011011010111100111001001111011011111100111111011 011100111011010111110 2335793
1111111111111111101111101111101000000000000000000000000000000000000000000000000 0       1208921134182166849126400   11010010110001010101 0000000000000010101100111101011111010111111010000100110010011110001110110010011 100110001110100111110 2737277
110111101111110101101111111100000000000000000000000000000000000000000000               4113439263260321775616      11010010110001010101 0000000000000000000010100000101101101111011001110111000110011111111101011101111 101011011100110110001 2915316
1110111111111010101101100101100000000000000000000000000000000                          2161541776039477248         11010010110001010101 0000000000000000000000000001001111111101011111001101101001111001111011110111100 111101011000111101101 3096661
11110011111010111110111111111111011000                                                 261908856792                11010010110001010101 0000000000000000000000000000000000000001111011111110111011111110111101011011111 110101111100111111111 187237
111111101101011101101101011101101111011000000000000000000000000000000                  587624523626472013824       11010010110001010101 0000000000000000000000101011011111110100010111000111111100011111100111100001011 101110011111100101101 324378
1101110011111111111010111111100000000000000000000000000000000000000000                 1019181200498545917952      11010010110001010101 0000000000000000000000111011111101101011101000010011010010001011010111111110011 101010010111111110111 3195532
111111011010101111101111111100000000000000                                             4358045417472               11010010110001010101 0000000000000000000000000000000000000110101111110111101111111111111011111111110 001011011111011111100 6086716
111110111001011011011001001100000000000000000000000000000                              141632157423501312          11010010110001010101 0000000000000000000000000000001111101111111000011101011001101111111101111111111 101110111101001101000 6186611
1011111111111110011001000000000000000000000000000000000000000000000                    110676840451932160000       11010010110001010101 0000000000000000000000001101111111111010111101110111000011101111111000110110111 110101101010000100011 6374746
111111111101100101111111111000                                                         1073111032                  11010010110001010101 0000000000000000000000000000000000000000001111101101111110111111111111111111111 111111101001101111110 7087942
11110111101111111110011101110000000000000000000                                        136201796845568             11010010110001010101 0000000000000000000000000000000000011101111111111110011111010110001111111111111 111111111100010110001 7247521

10000000000000000000000000000000000000000                                              1099511627776
1111111111111111111111111111111111111111                                               1099511627776(-1)


1000000000000000000000000000000000000000000000000000000000000000000000000000000 00       1208925819614629174706176
1111111111111111111111111111111111111111111111111111111111111111111111111111111 1        1208925819614629174706176(-1)

1000001100010010000010000100000010100000 0000000000                                     576453884411904             11010010110001010101
1000011000100111000001000000000000000000 000000000000000                                18880272506290176           11010010110001010101
1000000000001101000001110000000000000000 0000                                           8799590023168               11010010110001010101
1001010000000000100100000000000010000000 00000000000000000000000000000000000            21841269246843326300160     11010010110001010101
1000000011110001000001000000000000000000 00000000000000000000                           580700744018034688          11010010110001010101
1000000000000010010000101100000000001000 000000000000000000000000                       9224008379343568896         11010010110001010101
1010000100000100000000000000000001000000 000                                            5532454748672               11010010110001010101
1000101000011000000010010000000000000000 0000000000                                     607343339372544             11010010110001010101
1010000000001001110010000000100000000000 00000000000000000000000                        5765984128772079616         11010010110001010101
1011100000000010011010001100100110000000 000000000                                      404640974962688             11010010110001010101
1010100010000010010000010100000000000000 0000000                                        92638696964096              11010010110001010101
100000000000000101001010010010000000000                                                 274888729600                11010010110001010101
1000001000100000000111000000010000000000 000                                            4471075643392               11010010110001010101
1000000000000000100001000010010010010100 0000000000000000000000000000000                1180610218174911086592      11010010110001010101
10000101100101100100000001000000000000                                                  143437860864                11010010110001010101
1000011110010000000011000000100110000000 0000000000000000000000000                      19536641653416656896        11010010110001010101
1100000000001000000001001001010000010000 000000                                         52785167270912              11010010110001010101
1110000001000000100010001000000001000000 000000000000000000                             252485399178379264          11010010110001010101

10000000000000000000000000000000000000000                                               1099511627776
1111111111111111111111111111111111111111                                                1099511627776(-1)


1111111111111111111111111111111111111111 1099511627775
 
1011110111011111111111111110110111100000 815506910688    /1048576 777727,995574951171875
1011111111111110011001000000000000000000 824606720000    /1048576 786406,25
1101110011111111111010111111100000000000 949186459648    /1048576 905214,748046875
1101111011111101011011111111000000000000 957734711296    /1048576 913366,99609375
1110111110111101110101010111111101111100 1029682069372   /1048576 981981,343624114990234375
1110111110111111111011111101110111101111 1029717351919   /1048576 982014,99168300628662109375
1110111111111010101101100101100000000000 1030703437824   /1048576 982955,396484375
11110011111010111110111111111111011000   261908856792    /1048576 249775,74996185302734375
1111011011011101101111011100111110000000 1060282158976   /1048576 1011163,8631591796875
1111011110111111111001110111000000000000 1064076537856   /1048576 1014782,46484375
1111011111111111011111110101111100000000 1065143459584   /1048576 1015799,960693359375
1111101110010110110110010011000000000000 1080567607296   /1048576 1030509,57421875
1111110110101011111011111111000000000000 1089511354368   /1048576 1039038,99609375
1111111001111101011111011111111001111100 1093027102332   /1048576 1042391,874629974365234375
1111111011010111011011010111011011110110 1094535968502   /1048576 1043830,8415431976318359375
1111111011011111010111111111111111111000 1094669303800   /1048576 1043957,99999237060546875
1111111110111101111011011111101011110000 1098403150576   /1048576 1047518,8737640380859375
111111111101100101111111111000           1073111032      /1048576 1023,39842987060546875
1111111111111101011100111101011111111110 1099468888062   /1048576 1048535,2402324676513671875
1111111111111111101111101111101000000000 1099507366400   /1048576 1048571,93603515625

1000000000000000100001000010010010010100 549764474004    /1048576 524296,258930206298828125      7
100000000000000101001010010010000000000  274888729600    /1048576 262154,3212890625              6
1000000000000010010000101100000000001000 549793742856    /1048576 524324,17188262939453125       6
1000000000001101000001110000000000000000 549974376448    /1048576 524496,4375                    6
1000000011110001000001000000000000000000 553799385088    /1048576 528144,25                      6
1000001000000000000000000000001100010000 558345749264    /1048576 532480,0007476806640625        4
1000001000100000000111000000010000000000 558884455424    /1048576 532993,7509765625              6
1000001100010010000010000100000010100000 562943246496    /1048576 536864,515777587890625         8
1000010000100000001000001010010000000000 567474693120    /1048576 541186,0400390625              6
10000101100101100100000001000000000000   143437860864    /1048576 136793,00390625                8
1000011000100111000001000000000000000000 576180191232    /1048576 549488,25                      7
1000011110010000000011000000100110000000 582237292928    /1048576 555264,7523193359375           10
1000101000011000000010010000000000000000 593108729856    /1048576 565632,5625                    6
1001000000110000000000100100000000000000 619280744448    /1048576 590592,140625                  5
1001010000000000100100000000000010000000 635664597120    /1048576 606217,0001220703125           5
1010000000001001110010000000100000000000 687358871552    /1048576 655516,501953125               7
1010000100000100000000000000000001000000 691556843584    /1048576 659520,00006103515625          4
1010010100000000101001011001010001000000 708680455232    /1048576 675850,34869384765625          11
1010100010000010010000010100000000000000 723739820032    /1048576 690212,078125                  7
1011100000000010011010001100100110000000 790314404224    /1048576 753702,5491943359375           12
1100000000001000000001001001010000010000 824768238608    /1048576 786560,2861480712890625        7
1101000000010000000000000000010011       13962838035     /1048576 13316,00001811981201171875     6
1110000001000000100010001000000001000000 963155361856    /1048576 918536,53131103515625          7

40!/39!/1!  40
40!/38!/2!  780
40!/37!/3!  9880
40!/36!/4!  91390
40!/35!/5!  658008
40!/34!/6!  3838380
40!/33!/7!  18643560
40!/32!/8!  76904685
40!/31!/9!  273438880
40!/30!/10! 847660528
40!/29!/11! 2311801440
40!/28!/12! 5586853480

3838380/2^20 3,660564422607421875


1000000000000000000000000000000000000000 549755813888
549755813888/1048576 524288

524288 549755813888/1048576
524296
524324
524496

18446744073709551616
1844674407

1111111111111111111111111111111111011011111110101111111111111101111111111101111 1110111111111111111111111110111111111111111011010000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000 170141183460469231731687303715884105728
170141183460469231731687303715884105728/18446744073709551616 9223372036854775808

9223372036854775808 170141183460469231731687303715884105728/18446744073709551616

128!/127!/1!  128
128!/126!/2!  8128
128!/125!/3!  341376
128!/124!/4!  10668000
128!/123!/5!  264566400
128!/122!/6!  5423611200
128!/121!/7!  94525795200
128!/120!/8!  1429702652400
128!/119!/9!  19062702032000
128!/118!/10! 226846154180800
128!/117!/11! 2433440563030400
128!/116!/12! 23726045489546400
128!/115!/13! 211709328983644800
128!/114!/14! 1739040916651368000



below are scripts to demonstrate using the example of 20 puzzles and to search for 64 and others
12  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: February 22, 2022, 06:25:31 PM
faster "bit" there is a library from "ice" https://github.com/iceland2k14/secp256k1 there it is necessary to throw its libraries into the folder with the script.

***

and read (with a translator) https://istina.msu.ru/profile/FilatovOV/ , https://vk.com/@fil_post-eta-statya-rvet-vse-predstavleniya-o-veroyatnostyah , https://disk.yandex.ru/i/LsEWmhs3ArM7Tw

Quote
This article breaks all ideas about probabilities.

Everyone knows that it is impossible to guess the sides of a coin, but this article will show a mechanism that allows you to predict the sides of a coin, that is, you can actually guess. First, I will briefly describe the traditional way of working with probabilities, working in this way does not allow you to predict the sides of the coin. And then, in the same terse way, I will describe the way I discovered to work with probability, which allows you to predict the loss of the sides of the coin.

And so, the coin was tossed many times N and the result of its loss formed a sequence of ones and zeros. Let's determine the average length of a drop-down series of repeating identical events, for example: "00000.." or "11111.." in our large series of N flips.

It is described here: how to look at a random sequence so that the probabilities of guessing and not guessing are equal.

The traditional way to determine the average length of outliers from repeating identical events is to sequentially look through all the recorded values ​​and accurately count the number of runs of detected lengths.

The total number of series of unit lengths: "0" and "1" will be N/4. The total number of series of length two: "00" and "11" will be N/8. The total number of series of length three: "000" and "111" will be N/16. The total number of series of length four: "0000" and "1111" will be N/32. Etc. Of course, the detected numbers of series are unlikely to be exactly equal to the calculated values, since, despite the frequency stability, there are still random probabilistic fluctuations in the actual number of events around the theoretically obtained mats.expectations. Taking into account all elementary events N of our sequence, we find that the total number of all our series ("0" + "1" + "00" + "11" + "000" + "111" + ...) is equal to N / 2 (again up to random fluctuations). Now let's solve the problem: to determine the average length of the drop-down series, for this we need to divide the number of members of the sequence N by the sum of all series N / 2. Divide N / (N/2) = 2. That is, we found that the average length of a series with the traditional way of looking at and guessing the sides of a coin is two. That is, with an average length of a consecutive series of two events, it is impossible to guess the fallout of the sides. Obviously, if the average length of a consecutive series ("0"; "1"; "00"; "11"; "000"; "111"; ...) were three events, then we would begin to guess the fallout of the sides of the coin much more often than not guessing. Let's now look at my way of getting the average event length, which is three.

It describes how to look at a random sequence so that the probabilities of guessing and not guessing become different.

In order to influence the probability, it is necessary to change the average length of a series of events falling out in a row. This is achieved by applying a well-known geometric probability to the guessing process.
The principle of geometric probability states that objects with a larger size are hit more often than objects with a smaller size. With regard to our random sequence N, this means that if we count, for example, every hundredth member of the sequence and determine the length of the series ("0"; "1"; "00"; "11"; "000"; "111"; ... ) to which it belongs, it turns out that the frequency of hits of every hundredth event in long series increased, and decreased in short series.

That is, the average length of the detected series, in the case of a geometric set of statistics, will become equal to three. And it is precisely this increase in the average length of a series from two events (with sequential counting of each event) to three events (with gaps of sufficient length between guesses) that makes it possible to guess the side of the dropped coin more often than in half of the predictions. Here, now, I have described the fundamental principle of geometric probability, in relation to changing the average length of the found series in a random binary sequence.


he has studies of random events, sequences, there are formulas, I still don’t understand everything, he launches a probe there into a file with 20000000 random bits and...

pz64 ripmd160 hex to bin 1111101110010000010011001111011001100100011111010100101111110111110110101000100 1011100100110000011010011100000011101000101101011000111010000100100100010100100

11111 0 111 00 1 00000 1 00 11 00 1111 0 11 00 11 00 1 000 11111 0 1 0 1 00 1 0 111111 0 11111 0 11 0 1 0 1 000 1 00 1 0 111 00 1 00 11 00000 11 0 1 00 111 000000 111 0 1 000 1 0 11 0 1 0 11 000 111 0 1 0000 1 00 1 00 1 000 1 0 1 00 1 00

1       22
11      8
111     5
1111    1
11111   3
111111  1
1111111
11111111

0       17
00      14
000     5
0000    1
00000   2
000000  1
0000000
00000000

0, 1 - elementary events, they make waves 111 000 1111 0000... when nearby the same half-wavelength 111000 11110000...  

Quote
In order to influence the probability, it is necessary to change the average length of a series of events falling out in a row. This is achieved by applying a well-known geometric probability to the guessing process.
The principle of geometric probability states that objects with a larger size are hit more often than objects with a smaller size. With regard to our random sequence N, this means that if we count, for example, every hundredth member of the sequence and determine the length of the series ("0"; "1"; "00"; "11"; "000"; "111"; ... ) to which it belongs, it turns out that the frequency of hits of every hundredth event in long series increased, and decreased in short series.
what does this mean? we can run over the 2^256 range and generate these bit sets over several hashes...
13  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: January 29, 2022, 01:17:06 AM
Quote
Hi there Andzhig, you have a complete package of these things you are programming to start searching somehow.
thanks man,
not yet, there is too much to think about  Grin

***

It can be stuck in this shit for the rest of your life.

All this madness is described by the formula Ralph Hartley (I = K log2(N)) or easier log2(x)=

this means that for puzzle 20, 2^20 looks like that  log2(2^20) = 20  

in other words in 2^20 = 1048576 will fall out with equal probability 20 bit information from 00000000000000000000 to 11111111111111111111

can take a long string 1048576 random bit or 1048576 segments of 20 bits if you take a long string, it seems to fall out more often, since information is not lost when trimmed

although it is possible 1048576/20 = 52428,8 or pz64 9223372036854775808/64 144115188075855872 segments of 64 bits...

you can play with these

Quote
import random

list2 = ["1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum"] # pz 20 > dec 863317 bit 11010010110001010101

count0 = 0

pzbit = "11010010110001010101"

for X in range(100): # log2(x)=20 2^20 = 1048576, 1048576/20 = 52428,8
        
    count0 += 1

    random.seed()

    Nn = "0","1"

    RRR = [] #func()

    for RR in range(52428): # "bit" set log2(x)=20 2^20 = 1048576, 1048576/20 = 52428,8
        DDD = random.choice(Nn)
        RRR.append(DDD)

    d = ''.join(RRR)
    #print(d,count0)

    if pzbit in d:
        print("step",count0,d)
        break
    
print("pz end")
input() #"pause"

there is a so-called division method, but no one will tell us the desired number in which part after division, but simply iterating and 64 bit steps come out

Quote
How many questions do you need to ask to find the intended number from 1 to 100. Let's say the hidden number is 27. Dialogue option:

Over 50? No.
Over 25? Yes.
Over 38? No.
Less than 32? Yes.
Under 29? Yes.
Under 27? No.
Is it number 28? No.

If the number is not 28 and not less than 27, then it is clearly 27. To guess the number from 1 to 100 using the “halving” method, we needed 7 questions.

The amount of information embedded in the answer "yes" / "no", if these answers are equally likely, is equal to one bit (indeed, because a bit has two states: 1 or 0). So, to guess a number from 1 to 100, we needed seven bits (seven yes/no answers).

and collisions turn out to be like "frozen" probabilities

1048576 steps endless seed dropped in one place + 1048576 seed steps dropped out elsewhere and so on until all the places are moved and the newly mixed ones fall out the same as searching in a "long string 1048576 random bit" , if you imagine that 1048576 step collision steps gives 1 needed 20 bits, 1048576×1048576 = 1099511627776 and 1099511627776/1048576 = 1048576 collision. it means there will be such lines where the required 20 bits will be at 1 step somewhere at 2, 3, etc. but they are all mixed. (now someone smart should come and explain everything). so we have this 1099511627776 where half of "from 1 to 1048576/2=524288" 20 bit will be on the first step on the second on the third and so on from 1048576 (the other half is closer to the other end 524288-1048576), if we step through 1 step then we lose - 1 for each (is it necessary or is it 1099511627776 divided by 2 or 1048576/2, 524288, 524288×524288 = 274877906944) after 3 steps... in general, we need to shorten the general steps and at the same time get the side that will be closer either to the beginning or to the end of the 1048576 frozen "collisions of probability sets" to make the probability work faster  Roll Eyes

 if you understand how it works, you can crack any passwords and no hash functions will help even if you check them a million (maybe Cheesy)

someone finds connections with Blaise Pascal triangle, maybe Frank Ramsey ideas... and other alien language.

collisions by themselves do not increase the likelihood

40116600 28!/14!/14!  
1048576 2^20 (40116600 ~ 2^25)/(2^20) = 32
38,25817108154296875 collision

1/2^20  0,00000095367431640625
1-((1-0,00000095367431640625)^1000000) = 0,61467755323380387101550329885023410368873814360323

38/2^25,257696002689131014443589368702137499212705986576
1-((1-0,00000094723879890120299327460452780145874775030785260932)^1000000)  = 0,612189805130850082275327609457471664463427528904805418181047671964854503332114

unless of course you increase the chance of the desired segment appearing in the right place because 38/2^25 without rounding increase the chance (actually not) we are back to the beginning of the post...

***
and a little as the guru of observations himself wrote https://bitcointalk.org/index.php?topic=571.msg5754#msg5754 "analytical attack"

from the hash 3ee4133d991f52fdf6a25c9834e0745ac74248a4 can get dec 359043673790534646037006540730459475416853924004 bin 1111101110010000010011001111011001100100011111010100101111110111110110101000100 1011100100110000011010011100000011101000101101011000111010000100100100010100100

bin 158 len, 0 > 80, 1 > 78 158!/80!/78! = 22866556412845927056888423836329770613886986170 all perm, pz perm index 22537107205443855325270509529770241715849156734

if not filtered by length and number of bits everything happens according to formula Ralph Hartley log2(x)=

9223372036855015810 1000000000000000000000000000000000000000000000111010100110000010 9  240003   1111101110010000010011000111010111000111111100011011011001110110001101001010110 1001001101110000001111010101010001001110000110101101101111110011101111101000111 0 7180873256989556446556621835558134870175050461                  
9223372036856173927 1000000000000000000000000000000000000000000101010101010101100111 13 1398120  1111101110010000010011000011100101010001011111001101111110111110000100101000000 0100110110110101001010111111100001100001110110001100100100001111100011000011111 0 718087315411756854546296510280667756869467475006
9223372036856212177 1000000000000000000000000000000000000000000101011110101011010001 13 1436370  1111101110010000010000111101101001111001110100100000011101111001011010100110010 0111111111011100101001011111110100101001010100101010001000101011111011010000011 359043475413003167110670037757778762634123146883
9223372036856890237 1000000000000000000000000000000000000000001000000100001101111101 11 2114430  1111101110010000010001010101001101011110100011110110110100000111000011011111001 01100000100001000000001111010101110000100010110101000011101101110010010101000 89760876868889376100370289127772432756922311848
9223372036857266442 1000000000000000000000000000000000000000001001100000000100001010 7  2490635  1111101110010000010010100111011000111010111111110111011001010000001000111101010 01011100001101110111000100000100110100000110011001111010011100001011011011110 89760904832892002273251104243477641619552736990
9223372036857335565 1000000000000000000000000000000000000000001001110000111100001101 12 2559758  1111101110010000010011011000001100000110011010111001000000010111110001100101011 0001011000111010100011011101100000100110101110010011000100000001011010111010101 1 718087371508456404393008177736344416239946394539
9223372036857594444 1000000000000000000000000000000000000000001010110000001001001100 9  2818637  1111101110010000010001001111100010111010010111111001010100110100011011001001110 0001101011000000011011110000001111001010101001111010111001110000111101010101011 11 1436173999058575188054474948077251433121726982831
9223372036857826935 1000000000000000000000000000000000000000001011101000111001110111 15 3051128  1111101110010000010011110101010110100010000110000101001001000110110111100100001 1000110001000101111100101111111011010110010011011111100001001100111100110010010 1 718087450897711573434130801635077538092006830885
9223372036858012530 1000000000000000000000000000000000000000001100010110001101110010 12 3236723  1111101110010000010001001110111101101110001101111111000110101001101011100011110 0011011011000100111110101000010001100111010100101001110001110101100011010011011 1 718086997947403370741861272986691544035227962679
9223372036859320480 1000000000000000000000000000000000000000010001010101100010100000 9  4544673  1111101110010000010000001111101001000101110111111111110010100110100001110110010 0110010000011000110101001110111101001010011001111111100110011111111111001001110 0 718086825567571615737455690104698414644087225500
9223372036860047270 1000000000000000000000000000000000000000010100000110111110100110 13 5271463  1111101110010000010001110000001110000000101111010001100010001101000100110010010 0010000001001111000001011011110110000101010100110101111011011011010001101100111 01 1436174176949643411576885315413363742972568833437
9223372036860070794 1000000000000000000000000000000000000000010100001100101110001010 11 5294987  1111101110010000010011100110010101000011001010001010010000010111011110101001100 1000011011100110100101010000011010111010101001001100110100110000011100000000000 359043705000365790599054799634814692545330165760
9223372036860902238 1000000000000000000000000000000000000000010111010111101101011110 17 6126431  1111101110010000010001110101101011001010111111111101110110000001100101101000000 1001110110111100011110010011010101010010011110100001000000010111001010111111010 1 718087103326459445851943810622436577706585304053
9223372036861245274 1000000000000000000000000000000000000000011000101011011101011010 14 6469467  1111101110010000010010001101110100111111010101111100011111011010010100010000110 1111010000101101111010101111001011101000100010001001010011011011101000011011 44880448067392482926173035093376359281690786331
9223372036861628193 1000000000000000000000000000000000000000011010001000111100100001 11 6852386  1111101110010000010011110011110100111110011011110000110101111100111101001010100 001000011001011100011110101110001111100010111001100001011101011110000111100101 179521861687021734476616064965674768707389612517
9223372036861892836 1000000000000000000000000000000000000000011011001001100011100100 12 7117029  1111101110010000010001100011011100110100101110111001101001100110101000011100000 011101100100110100100010110101011111011000011001111011000111011010001111100000 179521763428876435137444313193721929344487367648
9223372036861947467 1000000000000000000000000000000000000000011011010110111001001011 15 7171660  1111101110010000010000011001100111110100111110010000010011110100010110101110110 1000101001000101111111010100011011001110100010110111000010111101011011000111000 0 718086852736392223506631086848100616858893118576
9223372036862265987 1000000000000000000000000000000000000000011100100100101010000011 11 7490180  1111101110010000010001001011110100111000110111011111001111110110110110010100101 011111110110111101101001100111100010100000000001101100100110000111101000110011 179521747351221506452705485581043535576301074995
9223372036862331902 1000000000000000000000000000000000000000011100110100101111111110 17 7556095  1111101110010000010011001101001001100101011000100010100001011000111110111011010 1101100000111101110101111000000011000110011111110010011101011001110001001000101 01 1436174682913161688503498477533112283699141118229
9223372036862506554 1000000000000000000000000000000000000000011101011111011000111010 16 7730747  1111101110010000010001000110100101001111110010010100101111011100111100011111011 1000010000101011000110000000011010111110101011101001010010011010000000100011000 01 1436173950256518218731585303577429277482264298593
9223372036862531880 1000000000000000000000000000000000000000011101100101100100101000 12 7756073  1111101110010000010000100000111010111100110110001100011110010010111111011111010 0110100111001010010011100001010110100100001100110001010101011010010010010010010 01 1436173745211217210558743667607337568893540799049
9223372036862744754 1000000000000000000000000000000000000000011110011001100010110010 13 7968947  1111101110010000010011000101100001110010011111011110110111001010011001011100100 00010011111111100101000111000100111000101111111001111111110100111010111101111 89760915088508567795605768827019024851757856239
9223372036863733714 1000000000000000000000000000000000000000100010001010111111010010 13 8957907  1111101110010000010011001000011010101001001001011100010010010111111101000100111 1101111111011001110001011000000001010001001011000101010111010010000111100101001 1 718087328570887872581080841805785257502617771603
9223372036863737516 1000000000000000000000000000000000000000100010001011111010101100 13 8961709  1111101110010000010010001111011000101111000001000101100011100100110001110000101 0001001000011110110111000110110110101000011111000000110111111011001011101110001 359043586660479441892627990740535085044334434161
9223372036865317982 1000000000000000000000000000000000000000101000001101110001011110 13 10542175 1111101110010000010010011000100001111011101100110100111110100111101100101010000 1110111110000100001111101000110111010000001001100110001011110111111011001100101 0 718087198212536565138252364124209929591732038858


at steps  (log2(x)=20 2^20 = 1048576) finds the first 20 bits of the hash, although he is here generously on 10542175 25 by 20 bits poured (should be 10542175 /1048576 = ~10, "frozen probability" ).  

when filtering, everything is transformed somewhere

9223372036885616568  1000000000000000000000000000000000000001110101101001011110111000 16 22537103149060538292017163274311134567780254106 30840761  1111101110010000010010100010110000100011000101110111000110110111110101011000001 1001001110101101111111010111110000000110101001101011110001000011000010011000010 359043613028399983562945167723792076799337399490
9223372037029689218  1000000000000000000000000000000000001010011011001111011110000010 16 22537101874911141106658805675039550989222719457 174913411 1111101110010000010010010100111001011110010010011100100110001010111000100010001 0000011011010001101111011001111100000100101001101011101001111101110110000000111 359043594162400081422090571493616731684910066695
9223372037031770991  1000000000000000000000000000000000001010100011001011101101101111 18 22537107574203928862325124755510621787207775646 176995184 1111101110010000010011010011011010110000001010010101100100001100011011100010011 0001000001101000111001001110101111111011101101011100100111010100001110001010011 359043679260198876783299078950464798741917998163
9223372037058474564  1000000000000000000000000000000000001100001001000011001001000100 10 22537103592731005799528051981089682732148344971 203698757 1111101110010000010010100111011111000001000111111000111010001010110011010110011 0000010101011000011110001001101110101011100000100110101010101100111001110000001 359043619461209399913287633908985905780119466881


only 4 per 200 million steps (but could be 203698757/1048576 = ~194)

are the permutation indices

22537107205443855325270509529770241715849156734 pz64
22537103149060538292017163274311134567780254106
22537101874911141106658805675039550989222719457
22537107574203928862325124755510621787207775646
22537103592731005799528051981089682732148344971

does it make sense to do something with this in search of "analytical attack"

divide up to 5 signed and collect statistics or something else

16169,5814232638689562143432562009521116008707624031369835027035608950872669432 pz
16153,5533775264321952269735570804750668963341349990553644343264675297401430888
16181,4699735846556996755461776490184756227607973040633725147294856365627617568
16185,1503837668620918566318996649467160755508899938504822869445787677713040070
16179,6817735469296456613873633125445961914982781727372100885964864332408993487
16153,6970565574610790826901021689464637807015377239042354189722685675176350481
16190,6635088900851730204004885232081983178955608845804638586660470304890338518
16157,8797916296129003863290552042679182640000395504078556841408290366099696895
16175,7751788632852421380331566366568529725406711580288457971208637282374131337
16167,2147331482160603431952405779044274472086659418012334815885384046033101030
16140,0690439666614661705398239915453571632329370682713054379439195260580545749
16158,4759908930506778003347436100751039440563712880665211532911595075679978952
16157,8061286871790467784305109191598032784456191195778051755983314706401974056
16151,4172150387504450853711611863511146513260901870546579554804901185534937987
16182,0031786348789876742354647759795337633119335192744071229767381262997539896
16155,7050285239593882946006590997299172487673304627256330600015171172885379131

in any case, it is difficult to select a step to find the right one...

if there are crazy ones who crank the minced meat back through the meat grinder (sha256,ripmd160). or calculate the most frequent bit positions in bin 2^64

this means calculating for each set bit 2^64 their most frequent positions (normal idea for a collision attack  Wink)

     1 count, 0 count
64!/32!/32!    1832624140942590534
64!/31!/32!    1777090076065542336
64!/53!/11!    743595781824

and the most average that can work to get

3ee4133d991f52fdf6a25c9834e0745ac74248a4
359043673790534646037006540730459475416853924004
1111101110010000010011001111011001100100011111010100101111110111110110101000100 1011100100110000011010011100000011101000101101011000111010000100100100010100100

which will also need to be calculated in order to understand how much they can take on themselves from those combinations... One Flew Over the Cuckoo's Nest...
14  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: December 10, 2021, 04:35:13 AM
there should be a lot in the folder

dc.py
fb.py
gb.py
hb.py
...
run.cmd

***

algorithm from here Answer #4: https://www.py4u.net/discuss/207582 because this one is slower https://combi.readthedocs.io/en/stable/intro.html

can also think about secondary sampling from the same seed

sample from 100 or 1000 can be done from a larger seed (like the idea of ​​a search itself) but you need an interesting method of screening out for example something like Newton's method (tangents)

***

and what is the ratio of large and small samples with the same number of possible collisions

for example, give 1000 samples of 60 (first samples, from 100 len by 60 len) for 5000 collisions = 25 different scripts (Aa,Bb,Cc,Dd,Ff...)

find count 986 5000 1000/60

i.e. under such conditions received 986 almost ~ 1000 i.e. almost every line of length 60 will have a chance to catch the desired particles again

what is the probability that choosing 1000 (len 30) for each of them (1000(60)*1000(30)) we will get the required number of chances...

if the odds and ratios persist 100*100 or 1000*1000, then there is no point in generating large files...

***

n general, it turns out like this, with 100000 collisions = 500 programs per 10000 (100(60)*100(30)), about 100 matches

collisions  set 100000 by 30 (0-10000 (100(60)*100(30)))

732   8952
1013  4718
4263  8990
5201  7208
5317  9447
5972  4138
6382  7743
8228  8802
8228  54  
8658  6593
11821 8061
11967 3368
18635 4430
20217 6170
20350 515  
20350 66  
20967 8981
20967 6    
21288 7486
21394 4745
24937 2703
26697 1169
26697 927  
26996 969  
27148 6372
27825 5242
27825 7    
27825 38  
31470 1855
32004 131  
33528 992  
40377 673  
44316 9828
44316 37  
45054 1781
45888 4105
46886 1113
48734 2496
49315 2783
49996 6705
51139 2123
53067 8820
53290 707  
54892 4615
55618 7325
57674 7129
65621 5935
66616 6513
67003 5289
67396 9643
67838 464  
68546 9056
68595 5199
71135 284  
71811 2444
77119 7743
78545 2782
80004 8813
80747 9743
81952 3990
82426 7174
86652 8665
86830 2063
86830 7    
87984 3067
88071 3674
88320 3625
89330 4132
89627 1327
92831 1589
93421 2548
93988 4662
94081 3599
96114 7171
96821 701  
98326 1249
98516 3997
99428 519  

some in the first 10, there are 6 7, slightly up to 100, 37 38 54...

in other words, with 500000 or 1000000 collisions = 3000-5000 prog-scripts there should be about 1000 good sets for the sample... 1000 from 10000

but can also reduce the primary samples 10*10 = 100 and hammer in steps, but you have to hammer every step at least 500 times with all 3000-5000 programs...

it is necessary to knock out the necessary 11-15 out of 30 and rearrange from 20000000 to 50000000 permutations.

we are looking for an unknown number or unknown collisions, just instead of 1 number, we have 200-300 for 1 program

below is the 500000 collision test script and sampling 10*10 = 100

Quote
import random
import time

Nn =['00', '01', '02', '03', '04', '05', '06', '07', '08', '09',
     '10', '11', '12', '13', '14', '15', '16', '17', '18', '19',
     '20', '21', '22', '23', '24', '25', '26', '27', '28', '29',
     '30', '31', '32', '33', '34', '35', '36', '37', '38', '39',
     '40', '41', '42', '43', '44', '45', '46', '47', '48', '49',
     '50', '51', '52', '53', '54', '55', '56', '57', '58', '59',
     '60', '61', '62', '63', '64', '65', '66', '67', '68', '69',
     '70', '71', '72', '73', '74', '75', '76', '77', '78', '79',
     '80', '81', '82', '83', '84', '85', '86', '87', '88', '89',
     '90', '91', '92', '93', '94', '95', '96', '97', '98', '99']

RRR3 = []

for X in range(500000): # hypothetical collisions, 1 prog 200-300 collisions
    random.seed()
    i = 1
    while i <= 1:
            
        RRR2 = []
                    
        for RR in range(11):        
            DDD = random.choice(Nn)
            RRR2.append(DDD)    

        i=i+1
        RRR3.append(RRR2)
        RRR2=[]

print(RRR3,len(RRR3))

RRR4 = []

for XX in range(10): # sample 60
    random.seed()
    i = 1
    while i <= 1:
            
        RRR7 = []
                    
        for RR2 in range(60):        
            DDD1 = random.choice(Nn)
            RRR7.append(DDD1)    

        i=i+1
        RRR4.append(RRR7)
        RRR7=[]

print(RRR4,len(RRR4))

print("")
print("from 60 start")
print("")

count3 = 0
count4 = 0

for elem in RRR3:
    count3 += 1
    count = 0
    count2 = 0

    #print(count3,"elem count","from 60")

    for elem2 in RRR4:

        i = 1
        while i <= 1:
            
            RRR = elem2
            
            count += 1
            
            i=i+1
            
            Nn1 = elem #['30', '56', '83', '77', '31', '20', '64', '20', '30', '28', '49']

            fff1 = len(Nn1)
            
            for ee in Nn1:
                if ee in RRR:
                    count2 += 1

            if count2 == fff1:
                print("")
                count4 += 1
                print(count3,count,"hurra...",Nn1,RRR)
                
                print("")
                count=0
                
                break
            
            RRR = []
            count2=0

print("")
print("find count",count4)

print("")
print("from 30 start")
print("")

RRR44 = []

for elem1 in RRR4:

    i = 1
    while i <= 10:    

        RRR6 = []

        for RR3 in range(30):                 # sample 30      
            DDD3 = random.choice(elem1)
            RRR6.append(DDD3)

        i=i+1        
        RRR44.append(RRR6)
        RRR6=[]

print(RRR44,len(RRR44))

count3 = 0
count4 = 0

for elem in RRR3:
    count3 += 1
    count = 0
    count2 = 0

    #print(count3,"elem count","from 30")

    for elem2 in RRR44:

        i = 1
        while i <= 1:
            
            RRR = elem2
            
            count += 1
            
            i=i+1
            
            Nn1 = elem #['30', '56', '83', '77', '31', '20', '64', '20', '30', '28', '49']

            fff1 = len(Nn1)
            
            for ee in Nn1:
                if ee in RRR:
                    count2 += 1

            if count2 == fff1:
                print("")
                count4 += 1
                print(count3,count,"hurra...",Nn1,RRR)
                
                print("")
                count=0
                
                break
            
            RRR = []
            count2=0        

print("")
print("find count",count4)
print("All end...")


approximate sample from 30 to 15 here for 1 set of 30 in which it has already dropped we will have several options thanks to collisions

Quote
import random
import time

Nnn1 = ['80', '47', '86', '31', '65', '83', '30', '77', '32', '28', '56', '66', '00', '66', '17', '00', '62', '88', '62', '75', '28', '64', '88', '56', '75', '28', '20', '57', '64', '57']

RRR = []

count = 0

ii = 1
while ii <= 1000:
    
    i = 1
    while i <= 1:
        RRR = []
        count += 1
        
        for RR in range(15): # sample
            DDD = random.choice(Nnn1)
            RRR.append(DDD)    

        i=i+1
        

        Nn1 =['30']
        Nn2 =['56']
        Nn3 =['83']
        Nn4 =['77']
        Nn5 =['31']
        Nn6 =['20']
        Nn7 =['64']
        Nn8 =['20']
        Nn9 =['30']
        Nn10 =['28']
        
        for elem1 in Nn1:
            if elem1 in RRR:
                
                for elem2 in Nn2:
                    if elem2 in RRR:
                        
                        for elem3 in Nn3:
                            if elem3 in RRR:
                        
                                for elem4 in Nn4:
                                    if elem4 in RRR:
                        
                                        for elem5 in Nn5:
                                            if elem5 in RRR:
                        
                                                for elem6 in Nn6:
                                                    if elem6 in RRR:
                        
                                                        for elem7 in Nn7:
                                                            if elem7 in RRR:
                        
                                                                for elem8 in Nn8:
                                                                    if elem8 in RRR:
                        
                                                                        for elem9 in Nn9:
                                                                            if elem9 in RRR:
                        
                                                                                for elem10 in Nn10:
                                                                                    if elem10 in RRR:

                                                                                        print(count,"huuuuuuuuuurraaaaaaaaaa...",RRR,"   ",Nn1,Nn2,Nn3,Nn4,Nn5,Nn6,Nn7,Nn8,Nn9,Nn10)
                                                                                        count=0
                                                                                        break
        #print(RRR)                                            
        RRR = []
    
    #print(RRR)
    ii=ii+1

the idea is simple if your processor is strong and can run several thousand scripts at the same time

then it is necessary for each of 100 to 30 samples to hammer several times from 100 to 500 times for each of 100

if all 3000-5000 programs run through 50000000 shuffles in a few minutes, hours, then you can run everything in the available time (besides, other puzzles can pop up, we check everything from 64 to 160 at once).

so you can probably catch something in weeks (?)
15  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: December 10, 2021, 03:35:55 AM
then the last option is to look for luck. who have 64-core processors.

different 2 symbols for seed give different results

pz 20 example...

step 1100006 seed 000000111011001011000011111101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 1532829 seed 000001001101100011010111111001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 1129134 seed AAAAAAaaaAaaaaAAaaAaaAaAAaaaAA bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...

step 494992 seed BBBBBBbBBBBbBbbbBbbbbbBbBbbBbb bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 548744 seed BBBBBBbBBbBbbbBBbbBBbbbbbbBBbb bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 896722 seed BBBBBBbbBbBBbBbbBbbbBbbBbbBBbb bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 1325957 seed SSSSSsSSSSsSssssSsSSsssssSsssS bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 5492813 seed RRRRrrRRrRrRRrrRrrrRRRrRRrrrrr bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 6988942 seed RRRRrrrRrrrrRRrrrRRrrRRRrRRRrr bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 7290958 seed RRRRrrrrRrrRRRrrrRRRrrRrrRRrrR bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 7721483 seed RRRRrrrrrrrrrRrrRrrRRrRRRRrRRR bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 8730248 seed RRRrRRrRRrrrrRrRrrrRrRrRrRRRrr bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 1811954 seed OOOOOoOoOooooOoOOOooooooooOOOO bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 1873426 seed VVVVVvVvvVVvvvVvvVvVvVVvVvvvvV bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 430546 seed WWWWWWWwwwwWwWwWWwwWwWwwWWwwww bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 3821040 seed XXXXxXXxxXXxXxxxXxxxXXxxxXXxXx bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 2652540 seed JJJJJjjjJJJjJjjjjjJjjjJJJJjjjJ bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 2777464 seed JJJJJjjjJjJJjjjjJjJJjjjjJJJJjj bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 765336 seed FFFFFFfFfffFfffffFffFFFFffFffF bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 2367636 seed FFFFFffFfFFfffFFFffFffffffFfFF bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...

it turns out for different 2 seed symbols we have 200-300 collisions

22 sym len
6892620648693261354600   76!/38!/38!
1000000000000000000000 =
5892620648693261354600 / 2^64 319,4396054473088187643 collision

that is, there are already 1000-1500 collisions on 5 different 2-sign seeds

200 Aa
200 Bb
200 Cc
200 Dd
200 Ff

5 1000 collisions

10 2000 collisions

15 3000 collisions

20 4000 collisions

25 5000 collisions

30 6000 collisions

35 7000 collisions

40 8000 collisions

45 9000 collisions

50 10000 collisions

100 20000 collisions

500 100000 collisions

now we test the sample, we do not know the required number of 1 puzzle or 200-300 num collisions, pz 20 num len (10 by 2), cillision 22 num len (11 by 2)

if we create random samples (from 100 to 2 numbers) for example 1000 samples of 60 pairs out of 100

Quote
import random
import time

Nn =['00', '01', '02', '03', '04', '05', '06', '07', '08', '09',
     '10', '11', '12', '13', '14', '15', '16', '17', '18', '19',
     '20', '21', '22', '23', '24', '25', '26', '27', '28', '29',
     '30', '31', '32', '33', '34', '35', '36', '37', '38', '39',
     '40', '41', '42', '43', '44', '45', '46', '47', '48', '49',
     '50', '51', '52', '53', '54', '55', '56', '57', '58', '59',
     '60', '61', '62', '63', '64', '65', '66', '67', '68', '69',
     '70', '71', '72', '73', '74', '75', '76', '77', '78', '79',
     '80', '81', '82', '83', '84', '85', '86', '87', '88', '89',
     '90', '91', '92', '93', '94', '95', '96', '97', '98', '99']

RRR = []
RRR3 = []

for X in range(200): # 2 seed symbols we have 200-300 collisions, 1000 5000 10000...
    random.seed()
    i = 1
    while i <= 1:
            
        RRR2 = []
                    
        for RR in range(11):        
            DDD = random.choice(Nn)
            RRR2.append(DDD)    

        i=i+1
        RRR3.append(RRR2)
        RRR2=[]

print(RRR3,len(RRR3))


#count = 0
#count2 = 0
count3 = 0
count4 = 0

for elem in RRR3:
    count3 += 1
    count = 0
    count2 = 0
    print(count3,"elem count")

    ii = 1
    while ii <= 1000: # 1000 by 60 from 100
        
        random.seed(ii)
        
        i = 1
        while i <= 1:
            
            RRR = []
            
            count += 1
            
            for RR in range(60): # 50:50
                DDD = random.choice(Nn)
                RRR.append(DDD)    

            i=i+1
            
            Nn1 =elem #['30', '56', '83', '77', '31', '20', '64', '20', '30', '28', '49']

            fff1 = len(Nn1)
            
            for ee in Nn1:
                if ee in RRR:
                    count2 += 1

            if count2 == fff1:
                print("")
                count4 += 1
                print(count3,count,"huuuuuuuuuurraaaaaaaaaa...",Nn1,RRR)
                
                print("")
                count=0
                
                break
            
                                              
            RRR = []
            count2=0

        ii=ii+1
print("")
print("find count",count4)

further and this 1000 to 60, we again choose 1000 for each one already for 30

out of 30 it is much easier to choose 11 or 15 successfully

but as collisions increase (and this is 200-300 = 1 working program)

we can reduce the sample to 100

and here we have a ratio 1000*1000/11 or 15  100*100/11 or 15

for example, for the first sample, 100 by 60 for 10000 collision, find count 228 10000 100/60

100 by 60 for 100000 collision find count 2143 100000 100/60

2143 this means that such a number out of has a chance of being sampled at 30, 100(60)*100(30)...

it seems that the chances are good so that in 100(60)*100(30) = 10000 to 30 there are many opportunities to catch the desired set

we will have 10000 rows with a sample of 30 for a sample of 11 or 15 for 100000 collisions

how many collisions can be obtained from these signs !"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~

4371 individual programs i.e. 4371*200 = 874200 collisions

100(60)*100(30) = 10000 / 4371*200 = 874200 collisions

if the 64 core processor does not die to run them all, it may only take about ~50 million step concurrent programs to run

11! 39916800
15! 1307674368000
17! 355687428096000
20! 2432902008176640000

I have encountered 2 problems so far, 1 is a random row selection string from file, although you can run step by step and 2 the algorithm is recursive for seed permutations.

but you can even try to run

1) write a sample of 30 to a file

Quote
import random
import time


for MMM in range(1):

    Nn =['00', '01', '02', '03', '04', '05', '06', '07', '08', '09',
         '10', '11', '12', '13', '14', '15', '16', '17', '18', '19',
         '20', '21', '22', '23', '24', '25', '26', '27', '28', '29',
         '30', '31', '32', '33', '34', '35', '36', '37', '38', '39',
         '40', '41', '42', '43', '44', '45', '46', '47', '48', '49',
         '50', '51', '52', '53', '54', '55', '56', '57', '58', '59',
         '60', '61', '62', '63', '64', '65', '66', '67', '68', '69',
         '70', '71', '72', '73', '74', '75', '76', '77', '78', '79',
         '80', '81', '82', '83', '84', '85', '86', '87', '88', '89',
         '90', '91', '92', '93', '94', '95', '96', '97', '98', '99']

    RRR1 = []
    RRR2 = []
    i = 1
    while i <= 100:
        random.seed(i)
        for x1 in range(60):                     # 100 by 60 from 100
            DDD = random.choice(Nn)
            RRR1.append(DDD)

        RRR2.append(RRR1)
        RRR1=[]
        i=i+1

    #for elem in RRR2:
        #print(elem)

    RR1 = []
    RR2 = []

    for elem in RRR2:
        i2 = 1
        while i2 <= 100:
            random.seed(i2)
            for x1 in range(30):                 # 100 by 30 from 60
                DDD = random.choice(elem)
                RR1.append(DDD)

            RR2.append(RR1)
            #print(RR1)
            RR1=[]
            i2=i2+1

    #print("")

    GGG=[]

    for elem1 in RR2:
        d = ''.join(elem1)
        GGG.append(d)
        #print(d)

    with open("tresher.txt", "a") as file:
        for line in GGG:
            file.write(line + '\n')

2) permutations for seed by 2

Quote
import random
from itertools import *

def reverse_string1(s):
    return s[::-1]

def brute_force(alphabet, min_len, max_len):
    joiner = ''.join
    for cur_len in range(min_len, max_len + 1):
        yield from map(joiner, product(alphabet, repeat=cur_len))

#alphabet = '!"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~'

alphabet = "abcdefghijklmnopqrstuvwxyz"

mo = []

b = brute_force(alphabet, 2, 2)
for v in b:
    if v[0] != v[1]:
        if v not in mo:
            l = reverse_string1(v)
            mo.append(l)

print(mo,len(mo))

3) 2 templates for writing, read line by line or randomly, they need to be called blablabla.txt

line by line

Quote
from os import system
system("title "+__file__)
import random
from bit import Key
#from bit.format import bytes_to_wif
#from PyRandLib import *
#rand = FastRand63()
#random.seed(rand())
import gmpy2
import time

def sym1():
    a1 = "0"

    return a1

def sym2():
    a2 = "1"

    return a2

def find_permutation(lst,K,numberbit1,numberbit0):
    l = lst
    N = numberbit0
    M = numberbit1

    if N == len(l):
        return sym2() * N
    
    if M == len(l):
        return sym2() * M

    result = ''    
    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)
        if (K < K0):
            result += sym1()
            l.remove (sym1())
        else:
            result += sym2()
            l.remove (sym2())
            M -=1
            K = K - K0
    result += l[0]

    return result

a1=sym1()*38
a2=sym2()*38

import time

list2 = ["16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN","13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so","1BY8GQbnueYofwSuFAT3USAhGjPrkxDdW9",
        "1MVDYgVaSN6iKKEsbzRUAYFrYJadLYZvvZ","19vkiEajfhuZ8bs8Zu2jgmC6oqZbWqhxhG","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF",
        "1PWo3JeB9jrGwfHDNpdGK54CRas7fsVzXU","1JTK7s9YVYywfm5XUH7RNhHJH1LshCaRFR","12VVRNPi4SJqUTsp6FmqDqY5sGosDtysn4",
        "1FWGcVDK3JGzCC3WtkYetULPszMaK2Jksv","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF","1Bxk4CQdqL9p22JEtDfdXMsng1XacifUtE",
        "15qF6X51huDjqTmF9BJgxXdt1xcj46Jmhb","1ARk8HWJMn8js8tQmGUJeQHjSE7KRkn2t8","15qsCm78whspNQFydGJQk5rexzxTQopnHZ",
        "13zYrYhhJxp6Ui1VV7pqa5WDhNWM45ARAC","14MdEb4eFcT3MVG5sPFG4jGLuHJSnt1Dk2","1CMq3SvFcVEcpLMuuH8PUcNiqsK1oicG2D",
        "1K3x5L6G57Y494fDqBfrojD28UJv4s5JcK","1PxH3K1Shdjb7gSEoTX7UPDZ6SH4qGPrvq","16AbnZjZZipwHMkYKBSfswGWKDmXHjEpSf",
        "19QciEHbGVNY4hrhfKXmcBBCrJSBZ6TaVt","1EzVHtmbN4fs4MiNk3ppEnKKhsmXYJ4s74","1AE8NzzgKE7Yhz7BWtAcAAxiFMbPo82NB5",
        "17Q7tuG2JwFFU9rXVj3uZqRtioH3mx2Jad","1K6xGMUbs6ZTXBnhw1pippqwK6wjBWtNpL","15ANYzzCp5BFHcCnVFzXqyibpzgPLWaD8b",
        "18ywPwj39nGjqBrQJSzZVq2izR12MDpDr8","1CaBVPrwUxbQYYswu32w7Mj4HR4maNoJSX","1JWnE6p6UN7ZJBN7TtcbNDoRcjFtuDWoNL",
        "1CKCVdbDJasYmhswB6HKZHEAnNaDpK7W4n","1PXv28YxmYMaB8zxrKeZBW8dt2HK7RkRPX","1AcAmB6jmtU6AiEcXkmiNE9TNVPsj9DULf",
        "1EQJvpsmhazYCcKX5Au6AZmZKRnzarMVZu","18KsfuHuzQaBTNLASyj15hy4LuqPUo1FNB","15EJFC5ZTs9nhsdvSUeBXjLAuYq3SWaxTc",
        "1HB1iKUqeffnVsvQsbpC6dNi1XKbyNuqao","1GvgAXVCbA8FBjXfWiAms4ytFeJcKsoyhL","12JzYkkN76xkwvcPT6AWKZtGX6w2LAgsJg",
        "1824ZJQ7nKJ9QFTRBqn7z7dHV5EGpzUpH3","18A7NA9FTsnJxWgkoFfPAFbQzuQxpRtCos","1NeGn21dUDDeqFQ63xb2SpgUuXuBLA4WT4",
        "1NLbHuJebVwUZ1XqDjsAyfTRUPwDQbemfv","1MnJ6hdhvK37VLmqcdEwqC3iFxyWH2PHUV","1KNRfGWw7Q9Rmwsc6NT5zsdvEb9M2Wkj5Z",
        "1PJZPzvGX19a7twf5HyD2VvNiPdHLzm9F6","1GuBBhf61rnvRe4K8zu8vdQB3kHzwFqSy7","17s2b9ksz5y7abUm92cHwG8jEPCzK3dLnT",
        "1GDSuiThEV64c166LUFC9uDcVdGjqkxKyh","1Me3ASYt5JCTAK2XaC32RMeH34PdprrfDx","1CdufMQL892A69KXgv6UNBD17ywWqYpKut",
        "1BkkGsX9ZM6iwL3zbqs7HWBV7SvosR6m8N","1PXAyUB8ZoH3WD8n5zoAthYjN15yN5CVq5","1AWCLZAjKbV1P7AHvaPNCKiB7ZWVDMxFiz",
        "1G6EFyBRU86sThN3SSt3GrHu1sA7w7nzi4","1MZ2L1gFrCtkkn6DnTT2e4PFUTHw9gNwaj","1Hz3uv3nNZzBVMXLGadCucgjiCs5W9vaGz",
        "1Fo65aKq8s8iquMt6weF1rku1moWVEd5Ua","16zRPnT8znwq42q7XeMkZUhb1bKqgRogyy","1KrU4dHE5WrW8rhWDsTRjR21r8t3dsrS3R",
        "17uDfp5r4n441xkgLFmhNoSW1KWp6xVLD","13A3JrvXmvg5w9XGvyyR4JEJqiLz8ZySY3","16RGFo6hjq9ym6Pj7N5H7L1NR1rVPJyw2v",
        "1UDHPdovvR985NrWSkdWQDEQ1xuRiTALq","15nf31J46iLuK1ZkTnqHo7WgN5cARFK3RA","1Ab4vzG6wEQBDNQM1B2bvUz4fqXXdFk2WT",
        "1Fz63c775VV9fNyj25d9Xfw3YHE6sKCxbt","1QKBaU6WAeycb3DbKbLBkX7vJiaS8r42Xo","1CD91Vm97mLQvXhrnoMChhJx4TP9MaQkJo",
        "15MnK2jXPqTMURX4xC3h4mAZxyCcaWWEDD","13N66gCzWWHEZBxhVxG18P8wyjEWF9Yoi1","1NevxKDYuDcCh1ZMMi6ftmWwGrZKC6j7Ux",
        "19GpszRNUej5yYqxXoLnbZWKew3KdVLkXg","1M7ipcdYHey2Y5RZM34MBbpugghmjaV89P","18aNhurEAJsw6BAgtANpexk5ob1aGTwSeL",
        "1FwZXt6EpRT7Fkndzv6K4b4DFoT4trbMrV","1CXvTzR6qv8wJ7eprzUKeWxyGcHwDYP1i2","1MUJSJYtGPVGkBCTqGspnxyHahpt5Te8jy",
        "13Q84TNNvgcL3HJiqQPvyBb9m4hxjS3jkV","1LuUHyrQr8PKSvbcY1v1PiuGuqFjWpDumN","18192XpzzdDi2K11QVHR7td2HcPS6Qs5vg",
        "1NgVmsCCJaKLzGyKLFJfVequnFW9ZvnMLN","1AoeP37TmHdFh8uN72fu9AqgtLrUwcv2wJ","1FTpAbQa4h8trvhQXjXnmNhqdiGBd1oraE",
        "14JHoRAdmJg3XR4RjMDh6Wed6ft6hzbQe9","19z6waranEf8CcP8FqNgdwUe1QRxvUNKBG","14u4nA5sugaswb6SZgn5av2vuChdMnD9E5",
        "174SNxfqpdMGYy5YQcfLbSTK3MRNZEePoy", "1NBC8uXJy1GiJ6drkiZa1WuKn51ps7EPTv"]


print("")
print("permut 11 15 17 (factorial)")
print("")
print("11! 39916800")
print("15! 1307674368000")
print("17! 355687428096000")
print("20! 2432902008176640000")

while True:
    #count2 = 0
    h2 = open("tresher.txt", "r")
    for elemm2 in h2:
        #count2 += 1
        
        Nn = ([elemm2[i:i + 2] for i in range(0, len(elemm2), 2)])[:-1]
        print("")
        K = print(elemm2, " from file")
        print("")
        RRR1 = []

        for RR in range(15):
            DDD = random.choice(Nn)
            RRR1.append(DDD)

        print(Nn)
        print("screening out...")
        print(RRR1)
            #print(RRR2)
            #time.sleep(3.0)
        print("loop start...")
        count = 0
   

        i=1
        while i <= 1000: # step for 11 15 17

                #random.seed(i) #  
                
            dD = ''.join(random.sample(RRR1,len(RRR1)))

            dDD = dD[0:22]
              
            count += 1
              
            bbb = int(dDD)
            #print(dD)
            if bbb <= 6892620648693261354600-1:

      #time.sleep(0.02) #cpu slowdown for many copies
                a3 = list(a1+a2)

                K = bbb
                numberbit1 = len(a1)
                numberbit0 = len(a2)

                aa = find_permutation(a3,K,numberbit1,numberbit0)

                ppp = aa
                    #print(bin(i),d2,i,int(d2,2),ppp)

                random.seed(ppp)
                
                Nn2 = "0","1" #"0","1"
                
                RRR = []
                
                for RR in range(160): # pz bit range
                    DDD = random.choice(Nn2)
                    RRR.append(DDD)

                d = ''.join(RRR)
                            
                print(count,bbb,ppp,"<seed, bit>",d)
                            
                ii = 64
                while ii <= 160:

           #time.sleep(0.02) #cpu slowdown for many copies
                                
                    dd = (d)[0:ii]
                                
                    b = int(dd,2)
                    if b >= 9223372036854775807:
                        key = Key.from_int(b)
                        addr = key.address
                        if addr in list2:
                            print ("found!!!",b,addr)
                            s1 = str(b)
                            s2 = addr
                            f=open("a.txt","a")
                            f.write(s1)
                            f.write(s2)      
                            f.close()
                            pass
                        else:
                            pass
                                #print(i,ppp,addr) #print(X,r1,b,addr)
                    ii=ii+1          
            i=i+1

        count = 0
            #RRR2=[]
        print("loop end...")
        time.sleep(2.0)

    h2.close()            

    pass

random

Quote
from os import system
system("title "+__file__)
import random
from bit import Key
#from bit.format import bytes_to_wif
#from PyRandLib import *
#rand = FastRand63()
#random.seed(rand())
import gmpy2
import time

def sym1():
    a1 = "0"

    return a1

def sym2():
    a2 = "1"

    return a2


#def tiime():
    
#    cz = time.sleep(0.02)
    
#    return cz

def fromfile():

    hu=0
    hu1=random.randrange(1,10000,1)

    h2 = open("tresher.txt", "r")
    for elemm2 in h2:
        hu +=1
        if hu == hu1:
            #ggg = elemm2
            #print(ggg)
            break

    h2.close()
      
    return elemm2


def find_permutation(lst,K,numberbit1,numberbit0):
    l = lst
    N = numberbit0
    M = numberbit1

    if N == len(l):
        return sym2() * N
    
    if M == len(l):
        return sym2() * M

    result = ''    
    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)
        if (K < K0):
            result += sym1()
            l.remove (sym1())
        else:
            result += sym2()
            l.remove (sym2())
            M -=1
            K = K - K0
    result += l[0]

    return result

a1=sym1()*38
a2=sym2()*38

import time

list2 = ["16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN","13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so","1BY8GQbnueYofwSuFAT3USAhGjPrkxDdW9",
        "1MVDYgVaSN6iKKEsbzRUAYFrYJadLYZvvZ","19vkiEajfhuZ8bs8Zu2jgmC6oqZbWqhxhG","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF",
        "1PWo3JeB9jrGwfHDNpdGK54CRas7fsVzXU","1JTK7s9YVYywfm5XUH7RNhHJH1LshCaRFR","12VVRNPi4SJqUTsp6FmqDqY5sGosDtysn4",
        "1FWGcVDK3JGzCC3WtkYetULPszMaK2Jksv","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF","1Bxk4CQdqL9p22JEtDfdXMsng1XacifUtE",
        "15qF6X51huDjqTmF9BJgxXdt1xcj46Jmhb","1ARk8HWJMn8js8tQmGUJeQHjSE7KRkn2t8","15qsCm78whspNQFydGJQk5rexzxTQopnHZ",
        "13zYrYhhJxp6Ui1VV7pqa5WDhNWM45ARAC","14MdEb4eFcT3MVG5sPFG4jGLuHJSnt1Dk2","1CMq3SvFcVEcpLMuuH8PUcNiqsK1oicG2D",
        "1K3x5L6G57Y494fDqBfrojD28UJv4s5JcK","1PxH3K1Shdjb7gSEoTX7UPDZ6SH4qGPrvq","16AbnZjZZipwHMkYKBSfswGWKDmXHjEpSf",
        "19QciEHbGVNY4hrhfKXmcBBCrJSBZ6TaVt","1EzVHtmbN4fs4MiNk3ppEnKKhsmXYJ4s74","1AE8NzzgKE7Yhz7BWtAcAAxiFMbPo82NB5",
        "17Q7tuG2JwFFU9rXVj3uZqRtioH3mx2Jad","1K6xGMUbs6ZTXBnhw1pippqwK6wjBWtNpL","15ANYzzCp5BFHcCnVFzXqyibpzgPLWaD8b",
        "18ywPwj39nGjqBrQJSzZVq2izR12MDpDr8","1CaBVPrwUxbQYYswu32w7Mj4HR4maNoJSX","1JWnE6p6UN7ZJBN7TtcbNDoRcjFtuDWoNL",
        "1CKCVdbDJasYmhswB6HKZHEAnNaDpK7W4n","1PXv28YxmYMaB8zxrKeZBW8dt2HK7RkRPX","1AcAmB6jmtU6AiEcXkmiNE9TNVPsj9DULf",
        "1EQJvpsmhazYCcKX5Au6AZmZKRnzarMVZu","18KsfuHuzQaBTNLASyj15hy4LuqPUo1FNB","15EJFC5ZTs9nhsdvSUeBXjLAuYq3SWaxTc",
        "1HB1iKUqeffnVsvQsbpC6dNi1XKbyNuqao","1GvgAXVCbA8FBjXfWiAms4ytFeJcKsoyhL","12JzYkkN76xkwvcPT6AWKZtGX6w2LAgsJg",
        "1824ZJQ7nKJ9QFTRBqn7z7dHV5EGpzUpH3","18A7NA9FTsnJxWgkoFfPAFbQzuQxpRtCos","1NeGn21dUDDeqFQ63xb2SpgUuXuBLA4WT4",
        "1NLbHuJebVwUZ1XqDjsAyfTRUPwDQbemfv","1MnJ6hdhvK37VLmqcdEwqC3iFxyWH2PHUV","1KNRfGWw7Q9Rmwsc6NT5zsdvEb9M2Wkj5Z",
        "1PJZPzvGX19a7twf5HyD2VvNiPdHLzm9F6","1GuBBhf61rnvRe4K8zu8vdQB3kHzwFqSy7","17s2b9ksz5y7abUm92cHwG8jEPCzK3dLnT",
        "1GDSuiThEV64c166LUFC9uDcVdGjqkxKyh","1Me3ASYt5JCTAK2XaC32RMeH34PdprrfDx","1CdufMQL892A69KXgv6UNBD17ywWqYpKut",
        "1BkkGsX9ZM6iwL3zbqs7HWBV7SvosR6m8N","1PXAyUB8ZoH3WD8n5zoAthYjN15yN5CVq5","1AWCLZAjKbV1P7AHvaPNCKiB7ZWVDMxFiz",
        "1G6EFyBRU86sThN3SSt3GrHu1sA7w7nzi4","1MZ2L1gFrCtkkn6DnTT2e4PFUTHw9gNwaj","1Hz3uv3nNZzBVMXLGadCucgjiCs5W9vaGz",
        "1Fo65aKq8s8iquMt6weF1rku1moWVEd5Ua","16zRPnT8znwq42q7XeMkZUhb1bKqgRogyy","1KrU4dHE5WrW8rhWDsTRjR21r8t3dsrS3R",
        "17uDfp5r4n441xkgLFmhNoSW1KWp6xVLD","13A3JrvXmvg5w9XGvyyR4JEJqiLz8ZySY3","16RGFo6hjq9ym6Pj7N5H7L1NR1rVPJyw2v",
        "1UDHPdovvR985NrWSkdWQDEQ1xuRiTALq","15nf31J46iLuK1ZkTnqHo7WgN5cARFK3RA","1Ab4vzG6wEQBDNQM1B2bvUz4fqXXdFk2WT",
        "1Fz63c775VV9fNyj25d9Xfw3YHE6sKCxbt","1QKBaU6WAeycb3DbKbLBkX7vJiaS8r42Xo","1CD91Vm97mLQvXhrnoMChhJx4TP9MaQkJo",
        "15MnK2jXPqTMURX4xC3h4mAZxyCcaWWEDD","13N66gCzWWHEZBxhVxG18P8wyjEWF9Yoi1","1NevxKDYuDcCh1ZMMi6ftmWwGrZKC6j7Ux",
        "19GpszRNUej5yYqxXoLnbZWKew3KdVLkXg","1M7ipcdYHey2Y5RZM34MBbpugghmjaV89P","18aNhurEAJsw6BAgtANpexk5ob1aGTwSeL",
        "1FwZXt6EpRT7Fkndzv6K4b4DFoT4trbMrV","1CXvTzR6qv8wJ7eprzUKeWxyGcHwDYP1i2","1MUJSJYtGPVGkBCTqGspnxyHahpt5Te8jy",
        "13Q84TNNvgcL3HJiqQPvyBb9m4hxjS3jkV","1LuUHyrQr8PKSvbcY1v1PiuGuqFjWpDumN","18192XpzzdDi2K11QVHR7td2HcPS6Qs5vg",
        "1NgVmsCCJaKLzGyKLFJfVequnFW9ZvnMLN","1AoeP37TmHdFh8uN72fu9AqgtLrUwcv2wJ","1FTpAbQa4h8trvhQXjXnmNhqdiGBd1oraE",
        "14JHoRAdmJg3XR4RjMDh6Wed6ft6hzbQe9","19z6waranEf8CcP8FqNgdwUe1QRxvUNKBG","14u4nA5sugaswb6SZgn5av2vuChdMnD9E5",
        "174SNxfqpdMGYy5YQcfLbSTK3MRNZEePoy", "1NBC8uXJy1GiJ6drkiZa1WuKn51ps7EPTv"]

print("")
print("permut 11 15 17 (factorial)")
print("")
print("11! 39916800")
print("15! 1307674368000")
print("17! 355687428096000")
print("20! 2432902008176640000")

while True:
    #count2 = 0
    #h2 = open("tresher.txt", "r")
    #for elemm2 in h2:
        #count2 += 1


    elemm2 = fromfile()
        
    Nn = ([elemm2[i:i + 2] for i in range(0, len(elemm2), 2)])[:-1]
    print("")
    K = print(elemm2, " from file")
    print("")
    RRR1 = []

    for RR in range(15):
        DDD = random.choice(Nn)
        RRR1.append(DDD)

    print(Nn)
    print("screening out...")
    print(RRR1)
            #print(RRR2)
            #time.sleep(3.0)
    print("loop start...")
    count = 0
   

    i=1
    while i <= 50000000: # permut step factorial 11 15 17
   
               #random.seed(i) # seed init?
                
        dD = ''.join(random.sample(RRR1,len(RRR1)))

        dDD = dD[0:22]
              
        count += 1
              
        bbb = int(dDD)
            #print(dD)

        if bbb <= 6892620648693261354600-1:

            a3 = list(a1+a2)
            K = bbb
            numberbit1 = len(a1)
            numberbit0 = len(a2)

            aa = find_permutation(a3,K,numberbit1,numberbit0)

            ppp = aa
                    #print(bin(i),d2,i,int(d2,2),ppp)

            random.seed(ppp)
                
            Nn2 = "0","1" #"0","1"
                
            RRR = []
                
            for RR in range(160): # pz bit range
                DDD = random.choice(Nn2)
                RRR.append(DDD)

            d = ''.join(RRR)
                            
            print(count,bbb,ppp,"<seed, bit>",d)
                            
            ii = 64
            while ii <= 160:
      
                dd = (d)[0:ii]
                                
                b = int(dd,2)
                if b >= 9223372036854775807:
                    key = Key.from_int(b)
                    addr = key.address
                    if addr in list2:
                        print ("found!!!",b,addr)
                        s1 = str(b)
                        s2 = addr
                        f=open("a.txt","a")
                        f.write(s1)
                        f.write(s2)      
                        f.close()
                        pass
                    else:
                        pass
                                #print(i,ppp,addr) #print(X,r1,b,addr)
                ii=ii+1
        i=i+1

    count = 0
            #RRR2=[]
    print("loop end...")
    time.sleep(2.0)
            
    break

4) write many different seed scripts, python dont use "re"

Quote
import time

GGG = ['ba', 'ca', 'da', 'ea', 'fa', 'ga', 'ha', 'ia', 'ja', 'ka', 'la', 'ma', 'na', 'oa', 'pa', 'qa', 'ra', 'sa', 'ta', 'ua', 'va', 'wa', 'xa', 'ya', 'za', 'Aa', 'Ba', 'Ca', 'Da',
       'Ea', 'Fa', 'Za', 'cb', 'db', 'eb', 'fb', 'gb', 'hb', 'ib', 'jb', 'kb', 'lb', 'mb', 'nb', 'ob', 'pb', 'qb', 'rb', 'sb', 'tb', 'ub', 'vb', 'wb', 'xb', 'yb', 'zb', 'Ab', 'Bb',
       'Cb', 'Db', 'Eb', 'Fb', 'Zb', 'dc', 'ec', 'fc', 'gc', 'hc', 'ic', 'jc', 'kc', 'lc', 'mc', 'nc', 'oc', 'pc', 'qc', 'rc', 'sc', 'tc', 'uc', 'vc', 'wc', 'xc', 'yc', 'zc', 'Ac',
       'Bc', 'Cc', 'Dc', 'Ec', 'Fc', 'Zc', 'ed', 'fd', 'gd', 'hd', 'id', 'jd', 'kd', 'ld', 'md', 'nd', 'od', 'pd', 'qd', 'rd', 'sd', 'td', 'ud', 'vd', 'wd', 'xd', 'yd', 'zd', 'Ad',
       'Bd', 'Cd', 'Dd', 'Ed', 'Fd', 'Zd', 'fe', 'ge', 'he', 'ie', 'je', 'ke', 'le', 'me', 'ne', 'oe', 'pe', 'qe', 're', 'se', 'te', 'ue', 've', 'we', 'xe', 'ye', 'ze', 'Ae', 'Be',
       'Ce', 'De', 'Ee', 'Fe', 'Ze', 'gf', 'hf', 'if', 'jf', 'kf', 'lf', 'mf', 'nf', 'of', 'pf', 'qf', 'rf', 'sf', 'tf', 'uf', 'vf', 'wf', 'xf', 'yf', 'zf', 'Af', 'Bf', 'Cf', 'Df',
       'Ef', 'Ff', 'Zf', 'hg', 'ig', 'jg', 'kg', 'lg', 'mg', 'ng', 'og', 'pg', 'qg', 'rg', 'sg', 'tg', 'ug', 'vg', 'wg', 'xg', 'yg', 'zg', 'Ag', 'Bg', 'Cg', 'Dg', 'Eg', 'Fg', 'Zg',
       'ih', 'jh', 'kh', 'lh', 'mh', 'nh', 'oh', 'ph', 'qh', 'rh', 'sh', 'th', 'uh', 'vh', 'wh', 'xh', 'yh', 'zh', 'Ah', 'Bh', 'Ch', 'Dh', 'Eh', 'Fh', 'Zh', 'ji', 'ki', 'li', 'mi',
       'ni', 'oi', 'pi', 'qi', 'ri', 'si', 'ti', 'ui', 'vi', 'wi', 'xi', 'yi', 'zi', 'Ai', 'Bi', 'Ci', 'Di', 'Ei', 'Fi', 'Zi', 'kj', 'lj', 'mj', 'nj', 'oj', 'pj', 'qj', 'rj', 'sj',
       'tj', 'uj', 'vj', 'wj', 'xj', 'yj', 'zj', 'Aj', 'Bj', 'Cj', 'Dj', 'Ej', 'Fj', 'Zj', 'lk', 'mk', 'nk', 'ok', 'pk', 'qk', 'rk', 'sk', 'tk', 'uk', 'vk', 'wk', 'xk', 'yk', 'zk',
       'Ak', 'Bk', 'Ck', 'Dk', 'Ek', 'Fk', 'Zk', 'ml', 'nl', 'ol', 'pl', 'ql', 'rl', 'sl', 'tl', 'ul', 'vl', 'wl', 'xl', 'yl', 'zl', 'Al', 'Bl', 'Cl', 'Dl', 'El', 'Fl', 'Zl', 'nm',
       'om', 'pm', 'qm', 'rm', 'sm', 'tm', 'um', 'vm', 'wm', 'xm', 'ym', 'zm', 'Am', 'Bm', 'Cm', 'Dm', 'Em', 'Fm', 'Zm', 'on', 'pn', 'qn', 'rn', 'sn', 'tn', 'un', 'vn', 'wn', 'xn',
       'yn', 'zn', 'An', 'Bn', 'Cn', 'Dn', 'En', 'Fn', 'Zn', 'po', 'qo', 'ro', 'so', 'to', 'uo', 'vo', 'wo', 'xo', 'yo', 'zo', 'Ao', 'Bo', 'Co', 'Do', 'Eo', 'Fo', 'Zo', 'qp', 'rp',
       'sp', 'tp', 'up', 'vp', 'wp', 'xp', 'yp', 'zp', 'Ap', 'Bp', 'Cp', 'Dp', 'Ep', 'Fp', 'Zp', 'rq', 'sq', 'tq', 'uq', 'vq', 'wq', 'xq', 'yq', 'zq', 'Aq', 'Bq', 'Cq', 'Dq', 'Eq',
       'Fq', 'Zq', 'sr', 'tr', 'ur', 'vr', 'wr', 'xr', 'yr', 'zr', 'Ar', 'Br', 'Cr', 'Dr', 'Er', 'Fr', 'Zr', 'ts', 'us', 'vs', 'ws', 'xs', 'ys', 'zs', 'As', 'Bs', 'Cs', 'Ds', 'Es',
       'Fs', 'Zs', 'ut', 'vt', 'wt', 'xt', 'yt', 'zt', 'At', 'Bt', 'Ct', 'Dt', 'Et', 'Ft', 'Zt', 'vu', 'wu', 'xu', 'yu', 'zu', 'Au', 'Bu', 'Cu', 'Du', 'Eu', 'Fu', 'Zu', 'wv', 'xv',
       'yv', 'zv', 'Av', 'Bv', 'Cv', 'Dv', 'Ev', 'Fv', 'Zv', 'xw', 'yw', 'zw', 'Aw', 'Bw', 'Cw', 'Dw', 'Ew', 'Fw', 'Zw', 'yx', 'zx', 'Ax', 'Bx', 'Cx', 'Dx', 'Ex', 'Fx', 'Zx', 'zy',
       'Ay', 'By', 'Cy', 'Dy', 'Ey', 'Fy', 'Zy', 'Az', 'Bz', 'Cz', 'Dz', 'Ez', 'Fz', 'Zz', 'BA', 'CA', 'DA', 'EA', 'FA', 'ZA', 'CB', 'DB', 'EB', 'FB', 'ZB', 'DC', 'EC', 'FC', 'ZC',
       'ED', 'FD', 'ZD', 'FE', 'ZE', 'ZF']

for elem in GGG[0:500]: # python dont use "re"
    #time.sleep(0.1)
    if elem != "re":
        ccc = elem
       
        f = open("blablabla.txt")
        #f.readline()
        f2= open(str(ccc+".py"), "w+")
        for l in f:
            if "    a1 = " in l:
                vvv = """ " """+str(ccc[0])+""" " """
                vvv2 = str(vvv)
                Ggg = vvv2.replace(' ', '')
                #print(Ggg)
                f2.writelines("    a1 =" + Ggg)
                continue
            if "    a2 = " in l:
                vvv = """ " """+str(ccc[1])+""" " """
                vvv2 = str(vvv)
                Ggg = vvv2.replace(' ', '')
                #print(Ggg)
                f2.writelines("    a2 =" + Ggg)
                continue
            else:
                f2.writelines(l)

             
    f.close()
    f2.close()


5) create cmd to run all scripts

Quote
import time
from os import system
system("title "+__file__)
import os

mmm = os.path.dirname(__file__)
mmm1 = str(mmm)#[:6]
print(mmm1)
FFF = []

for root, dirs, files in os.walk("."):
    print(root, dirs, files)
    for filename in files:
        if filename[2:5] == ".py":
            FFF.append(filename)
            #print(filename)


f2= open("run.cmd", "w+")

f2.writelines("@echo off"+ '\n')

vvv = """ " """+mmm1+""" " """
vvv2 = str(vvv)
Ggg = vvv2.replace(' ', '')
Ggg2 = "cd "+Ggg

f2.writelines(Ggg2+ '\n')

for F in FFF:

    f2.writelines("start /min "+str(F)+ '\n')

f2.writelines("exit"+ '\n')

f2.close()

everything should be in the 1st folder    
16  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: November 28, 2021, 05:14:40 PM
It was misleading. I was delighted and did not notice the catch. "collisions" are simply out of range.

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03C3CA0BD8A7D05A949 pz63

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A0705B5714CFEAA29032 pz70

***

but there should be collisions. for example, how many 2 ^ 64 (16 ^ 16) fit in 2 ^ 160 (16 ^ 40) ripmd160

1461501637330902918203684832716283019655932542976/18446744073709551616 = 79228162514264337593543950336 (hex from 0000000000000000-FFFFFFFFFFFFFFFF)

79228162514264337593543950336/18446744073709551616 = 4294967296 and repeating numbers.

or

18446744073709551616*18446744073709551616 = 340282366920938463463374607431768211456

1461501637330902918203684832716283019655932542976 / 340282366920938463463374607431768211456 = 4294967296

all space 2^160 can be run for 4294967296 steps by 18446744073709551616 step.

that is, there is a repetition

0000000000000000 0
FFFFFFFFFFFFFFFF 18446744073709551616

0000000000000000 18446744073709551616
FFFFFFFFFFFFFFFF 18446744073709551616 + 18446744073709551616  

0000000000000000 18446744073709551616 + 18446744073709551616
FFFFFFFFFFFFFFFF 18446744073709551616 + 18446744073709551616 + 18446744073709551616  

0000000000000000 18446744073709551616 + 18446744073709551616 + 18446744073709551616
FFFFFFFFFFFFFFFF 18446744073709551616 + 18446744073709551616 + 18446744073709551616 + 18446744073709551616  

etc  

18446744073709551616 / 4294967296 = 4294967296

in the hash they are all mixed, therefore, these random mixed numbers are rotated

1
2  (2^64)
3

2
1  (2^64)
3

3
2  (2^64)
1

etc

get a chance to find what you need 50%? and you need to somehow find the rest of the hash ripmd160 16^24...

***

or screw quasi-random distribution or gauss

2^64×2^64
340282366920938463463374607431768211456
93820969697840041204785894580506297666600
140!/70!/70

93820969697840041204785894580506297666600 / 2^64 = 5086044958554742658699 collisions

step 10000000000000000000000 + gauss (thanks to someone from the Inet)

10000000000000000000000 / 2^64 = 542,1010862427522170037 collision


Quote
from os import system
system("title "+__file__)
import random
from bit import Key
from combi import *

list2 = ["16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN","13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so","1BY8GQbnueYofwSuFAT3USAhGjPrkxDdW9",
        "1MVDYgVaSN6iKKEsbzRUAYFrYJadLYZvvZ","19vkiEajfhuZ8bs8Zu2jgmC6oqZbWqhxhG","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF",
        "1PWo3JeB9jrGwfHDNpdGK54CRas7fsVzXU","1JTK7s9YVYywfm5XUH7RNhHJH1LshCaRFR","12VVRNPi4SJqUTsp6FmqDqY5sGosDtysn4",
        "1FWGcVDK3JGzCC3WtkYetULPszMaK2Jksv","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF","1Bxk4CQdqL9p22JEtDfdXMsng1XacifUtE",
        "15qF6X51huDjqTmF9BJgxXdt1xcj46Jmhb","1ARk8HWJMn8js8tQmGUJeQHjSE7KRkn2t8","15qsCm78whspNQFydGJQk5rexzxTQopnHZ",
        "13zYrYhhJxp6Ui1VV7pqa5WDhNWM45ARAC","14MdEb4eFcT3MVG5sPFG4jGLuHJSnt1Dk2","1CMq3SvFcVEcpLMuuH8PUcNiqsK1oicG2D",
        "1K3x5L6G57Y494fDqBfrojD28UJv4s5JcK","1PxH3K1Shdjb7gSEoTX7UPDZ6SH4qGPrvq","16AbnZjZZipwHMkYKBSfswGWKDmXHjEpSf",
        "19QciEHbGVNY4hrhfKXmcBBCrJSBZ6TaVt","1EzVHtmbN4fs4MiNk3ppEnKKhsmXYJ4s74","1AE8NzzgKE7Yhz7BWtAcAAxiFMbPo82NB5",
        "17Q7tuG2JwFFU9rXVj3uZqRtioH3mx2Jad","1K6xGMUbs6ZTXBnhw1pippqwK6wjBWtNpL","15ANYzzCp5BFHcCnVFzXqyibpzgPLWaD8b",
        "18ywPwj39nGjqBrQJSzZVq2izR12MDpDr8","1CaBVPrwUxbQYYswu32w7Mj4HR4maNoJSX","1JWnE6p6UN7ZJBN7TtcbNDoRcjFtuDWoNL",
        "1CKCVdbDJasYmhswB6HKZHEAnNaDpK7W4n","1PXv28YxmYMaB8zxrKeZBW8dt2HK7RkRPX","1AcAmB6jmtU6AiEcXkmiNE9TNVPsj9DULf",
        "1EQJvpsmhazYCcKX5Au6AZmZKRnzarMVZu","18KsfuHuzQaBTNLASyj15hy4LuqPUo1FNB","15EJFC5ZTs9nhsdvSUeBXjLAuYq3SWaxTc",
        "1HB1iKUqeffnVsvQsbpC6dNi1XKbyNuqao","1GvgAXVCbA8FBjXfWiAms4ytFeJcKsoyhL","12JzYkkN76xkwvcPT6AWKZtGX6w2LAgsJg",
        "1824ZJQ7nKJ9QFTRBqn7z7dHV5EGpzUpH3","18A7NA9FTsnJxWgkoFfPAFbQzuQxpRtCos","1NeGn21dUDDeqFQ63xb2SpgUuXuBLA4WT4",
        "1NLbHuJebVwUZ1XqDjsAyfTRUPwDQbemfv","1MnJ6hdhvK37VLmqcdEwqC3iFxyWH2PHUV","1KNRfGWw7Q9Rmwsc6NT5zsdvEb9M2Wkj5Z",
        "1PJZPzvGX19a7twf5HyD2VvNiPdHLzm9F6","1GuBBhf61rnvRe4K8zu8vdQB3kHzwFqSy7","17s2b9ksz5y7abUm92cHwG8jEPCzK3dLnT",
        "1GDSuiThEV64c166LUFC9uDcVdGjqkxKyh","1Me3ASYt5JCTAK2XaC32RMeH34PdprrfDx","1CdufMQL892A69KXgv6UNBD17ywWqYpKut",
        "1BkkGsX9ZM6iwL3zbqs7HWBV7SvosR6m8N","1PXAyUB8ZoH3WD8n5zoAthYjN15yN5CVq5","1AWCLZAjKbV1P7AHvaPNCKiB7ZWVDMxFiz",
        "1G6EFyBRU86sThN3SSt3GrHu1sA7w7nzi4","1MZ2L1gFrCtkkn6DnTT2e4PFUTHw9gNwaj","1Hz3uv3nNZzBVMXLGadCucgjiCs5W9vaGz",
        "1Fo65aKq8s8iquMt6weF1rku1moWVEd5Ua","16zRPnT8znwq42q7XeMkZUhb1bKqgRogyy","1KrU4dHE5WrW8rhWDsTRjR21r8t3dsrS3R",
        "17uDfp5r4n441xkgLFmhNoSW1KWp6xVLD","13A3JrvXmvg5w9XGvyyR4JEJqiLz8ZySY3","16RGFo6hjq9ym6Pj7N5H7L1NR1rVPJyw2v",
        "1UDHPdovvR985NrWSkdWQDEQ1xuRiTALq","15nf31J46iLuK1ZkTnqHo7WgN5cARFK3RA","1Ab4vzG6wEQBDNQM1B2bvUz4fqXXdFk2WT",
        "1Fz63c775VV9fNyj25d9Xfw3YHE6sKCxbt","1QKBaU6WAeycb3DbKbLBkX7vJiaS8r42Xo","1CD91Vm97mLQvXhrnoMChhJx4TP9MaQkJo",
        "15MnK2jXPqTMURX4xC3h4mAZxyCcaWWEDD","13N66gCzWWHEZBxhVxG18P8wyjEWF9Yoi1","1NevxKDYuDcCh1ZMMi6ftmWwGrZKC6j7Ux",
        "19GpszRNUej5yYqxXoLnbZWKew3KdVLkXg","1M7ipcdYHey2Y5RZM34MBbpugghmjaV89P","18aNhurEAJsw6BAgtANpexk5ob1aGTwSeL",
        "1FwZXt6EpRT7Fkndzv6K4b4DFoT4trbMrV","1CXvTzR6qv8wJ7eprzUKeWxyGcHwDYP1i2","1MUJSJYtGPVGkBCTqGspnxyHahpt5Te8jy",
        "13Q84TNNvgcL3HJiqQPvyBb9m4hxjS3jkV","1LuUHyrQr8PKSvbcY1v1PiuGuqFjWpDumN","18192XpzzdDi2K11QVHR7td2HcPS6Qs5vg",
        "1NgVmsCCJaKLzGyKLFJfVequnFW9ZvnMLN","1AoeP37TmHdFh8uN72fu9AqgtLrUwcv2wJ","1FTpAbQa4h8trvhQXjXnmNhqdiGBd1oraE",
        "14JHoRAdmJg3XR4RjMDh6Wed6ft6hzbQe9","19z6waranEf8CcP8FqNgdwUe1QRxvUNKBG","14u4nA5sugaswb6SZgn5av2vuChdMnD9E5",
        "174SNxfqpdMGYy5YQcfLbSTK3MRNZEePoy", "1NBC8uXJy1GiJ6drkiZa1WuKn51ps7EPTv"]


#w1= # 600 0000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000001111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111 1111111111111111111111111111111111111111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111111
#w2= # 600 0101010101010101010101010101010101010101010101010101010101010101010101010101010 1010101010101010101010101010101010101010101010101010101010101010101010101010101 0101010101010101010101010101010101010101010101010101010101010101010101010101010 1010101010101010101010101010101010101010101010101010101010101010101010101010101 0101010101010101010101010101010101010101010101010101010101010101010101010101010 1010101010101010101010101010101010101010101010101010101010101010101010101010101 0101010101010101010101010101010101010101010101010101010101010101010101010101010 10101010101010101010101010101010101010101010101
#w3= "0000000000111111111122222222223333333333444444444455555555556666666666777777777 788888888889999999999" # 0000000000111111111122222222223333333333444444444455555555556666666666777777777 788888888889999999999

#aaa666 = ["00000000000000000000","00000000000000000000","00000000000000000000","00000000000000000000","00000000000000000000","00000000000000000000","00000000000000000000",
#       "00000000000000000000","00000000000000000000","00000000000000000000","00000000000000000000","00000000000000000000","00000000000000000000","00000000000000000000",
#       "00000000000000000000","11111111111111111111","11111111111111111111","11111111111111111111","11111111111111111111","11111111111111111111","11111111111111111111",
#       "11111111111111111111","11111111111111111111","11111111111111111111","11111111111111111111","11111111111111111111","11111111111111111111","11111111111111111111",
#       "11111111111111111111","11111111111111111111"]

a1="0"*70
a2="1"*70
a3 = a1+a2
perm_space = PermSpace(a3)

#aa = perm_space[0]
#GG = ([a3[i:i + 10] for i in range(0, len(a3), 10)])
#random.seed()
#aaa777 = ''.join(random.sample(GG,len(GG)))

i = 0
while i <= 93820969697840041204785894580506297666600-1:
    #DDD = [10238746,11234789,12334458,13489004,14844639,15093768,16663890,17877737,18990390,19234412,99873218,10093241]
    fff=i
    if 0 == 0: #for lem in DDD:
        #kkk = int(lem)
        ffff = fff#+kkk
        if ffff >= 93820969697840041204785894580506297666600-1:
            break
        else:
            pass
        aa = perm_space[ffff]
        aaa777 = "".join(aa)
    
#    random.seed()
#    s = a3
#    sv = ''.join(random.sample(s,len(s)))
    
        orderliness = 1 #0.75
        for uuu in range(1,5,1): # dispersion
            def tuplify(x, y):
                
                random.seed()
                
                return (orderliness * y + random.gauss(0,uuu), x)

            for iii in range(0,1000,1): # dispersion
                #a1="0"*50
                #a2="1"*50
                #a3 = a1+a2
                values = aaa777#"0101010101010101010101010101010101010101010101010101010101010101010101010101010 1010101010101010101010101010101010101010101010101010101010101010101010101010101 0101010101010101010101010101010101010101010101010101010101010101010101010101010 1010101010101010101010101010101010101010101010101010101010101010101010101010101 0101010101010101010101010101010101010101010101010101010101010101010101010101010 1010101010101010101010101010101010101010101010101010101010101010101010101010101 0101010101010101010101010101010101010101010101010101010101010101010101010101010 10101010101010101010101010101010101010101010101"
                #print(values)
                pairs = list(map(tuplify, values, range(len(values))))
                pairs.sort()
                partially_ordered_values = [p[1] for p in pairs]
                ppp = "".join(partially_ordered_values)
                #print(ppp)

                random.seed(ppp)

                Nn = "0","1" #"0","1"
                RRR = []

                for RR in range(160): # pz bit range
                    DDD = random.choice(Nn)
                    RRR.append(DDD)

                d = ''.join(RRR)
                #print(d,len(d))
                
                print(ffff,aaa777,ppp) #print(ffff,aaa777,ppp,perm_space.index(ppp),"< combi count")
                
                ii = 64
                while ii <= 160:
                    
                    dd = (d)[0:ii]
                    
                    b = int(dd,2)
                    if b >= 9223372036854775807:
                        key = Key.from_int(b)
                        addr = key.address
                        if addr in list2:
                            print ("found!!!",b,addr)
                            s1 = str(b)
                            s2 = addr
                            f=open("a.txt","a")
                            f.write(s1)
                            f.write(s2)      
                            f.close()
                            pass
                        else:
                            pass
                            #print(i,ffff,aaa777,ppp,addr) #print(X,r1,b,addr)

                    ii=ii+1
        print("loop end...")

    i=i+10000000000000000000000    

17  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: November 25, 2021, 04:40:36 AM
Andzhig, I guess this approach is confusing due to small sample size.

If you take any random 4 numbers, you will find the dependencies between them for sure. The same could be done for 10, 30, or even 100 random numbers. So, our brain thinks that we found the dependencies between several numbers, but it could be wrong just because of the small sample size.
it works like this.

all permutations ripmd160 in hex format 40 length

from

0000000000000000000000000000000000000000

to

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

for example, puzzle 64 is somewhere there

0000000000000000000000000000000000000000
...
3ee4133d991f52fdf6a25c9834e0745ac74248a0
...
3ee4133d991f52fdf6a25c9834e0745ac74248a1
...
3ee4133d991f52fdf6a25c9834e0745ac74248a2
...
3ee4133d991f52fdf6a25c9834e0745ac74248a3
...
3ee4133d991f52fdf6a25c9834e0745ac74248a4
...
3ee4133d991f52fdf6a25c9834e0745ac74248a5
...
3ee4133d991f52fdf6a25c9834e0745ac74248a6
...
etc
...
3ee4133d991f52fdf6a25c9834e0745ac74248af
...
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

in other words into space

0000000000000000000000000000000000000000
...
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

there is only 1 such key 3ee4133d991f52fdf6a25c9834e0745ac74248a4 but it is obtained by numbers from space (dec 9223372036854775808-18446744073709551616) and the rest where then are located which end with 0 1 2 3 ... D E F

the ripmd160 key can start in hex format with only 16 characters 0 1 2 3 4 5 6 7 8 9 a b c d e f

this means 16 options

combinations of 2 characters of the key

16 * 16 = 256 i.e 16^2

this implies that if we start looking for a double match step by step

256 * 16 4096 (each step of 2 characters occurs 16 times over the entire space 4096, ok approximately)

and so that all possible combinations of brute force occur

256 * 256 = 65536

this means that the minimum gap for 2-symbol statistical analysis can be 1 and the maximum is not more 65536 (this is the start of the sample for 3 characters).

probably all sorts of chi-squares and other statistical analysts (searching for the mean-mathematical expectation) will not work here.. although who knows

that is, if we are looking for 2 characters each and step by segments along 4096

they will be the same combined small steps 256 but in order for us to collect statistics for 4096

instead of 16, you will have to save for 256 values ​​(all double combinations) the larger numbers of steps at which they fall out

so it will be clear, take any half of the 64 puzzle key

3ee4133d991f52fdf6a25c9834e0745ac74248a4

length 20 3ee4133d991f52fdf6a2 (16^20 1208925819614629174706176)

how many keys will start with these 20 characters in the whole space?

16^40 1461501637330902918203684832716283019655932542976 / 16^20 1208925819614629174706176 = 1208925819614629174706176 (2^80)

how many 2 characters will there be

3ee4133d991f52fdf6a25c9834e0745ac74248a4
 
16^40 1461501637330902918203684832716283019655932542976 / 16^2  256 = 5708990770823839524233143877797980545530986496 (2^152)

if we take 1 character out of 16 possible

1461501637330902918203684832716283019655932542976/16 91343852333181432387730302044767688728495783936 for each of 16 characters 0 1 2 3 4 5 6 7 8 9 a b c d e f

now what do we have, we have 40 independent experiments (tossing 40 coins or 40 dice)

space 9223372036854775808-18446744073709551616 conditionally time of these 40 parallel experiments and we can rewind this timeline to find the desired combination of the drop

it turns out if for 2 symbols complete cycles of all possible permutations 65536

1461501637330902918203684832716283019655932542976/65536 22300745198530623141535718272648361505980416 full cycles for each of the parallel experiments

first 2 character of 40 ripmd160 3ee4133d991f52fdf6a25c9834e0745ac74248a4
0000000000000000000000000000000000000000
22300745198530623141535718272648361505980416  cycles
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

second 2 character of 40 ripmd160 3ee4133d991f52fdf6a25c9834e0745ac74248a4
0000000000000000000000000000000000000000
22300745198530623141535718272648361505980416  cycles
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

third 2 character of 40 ripmd160 3ee4133d991f52fdf6a25c9834e0745ac74248a4
0000000000000000000000000000000000000000
22300745198530623141535718272648361505980416  cycles
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

etc...

in general, if nothing messed up, then something like that  Grin on the right is the distance between finding the desired

by 4

step 9223372036854780064 count 4257 3ee4 ('3ee401f1439e871f3b7bf15a73b9205016f62b37', '16jY392cGUQDeoLLUQDY1Z7Voi9vzAAJG9', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbdRaaVwNMEs9') 4257
step 9223372036854872143 count 96336 3ee4 ('3ee4486ffc3f440f69214109ab6fecb014ae951b', '16jYNGkRdkw7jLmd9Rtsqpgbq7wDexn99H', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbdfD99kANG93') 92079
step 9223372036854966320 count 190513 3ee4 ('3ee4e10590e5f08060df033d8e649bdfa71556f8', '16jZ5ghxKD2shjWM9vXzTbGcnRVh4fc8mV', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbdu9iYiH9sMz') 94177
step 9223372036854979739 count 203932 3ee4 ('3ee47cfd082608b52863b69fccb242194f53c8cc', '16jYcXzrVY9iwimcGYRuzRTrZg9NPAjtmY', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbdw8vpM3Ug7g') 13419
step 9223372036855207002 count 431195 3ee4 ('3ee445d81358b6ceb2f2a2592eb7a0f7107ce6a7', '16jYMZvarbTTi45uHsiitMmJchGrdZE8kU', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbeWn99ovPCzn') 227263
step 9223372036855222086 count 446279 3ee4 ('3ee42d68dbc5e3d603b5aea8bf241f4dc19ee9e3', '16jYEwHHgkqGw8R2vSiiR2yJASdjYdiu6T', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbeZ1eYbAmaoW') 15084
step 9223372036855231312 count 455505 3ee4 ('3ee4db94312d8371a7065ddacc07427f53d4a753', '16jZ4D2ULXqvC9uxTzj9UQUFU6ETuonbxy', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbeaNrpjb9hDP') 9226
step 9223372036855418954 count 643147 3ee4 ('3ee408f34da23b61aca6dab2d9b7650e95a50a1b', '16jY53M4tQob3yXt8RVTgqS5fnmPLGrGva', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbf49u4LCTz6x') 187642
step 9223372036855559079 count 783272 3ee4 ('3ee4db2c244a94c6c51b529d2eeaefca64160a0b', '16jZ46dNjaDsYWRZty1n31mWvx7vLEnjkQ', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbfQtyDa4FjWD') 140125
step 9223372036855579887 count 804080 3ee4 ('3ee493a274e850f7606a848062b0e72c65dfd26b', '16jYigVRrnaYGSNVTPpqD4P5HNE4EjLdj2', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbfTyczV8TLMR') 20808
step 9223372036855597340 count 821533 3ee4 ('3ee4b8a794345e85508d74efaa3faf7e01ee8c63', '16jYtjFgb2QjqsJxZKjhENKiPGhhfhs6mZ', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbfWZU5QKrEpS') 17453
step 9223372036855603379 count 827572 3ee4 ('3ee4d5f5b6daf23ff43de92e8a40d7b82dc3d1c4', '16jZ2ga8Gns9dQ8pdwWn2BhF8JupSZSwZz', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbfXTKKiT6KWS') 6039

9223372036855824384 9223372036856872960

step 9223372036855839628 count 15245 3ee4 ('3ee4c5ba97427a170426f6a056380348d311cc3a', '16jYxH4qRvVeykfAd5nFjEUQBVW7So37PM', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbg8RgReB4MXh') 15245
step 9223372036855874015 count 49632 3ee4 ('3ee432987de45e5ed3c3a85950227729b33d5c40', '16jYGLvJiQQeTA4c1wWMESc5e1j6G5BwTL', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbgDWv9SkTNMG') 34387
step 9223372036855877106 count 52723 3ee4 ('3ee4618b010f44a7b772efd8a61254247e45e6aa', '16jYV5xTJ12Pxi78SsJoqVWPxvQmLhjnCe', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbgDyTNesZMuH') 3091
step 9223372036855892671 count 68288 3ee4 ('3ee4ea2cd49b4f4d35c0cf1b0bbd664d40159dae', '16jZ8AoENczbSwXrYanRwrF9FiPJrFL85B', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbgGH6HkT1qYH') 15565
step 9223372036855922499 count 98116 3ee4 ('3ee4de402152f42ce05424f1a85e46971b848cdf', '16jZ4w5k85pN1BJeiT1ZFwYSzusVQ8Dntu', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbgLhBmDfmTUp') 29828
step 9223372036856034098 count 209715 3ee4 ('3ee420a5729e0d288b3f89eb70788b6eefcc5e2b', '16jYBUN2x3Xu6KEUrVfTrbrZVsEoFurr4K', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbgdDLoexJNFd') 111599
step 9223372036856176890 count 352507 3ee4 ('3ee435f3779f555e000b062cc3309d300ba3ff14', '16jYHFjrKj4opLwRMvcXdszLWYQ6jAxEdY', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbgzMK3si26bT') 142792
step 9223372036856212177 count 387794 3ee4 ('3ee410f69e7481de5a993fee52fe94a95115f683', '16jY7DV788LVBrSk7kdq3bKaoVEKr1p4Sz', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbh5aGwoXH8H9') 35287
step 9223372036856239874 count 415491 3ee4 ('3ee4bc6375cb2bbdd156074941cdeebb6ee7d2ce', '16jYuk2qsms5YemqzxBZPw5ajGhCYasHKx', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbh9g5F6Gw7ZE') 27697
step 9223372036856253722 count 429339 3ee4 ('3ee40b2255243f5a50e24c9c58517915ea8dd8eb', '16jY5dirMG2pJefRzsHq1GHNnALRekavUg', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhBiy9BJFhnK') 13848
step 9223372036856289852 count 465469 3ee4 ('3ee4c264bcf29780b7a0f3b6e1c86323cfff59ea', '16jYwNZZVkyGTXwJDVqWFo3z8Tnv2Mibxa', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhH5ApwvkbBq') 36130
step 9223372036856330181 count 505798 3ee4 ('3ee4239facbfe89a1fb39f14f7a21e945967035a', '16jYCHEXQoTViNWWWMhwFqSgMFLso3Jnc2', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhP3RVUFvdd8') 40329
step 9223372036856374507 count 550124 3ee4 ('3ee497c2bc587ac829ea0397195190abef5b16e0', '16jYjoSfCsQiAwxt6Ur113PfMHbrgYuzHn', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhVbzYahtihs') 44326
step 9223372036856419941 count 595558 3ee4 ('3ee4a63d1ab6090a42fa9e2e682ff780ca2b601a', '16jYojMTi15WfzWhv6mNPY7tcJgATo1amk', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhcL5MCi5NaJ') 45434
step 9223372036856425767 count 601384 3ee4 ('3ee4ec2308650ffac9efa5ec2ddc1369fd3bf25f', '16jZ8hgLjW4MJ3hQwYgZMjwJdqduhPxn8z', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhdC6XbHuFVJ') 5826
step 9223372036856425834 count 601451 3ee4 ('3ee4d4cf0485a91bbcea603600a3cb2b191dc14f', '16jZ2NT63GZb18wKU6hKNh47ry2wYBSKLp', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhdCfthj6oRE') 67
step 9223372036856449953 count 625570 3ee4 ('3ee4297f89c5ab5a30cec2ac795ee602242a3b3f', '16jYDsi4yNT4o9fRYAQmDnCyWj3vo12soo', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhgmkT1tgcpK') 24119
step 9223372036856490639 count 666256 3ee4 ('3ee4937306d9acc17b63fb882e36dfc342e334ec', '16jYidaGd2771Q2itov6TSYuR2yJv3X9zE', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhno4tXrsfV8') 40686
step 9223372036856513721 count 689338 3ee4 ('3ee42e1f8610c9080917c0cd94a204068050c872', '16jYF8WmNW75CVs3fyM6uXWyfRw3RFwcxi', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhrDF3wWxb5x') 23082
step 9223372036856558120 count 733737 3ee4 ('3ee45c74fe867cedb2fd9b8cfcb0725374f70076', '16jYThtpezfNYEJ9SkyimmGEXDozLwf7QH', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbhxnSTTNCVhi') 44399
step 9223372036856605325 count 780942 3ee4 ('3ee4203d680887f7358b5799f438c3dfbe0b4e54', '16jYBMxyCzMiuAxPmp3H1uUxqBPzbDDrkM', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbi5mjAcZd6Xb') 47205
step 9223372036856688316 count 863933 3ee4 ('3ee4cb07eda41f9ef43671ea94b1d2ade8308ab3', '16jYyiXnzFn7zeXbU7VNp74HUbJrKezS1m', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbiJ4GG6y7AHs') 82991
step 9223372036856764183 count 939800 3ee4 ('3ee4e9c6f3b6506805a92d97f9749c3562d13e09', '16jZ84Xt2sr42E2xBPueqaJ2RNimPmyTRE', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbiVHdoyWEgLN') 75867
step 9223372036856777525 count 953142 3ee4 ('3ee4ffea49f0d228533f70927cd7d842c5438588', '16jZE52VhwPnjhUNAiQuea8Rw2EMDJwfAa', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbiXGBjmZdcW9') 13342
step 9223372036856803293 count 978910 3ee4 ('3ee45f516b85323f47da64b3803c490f829f6feb', '16jYUUw2VGuaK75QQVvMf63fZu9sfjWavw', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbib5RT21qPej') 25768

9223372036856872960 9223372036857921536

step 9223372036856918061 count 45102 3ee4 ('3ee435344587f985f3dfe9a447225b09b9d08d9a', '16jYH3yx3h1EqhrFNfhNCgwqT2ZVUGJnHP', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbit4nZVq6NzD') 45102
step 9223372036857063933 count 190974 3ee4 ('3ee43a01968043d0ea053f8071ac42db9eafd9ce', '16jYJMaKTcMaqnEMcfNqAPuEA9EGoj5EJq', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbjFfCZDLyWdt') 145872
step 9223372036857069260 count 196301 3ee4 ('3ee4c909146b9411cf2c09120a2d8fa154bf0312', '16jYyB7r6FPfJ68eKcp7fdUZxfcQzixh73', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbjGSwFFyKxu5') 5327
step 9223372036857102786 count 229827 3ee4 ('3ee459e65354041a82c5528963e273d72a51b024', '16jYT1dwTJQASM4etMVkHmiN1UM4oRhU3h', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbjMQnDUVx8Jr') 33526
step 9223372036857110326 count 237367 3ee4 ('3ee4382dbb298a02c0c46d5788c8b43c1205680c', '16jYHrohjC2tjPY99YDiKfB2FR13DBFHK3', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbjNXWv5zFUt8') 7540
step 9223372036857432991 count 560032 3ee4 ('3ee40a6de4afc9df174ab2c03f91c4434db91267', '16jY5SdK7d9cTz3DMNBAUuQ32A1vKZfszU', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbkCHpfN912vr') 322665
step 9223372036857434857 count 561898 3ee4 ('3ee43d2e9718e1065ce4dfe94b7f861157ef3912', '16jYKDZuAe5P78bYAjeFL9ZNxa6QCfdKKR', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbkCZqsh2cqkN') 1866


by 6

step 9223372036860070794 count 5294987 3ee413 ('3ee4139950ca2905dea643734a835d5266983800', '16jY7vyRF8tjBqc5b8QEzPT62aGT7WweE2', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frbrvmDWqhVFHb') 5294987
step 9223372036866863194 count 12087387 3ee413 ('3ee413e35ff2396cd0f35fe9cd4a7fca901abb47', '16jY81XYxGS4Bcw7NbXTN2P1YZxrqhcjpd', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frcAGEkLF5jxZB') 6792400
step 9223372036887603495 count 32827688 3ee413 ('3ee413bce3244402b7ace1bed44552f68473a309', '16jY7yAHX1nBmmeobfpK95Up4Aqz9rNa1J', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frd5CQpUdENVhP') 20740301
step 9223372036918717995 count 63942188 3ee413 ('3ee41368f2bcd25a58c199849647addb39d2f31d', '16jY7szv5j7L75vGBJkbWXYjgJmGSnLXVj', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3freScGgjEj5M9N') 31114500
step 9223372036972007988 count 117232181 3ee413 ('3ee413a03d105b6429accf2f1322fddfb9d1536a', '16jY7wQ7JrAQUKswbxc1w4YurpgA9ff9Ex', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frgnckkpmH1Qn9') 53289993
step 9223372037016876672 count 162100865 3ee413 ('3ee413f755d672b955e248c3f07fc7b4cb4945fd', '16jY82kjwLC7Hy8bZy7GGeUB74rhgHxUvq', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frim8dxzec7Qao') 44868684
step 9223372037031770991 count 176995184 3ee413 ('3ee4134dac0a56431b8988347275fddae4ea1c53', '16jY7rKdoRXQ6rRUapMSvCSG1qMoRUknwH', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frjR9SAqzZo9ER') 14894319
step 9223372037036791970 count 182016163 3ee413 ('3ee4136e78578857bc1c636689c137af321d6df1', '16jY7tLcKxHQ5PVoxZ2wcS3jvFascz92oD', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frjdxgojvY9JAc') 5020979
step 9223372037052209248 count 197433441 3ee413 ('3ee41388c5d99901c507462170a419d97b48f591', '16jY7uxRFiTRJKHRg5p7TkUJcn4SfEismm', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frkKJtyu6LBdvU') 15417278
step 9223372037071704787 count 216928980 3ee413 ('3ee413288d9894877b5b87fa1ec5792e3137c5ae', '16jY7p3FUDDZVFWj6C7xyciRnvvnhoedWK', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frmB4otvV7Q9Vk') 19495539
step 9223372037082585716 count 227809909 3ee413 ('3ee4139a2d4769ce009037abe4cc774e09cec718', '16jY7w2VQdE5V37iPehRkfGtSZcq2Z24Dz', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frmeqWKmivAUYi') 10880929
step 9223372037085839130 count 231063323 3ee413 ('3ee4138f2291ca65e6b270ea951f3c452e1a3401', '16jY7vM7KZs8UdQc3rERLgkyenCdfWjVAT', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frmo97AvUm9mnj') 3253414
step 9223372037109661797 count 254885990 3ee413 ('3ee413eadb3c132820c88b2f9a056839d63af94f', '16jY81zEaWYhutxrYruJ5H7TN5P13tqssS', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frnqwZXJxBRzxt') 23822667

9223372037123211264 9223372037391646720

step 9223372037123362487 count 151224 3ee413 ('3ee41340871ee005bfe502245b542e20adb0071a', '16jY7qWkpWPsZtUYmSFEUcaJRdVAHXTmGM', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3froSufan8jHA7m') 151224
step 9223372037133083111 count 9871848 3ee413 ('3ee4132378def6db61d03bc1fad36f6a80a8a17a', '16jY7oj8SCo87NuW7ucSEmFPC6KAmmoPXK', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frosibydEXqVQe') 9720624
step 9223372037149154239 count 25942976 3ee413 ('3ee413a8a6e172b007cdbf73809f7acacab113ec', '16jY7wv7fzwkWyu2AH8bBaJ5o78zzwNDgr', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frpajbuz8DtSWN') 16071128
step 9223372037159732955 count 36521692 3ee413 ('3ee4135b0e10cf4808cdff781adaa8e832032640', '16jY7s9NA7yytbWBwxkhQ5nGAcQ2XPRfFQ', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frq3jZdazuSjiG') 10578716
step 9223372037181335700 count 58124437 3ee413 ('3ee4137590c1b4a85320e66d67af769758a04d92', '16jY7tmv4N2mpSjTiWgni2i722VZ77EKKa', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frqzsQPeu2FoNU') 21602745
step 9223372037184158484 count 60947221 3ee413 ('3ee413dbbe6bdb86a6bd43ea364dd26680a91a8b', '16jY814LS2hdgGNZzaQcmu9rCqALEaaWXC', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frr85Fye942AYE') 2822784
step 9223372037206185330 count 82974067 3ee413 ('3ee41384712494ba310fe9e454af19bb0a93e3b7', '16jY7ugyNrasq4GBpWX9sWNJQYB5LSWzC8', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frs6Hswd1msW5j') 22026846
step 9223372037209804431 count 86593168 3ee413 ('3ee4135ffd953252a69c252c8e57bdd1e00f257d', '16jY7sSy8LQKMg3qg2J8v8GpcLHJCnWNRi', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frsFXcUDYtbwSQ') 3619101
step 9223372037210884925 count 87673662 3ee413 ('3ee413eb46e26bbfe674e76e1a1f2cdb768d7995', '16jY821jZeJiR4DJeZANpS1iTrBMCUxDxE', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frsJHZGfwRw7YN') 1080494
step 9223372037225629660 count 102418397 3ee413 ('3ee4131921ebbc86e6cc96291873032d889ec63e', '16jY7o6FbnALsZUk6Y8aT6etwAujKGZzvm', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frswvDC4KZPWa2') 14744735
step 9223372037227399855 count 104188592 3ee413 ('3ee413215c938ce5ec378f0c57c48afe0381b275', '16jY7obbrfU85Zea2H8mdrCvSTc3NTizhH', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frt2SFZU6tFa8p') 1770195
step 9223372037229220480 count 106009217 3ee413 ('3ee41392d3c474e48cacdc4f12b1179c22d7e02f', '16jY7vaH5Nr5Rz5VV5Mn4bWdqKco3SXHwG', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frt75kuYUFnxf9') 1820625
step 9223372037261004114 count 137792851 3ee413 ('3ee413615c9ad4d7806400bddd86b70ed6b50298', '16jY7sXrmPomtSApV3tBYHq7y4bNGqhjtU', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3fruWCfkz1B6PUB') 31783634
step 9223372037264602683 count 141391420 3ee413 ('3ee41324c37666478d8d3df973cc20987664fd1a', '16jY7oojZmKse3WsEjGBq3isUqFFiGJVq8', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frufPN1F6gXETd') 3598569
step 9223372037274269021 count 151057758 3ee413 ('3ee413182a12ed0fa6784d061063deb625d72f87', '16jY7o2oL9ETJ7s6jnEoT2LGe2Ea2MhxUQ', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frv64GKFFMbcvg') 9666338
step 9223372037308198692 count 184987429 3ee413 ('3ee4136ebbea8371f9d97846a9ba29da91eeaec8', '16jY7tMYvttwfvvumAFWtQyJbpZwGxVxRR', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frwaerQSDQ9Ju9') 33929671
step 9223372037339496108 count 216284845 3ee413 ('3ee41349b0704e47002f41c6facb645406ec9579', '16jY7r5RvbNzBHnPq33kP9oWsyBbBe395t', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frxxXnjWiL3f6N') 31297416
step 9223372037348906059 count 225694796 3ee413 ('3ee413c7fb1f35cc0d922e7f13dca22307546f04', '16jY7yqrL2JYh5NsCZcDRnG7TtBZCPJQMS', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3fryNYjnHAERUjY') 9409951
step 9223372037375177780 count 251966517 3ee413 ('3ee413a24ee3ee7b9308407fb74a15092851987d', '16jY7wXVRneAJVGK6PeXQT4c3ogJu74uCa', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frzXbiz2gSu9tm') 26271721
step 9223372037381197046 count 257985783 3ee413 ('3ee41379aa2d2bfaee993b4a69e99b15f39c0205', '16jY7u2Y2etLH2Hz5WZgbGvvq8ei7vSM7A', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3frznxkchKGA2jR') 6019266

9223372037391646720 9223372037660082176

step 9223372037392271817 count 625098 3ee413 ('3ee41362711b3a34f8b41e0b7585ac86d5d9c5cb', '16jY7sbiBxr2reECZdpSjkX6awDVeYzhVc', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3fs1HE9KCMtLKCv') 625098
step 9223372037412706782 count 21060063 3ee413 ('3ee4131e5a19abdaaa8cadd8446cd045b8f50e48', '16jY7oQsHQ1FeXSNqvpUKRTMBUVa1v6n7X', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3fs2BP7rw3T69aW') 20434965
step 9223372037414045444 count 22398725 3ee413 ('3ee41347a2437302c16fae5056b1c6e1b53acd21', '16jY7qx6kmr7nbRUjqvc2zj4L63FXpDNAD', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3fs2EoHDWYBn1WF') 1338662
step 9223372037428025256 count 36378537 3ee413 ('3ee4138902811c94d6faebf5e85fe35250c409ad', '16jY7uyGGMRcq4WnWYcwyWU8V8isXZpkun', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3fs2rUhjapqM9h6') 13979812
step 9223372037432204086 count 40557367 3ee413 ('3ee41365d963262dcee2c16a613bc742311563bd', '16jY7sos2S9FQzgG6FNbFn7BbQT1aFb9KH', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3fs339HvsfP6Kim') 4178830
step 9223372037454561642 count 62914923 3ee413 ('3ee413f76f076e10e79ad9098bf9014bf9695bc9', '16jY82m6HxEqc2XgRD8pUbZg7TTQj8U6SA', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3fs42CsGmrErwkK') 22357556
step 9223372037489344010 count 97697291 3ee413 ('3ee4133c5aad1786d1f39f901d1a8637cd81a394', '16jY7qFsUbwYencRHfnpsLhrjwFvaBx4Jv', 'KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYvLz3fs5YygNAVwxa6r') 34782368


well, returning to collisions (they work on the same principle)

155117520 30!/15!/15!
155117520/2^20 147,9315948486328125 collision, pz20 863317
1048576 2^20

step 1100006 seed 000000111011001011000011111101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 1532829 seed 000001001101100011010111111001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 3057416 seed 000001111011011100110000110101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 3377366 seed 000010000111110110101100101011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 4883284 seed 000010111000010101111010011110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 6215864 seed 000011011100101011000001111101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 7278835 seed 000011110101111011010011100000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 13358221 seed 000110100001011111100111001100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 15244257 seed 000111001110001110100110011001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 16213688 seed 000111100100011001101010011011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 18099879 seed 001000011101110101010101000111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 18762243 seed 001000110010100100001111111011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 20871509 seed 001001101010010111110000110110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 23071996 seed 001010100011001011011011010011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 26961189 seed 001011111101000010001011010011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 26971336 seed 001011111101010000100101101010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 27218776 seed 001100000111011101101100110010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 28383269 seed 001100100101111010110101001100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 28675678 seed 001100101100101100111010010011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 28744087 seed 001100101110000111001010101011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 30778835 seed 001101011101001010010010110101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 31839022 seed 001101110101001100100110100101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 32561312 seed 001110001000111000011110011011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 33557684 seed 001110011110110100100110010010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 34368032 seed 001110110001100001001110111010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 38741650 seed 010000101111101011000111001001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 38820746 seed 010000110010100100111111100011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 39398453 seed 010000111111110100000011010101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 39607029 seed 010001001000000101101111111101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 39708006 seed 010001001011011111001110000011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 40028071 seed 010001010100000111111010011110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 40439634 seed 010001011101101010101101100001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 40510587 seed 010001011111001000101001101101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 40791557 seed 010001100110111110000011101100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 44608289 seed 010011000110010101101111000110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 46280468 seed 010011101011110100001101000110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 46749955 seed 010011110110011000010110000111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 46792397 seed 010011110111011011000100010010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 48368169 seed 010100100011111101010101011000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 49122280 seed 010100110101011010011011010010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 50177321 seed 010101001110100011101100001011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 50576038 seed 010101010111100000001111111000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 51189591 seed 010101100101100110110010100110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 53509633 seed 010110011100100001110001011101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 54882674 seed 010110111100000101100100111100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 58174437 seed 011000010101011111000110101100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 58813109 seed 011000100101010101011101011010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 59694165 seed 011000111001001010011010010111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 60089930 seed 011001000011010101110100111001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 61825890 seed 011001101010101001100111001001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 63893071 seed 011010011100001100010111000111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 64215156 seed 011010100011110110101100001100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 64493197 seed 011010101001111000010100011101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 64941835 seed 011010110011111011000001011000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 64964238 seed 011010110100011011110001001010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 65916237 seed 011011001011010101011000001101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 66012228 seed 011011001101011010001100001101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 66925284 seed 011011100011100011010100111000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 67780259 seed 011011111010001000101100101001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 70156056 seed 011100110100010010000011011111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 70181891 seed 011100110100110001101000011110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 70670982 seed 011101000001110100001011010111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 72313879 seed 011101101000000110110011001110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 72323741 seed 011101101000010011010000101111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 73159416 seed 011110000001101010101101010110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 74296890 seed 011110011011000001011110100100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 74750148 seed 011110100110011000010100011110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 75056519 seed 011110101110001000011010110001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 75274571 seed 011110110100001000001110101011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 77158506 seed 011111101011101000010000100011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 77296422 seed 011111110001010010100011000011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 77741810 seed 100000001011110001111110011100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 77986628 seed 100000010101011111100110011010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 79242234 seed 100000111001111110101011000001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 79348636 seed 100000111100011000110111101001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 80711250 seed 100001100001111100011001010111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 82793147 seed 100010010111101100000111101100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 84309970 seed 100010111011001011010011000101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 86669326 seed 100011110010001011000110001111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 88542748 seed 100100100101100111111100000110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 90742671 seed 100101011000101111101001000011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 91084332 seed 100101100000101111001110101010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 91244674 seed 100101100100010110111011101000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 91585622 seed 100101101011100011010001011010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 92418391 seed 100110000000001111110011101101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 93144101 seed 100110010010001100011011111010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 94113944 seed 100110100111110000011011010001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 95075592 seed 100110111110000101110010000011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 95353254 seed 100111000101011011000110101001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 95400634 seed 100111000110011001101111010000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 95453948 seed 100111000111011110110100000001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 95652871 seed 100111001011110010111001001000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 96650943 seed 100111100011110001010001011100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 97087166 seed 100111101110011010001011100000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 98801466 seed 101000100001110011010110111001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 99036688 seed 101000100111100111010010100101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 99088101 seed 101000101001000100111111111000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 99954219 seed 101000111100001101001101111000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 103561501 seed 101010010010100100111110001101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 103698368 seed 101010010101011101011001110000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 105549278 seed 101011000000111011010101100110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 105761062 seed 101011000101100100101110011100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 106489713 seed 101011010101100101110011000001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 109193275 seed 101100011011101110010000011100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 110048834 seed 101100101111000110010100110010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 110582918 seed 101100111011011100101101000000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 112668344 seed 101101101101110101000100010001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 114255000 seed 101110010111001101110110000000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 116921964 seed 101111100001010010100111110000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 117006980 seed 101111100011010001010011000110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 117868027 seed 110000000111110010111101001001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 117920933 seed 110000001001110101110110010110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 118591969 seed 110000011011001001101000111101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 118866559 seed 110000100001111100010110101101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 119313131 seed 110000101100110001101001110110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 119452641 seed 110000101111100111000100010110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 119915872 seed 110000111010000111101010001011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 120576163 seed 110001001010110101100000101111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 123229375 seed 110010001001101100101101111000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 125201601 seed 110010110101101110000001010011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 125247571 seed 110010110110110001101000010011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 125302119 seed 110010111000010110000111011100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 130285712 seed 110100110011001101011101001000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 131056143 seed 110101000110010101011110100100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 131116177 seed 110101000111100011001001100101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 133481152 seed 110110000100110111011001000110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 134167546 seed 110110010100000010111001101101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 134275046 seed 110110010110010011110010000110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 135394878 seed 110110110010100011100101101000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 135914109 seed 110111000011000001011001010111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 136719363 seed 110111011000000111110100100010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 137620533 seed 110111111000000011100010101100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 137852191 seed 111000000011110110101111001000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 137884461 seed 111000000100110111011001101010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 138008646 seed 111000000111100110101011001001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 138195551 seed 111000001100000000001111111111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 139639240 seed 111000101100010101110100100011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 141683942 seed 111001011100011000101111010000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 142725688 seed 111001110111100010000110101000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 146071951 seed 111011001111100010000101100010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 146674357 seed 111011100010001001100111010100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 148684714 seed 111100011101100101010001110000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 150523524 seed 111101001111001110110000100000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 150565504 seed 111101010000101000110100111001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 150744653 seed 111101010100111011000000010101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 150921957 seed 111101011010011011000100100010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 151158506 seed 111101100010101101000001001101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 152433571 seed 111110001101100001000000111101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum


148 collision

there is such an effect that every number 2^20 1048576 (including puzzle 863317) selects 148 numbers at random

i.e.
1 > 148 num from 155117520 30!/15!/15!
2 > 148 num from 155117520 30!/15!/15!
3 > 148 num from 155117520 30!/15!/15!
...
500 > 148 num from 155117520 30!/15!/15!
...
1000 > 148 num from 155117520 30!/15!/15!
...
11111 > 148 num from 155117520 30!/15!/15!
...
123456789 > 148 num from 155117520 30!/15!/15!

from 1 to 155117520 / 148 = 1048091,351351351351351 = 1048576 2^20

it can be pondered indefinitely. if collisions occurred in the first iteration, and the rest of the numbers did not give collisions, but during the next iterations, other numbers will give collisions, and those that fell out in the first will no longer give collisions, until the cycle starts anew, but it will be with all the numbers already mixed, provided that we divide the space into steps-range (in principle, you can even count all possible start num for cycles that will begin by simply raising the length of the full cycle to itself, cycle^cycle (probably: D they constantly mix).

and if we take only collisions of the length we need (and the length grows simply by counting the number of permutations) in the example above

from
step 13358221 seed 000110100001011111100111001100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
to
step 99954219 seed 101000111100001101001101111000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum

what we can distinguish is the first 2 digits of them they follow

13358221
15244257
16213688
18099879
18762243
20871509
23071996
26961189
26971336
27218776
28383269
28675678
28744087
30778835
31839022
32561312
33557684
34368032
38741650
38820746
39398453
...
95453948
95652871
96650943
97087166
98801466
99036688
99088101
99954219

we can initially assume that with 99% (?) probability the first digits in the interval 10 to 50 or from 50 to 90... and with what probability the next 2 will be 10 to 50 end next (what does it even depend on)?

these 3 pairs have less than 50
15244257
16213688

but the main interest is if we select a seed of this length and select all possible combinations of 8 digits in a fixed step

i.e seed even endless but steps from 1 to 99999999 we will have to drop out various combinations for our 863317 (that is, the process will be repeated from 1 to 155117520 / 148 = 1048091,351351351351351 = 1048576 2^20)

and you can calculate how many all possible combinations will fall out, 99999999 > 2^26 or 155117520 30!/15!/15! ~2^27 (these are our steps from the endless seed)

2^26*2^26 = 4503599627370496 or 2^27*2^27 18014398509481984 something long steps turn out  Grin  Cry

but taking any number at random we have to catch the desired collision (one flew over the cuckoo's nest across the seed)

and we return to statistics, if other numbers have already dropped out, then when they give out a collision

we run along the endless seed but count the steps again (the seed itself continues to incrementally increase the count of its permutations)

the same thing happens with space 2^160 and 2^256

2^160*2^160 = 2135987035920910082395021706169552114602704522356652769947041607822219725780640 550022962086936576 (ohh my god)

2^256×2^256 = 1340780792994259709957402499820584612747936582059239337772356144372176403007354 6976801874298166903427690031858186486050853753882811946569946433649006084096

2^64×2^64 340282366920938463463374607431768211456 if we take any number 22 characters long (373 collision), we have to run through this space so that it gives a collision? although we take any 22 lenght number at random and start adding it to our step (0+number 22 characters long,pass 0 + 2^69-73, 0 + number 22 characters long, again pass 2^69-73, etc)? 340282366920938463463374607431768211456/2^66 = 4611686018427387904 steps , 19 lenght))  Shocked Grin the probability of success grows in proportion to the number of experiments, that is, programs launched with different numbers? which number will collide faster from 1000000000000000000000 to 9999999999999999999999? to think of something more interesting...  although here 22 characters 1000000000000000000000 ~ 69,76048999263460930528, 9999999999999999999999 ~ 73,08241808752197165315, there are even fewer of steps 340282366920938463463374607431768211456/2^69 = 576460752303423488, 340282366920938463463374607431768211456/2^73 = 36028797018963968, did we make a discovery?  Roll Eyes what is more profitable and faster to take numbers starting from 50-99, more precisely 99-50 for the run?  36028797018963968 ~ 2^55 vs 2^64 ?  Shocked

(76!/38!/38!)/2^64 373,6497140715840404646 collision
6892620648693261354600 22 num len
18446744073709551616   20 2^64
**____________________ 20
****__________________ 18
******________________ 16
********______________ 14
**********____________ 12
************__________ 10
**************________ 8
****************______ 6


50×50×50                      125000
50×50×50×50                   6250000
50×50×50×50×50                312500000
50×50×50×50×50×50             15625000000
50×50×50×50×50×50×50          781250000000
50×50×50×50×50×50×50×50       39062500000000
50×50×50×50×50×50×50×50×50    1953125000000000
50×50×50×50×50×50×50×50×50×50 97656250000000000

if we were looking for 6 digits, at the beginning, a little 7 digits were poured and 8 digits went

then from 6892620648693261354600 should fall out a little 21 lengths and pour out a lot of 22 lengths

Let me remind you that if we constantly choose a new step from the infinite seed, then our numbers will constantly start from 10 to 99

make a step 2^66 from endless seed we get a set of 22 long collision numbers etc.

18  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: November 22, 2021, 11:59:49 PM
something this damn shit doesn't want to give up  Grin maybe we can try to get in through ripemd160...

Quote
These stories abour lot's of BTC being lost are just legends


"from Russia with love"


Quote
The head of Qiwi told how the ex-employee secretly mined 500 thousand bitcoins at the terminals in 2011

In 2011, a former Qiwi employee received 500,000 bitcoins through the company's self-service terminals.

According to Solonin, the activity was noticed by the security service - its employees found that in shops where there are no people, at night the terminals work under heavy load and constantly transmit information. After a three-month investigation, it turned out that the technical director of Qiwi had installed applications for mining bitcoins on the terminals and had already managed to get 500 thousand coins.

Solonin demanded the return of the mined bitcoins, since the resources of the company were used for their production, but the technical director filed a letter of resignation and left the company. According to the head of Qiwi, in fact, there was no damage to the company: "there is no direct loss, it did not cause damage - only to landlords who pay for electricity somewhere out there."

Qiwi representatives told vc.ru that the employee who mined bitcoins was a developer, and he was named the technical director for better understanding among the MACS audience. At the same time, he could not use the mined cryptocurrency.

According to our information, these bitcoins were lost.
Qiwi Press Office

***

ripemd160

there is an opinion that to find all bitcoin, it is enough to run 160 bits of space (ripemd160 160 bit bin, 0123456789abcdef 16, hex 40 length)

an interesting point is that 256-bit space acts as a seed and collisions are obtained 2^256/2^160 = 2^96

the space of the puzzle is smaller and he also takes his numbers.

pz64 base58 <> hash160 converter

Quote
from hashlib import sha256
from base58 import b58encode

def get_address_from_ripemd160(ripemd_hash):
    #  steps from https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses
    h3 = ripemd_hash
    h4 = '00' + h3
    h5 = sha256(bytes.fromhex(h4)).hexdigest()
    h6 = sha256(bytes.fromhex(h5)).hexdigest()
    h7 = h6[0:8]
    h8 = h4 + h7
    h9 = b58encode(bytes.fromhex(h8))
    return h9.decode('ascii')

hash = '3ee4133d991f52fdf6a25c9834e0745ac74248a4' #returns 1F3sAm6ZtwLAUnj7d38pGFxtP3RVEvtsbV
print(get_address_from_ripemd160(hash))


#cat base58.txt | python3 address_to_hash160.py > hex.txt
import sys
from bit.base58 import b58decode_check
from bit.utils import bytes_to_hex

def address_to_hash160(address):
    address_bytes = b58decode_check(address)
    address_hash160 = bytes_to_hex(address_bytes)[2:]

    return address_hash160

print(address_to_hash160("16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN"))

#for line in sys.stdin:
    #print (address_to_hash160(line.rstrip()))

pz 64 16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN hash160 3ee4133d991f52fdf6a25c9834e0745ac74248a4

how uniform is the hash160 mixing?

for example, we will take in steps of 256 and look at what steps the symbols (hex 40) will fall out in space

3ee4133d991f52fdf6a25c9834e0745ac74248a4

first "3" second "e" third again "e" 4th "4" etc...

an increase in the number of permutations with an increase in the number of characters

16^1  16
16^2  256
16^3  4096
16^4  65536
16^5  1048576
16^6  16777216
16^7  268435456
16^8  4294967296
16^9  68719476736
16^10 1099511627776
16^11 17592186044416
16^12 281474976710656
16^13 4503599627370496
16^14 72057594037927936
16^15 1152921504606846976
16^16 18446744073709551616
16^17 295147905179352825856
16^18 4722366482869645213696
16^19 75557863725914323419136
16^20 1208925819614629174706176  
16^21 19342813113834066795298816
16^22 309485009821345068724781056
...
16^36 22300745198530623141535718272648361505980416
16^37 356811923176489970264571492362373784095686656
16^38 5708990770823839524233143877797980545530986496
16^39 91343852333181432387730302044767688728495783936
16^40 1461501637330902918203684832716283019655932542976

if we write all the dropped characters when stepping through at 256 steps (from 0 to 2^256 or 2^63-2^64)

then each of the 16 characters will fall out according to their hash mixing

something like

0 [2, 62, 90, 102, 124, 154, 182, 199, 209, 214, 232, 237, 246]
1 [10, 26, 46, 47, 92, 93, 117, 125, 151, 153, 155, 161, 179, 189, 205, 241]
2 [27, 31, 36, 57, 64, 87, 91, 103, 104, 122, 123, 132, 140, 141, 219, 223, 229, 240, 252]
3 [11, 20, 39, 44, 85, 108, 134, 142, 145, 158, 176, 186, 188, 212, 215, 220, 245]
4 [5, 17, 25, 67, 100, 111, 113, 118, 127, 135, 147, 194, 239]
5 [7, 13, 23, 77, 159, 187, 192, 197, 203, 226, 251]
6 [16, 19, 54, 60, 65, 66, 79, 116, 143, 162, 167, 191, 201, 211, 230, 238, 243]
7 [1, 3, 6, 14, 40, 78, 89, 128, 144, 170, 173, 177, 196, 221]
8 [21, 30, 70, 75, 80, 84, 98, 109, 119, 121, 171, 185, 190, 217, 218, 222, 225, 228, 255]
9 [8, 15, 35, 38, 42, 72, 74, 83, 107, 126, 163, 178, 180, 183, 193, 207, 249]
a [22, 59, 81, 112, 146, 150, 156, 160, 169, 198, 202, 231, 233, 235]
b [9, 33, 52, 58, 86, 94, 114, 115, 157, 227, 234, 244]
c [4, 24, 41, 43, 55, 61, 68, 71, 73, 82, 88, 96, 129, 152, 166, 168, 175, 181, 204, 206, 216, 248]
d [12, 28, 29, 45, 48, 51, 63, 95, 99, 105, 130, 131, 139, 195, 213, 224, 236]
e [34, 37, 56, 76, 97, 101, 110, 133, 136, 137, 149, 164, 165, 174, 184, 210, 242, 247]
f [18, 32, 49, 50, 53, 69, 106, 120, 138, 148, 172, 200, 208, 250, 253, 254]

0 [16, 18, 23, 27, 73, 99, 116, 129, 136, 140, 142, 158, 161, 182, 185, 186, 196, 199, 201, 212, 222, 252]
1 [26, 34, 53, 69, 75, 85, 91, 104, 123, 132, 148, 153, 171, 183, 191, 218, 221, 236, 237]
2 [14, 40, 42, 62, 71, 76, 84, 102, 124, 127, 155, 168, 205, 220, 227]
3 [61, 78, 100, 125, 164, 172, 181, 192, 228, 241, 247]
4 [4, 9, 47, 50, 58, 89, 90, 96, 106, 120, 152, 154, 189, 202, 211, 229, 233]
5 [1, 44, 83, 88, 112, 144, 146, 151, 175, 176, 197]
6 [2, 8, 11, 46, 48, 82, 108, 114, 119, 137, 143, 147, 193, 203, 223, 255]
7 [5, 13, 29, 37, 39, 56, 65, 66, 77, 86, 111, 130, 195, 206]
8 [10, 20, 38, 41, 52, 60, 87, 101, 117, 131, 145, 162, 194, 208, 210, 231, 235, 250]
9 [30, 33, 49, 59, 68, 72, 94, 105, 115, 126, 149, 163, 166, 167, 204, 207, 216]
a [22, 45, 57, 64, 95, 98, 128, 134, 141, 184, 190, 198, 213, 234, 239, 243]
b [19, 55, 63, 79, 92, 103, 110, 133, 165, 173, 188, 209, 226, 238, 245, 248]
c [32, 35, 70, 74, 80, 121, 139, 157, 160, 170, 177, 178, 217, 224, 230, 232, 246]
d [3, 7, 12, 25, 43, 51, 107, 122, 138, 150, 156, 174, 179, 244, 249, 251, 253]
e [24, 28, 67, 97, 109, 113, 118, 159, 180, 187, 215, 219]
f [6, 15, 17, 21, 31, 36, 54, 81, 93, 135, 169, 200, 214, 225, 240, 242, 254]

200

as you can see in step 200, the first and second symbols of the hash160 match "f", "f" the question is whether it makes sense to try to find some regularity in this distribution by collecting statistics

for example, after a certain number of popping out of all numbers, repetitions should begin are there any cycles here. and how to keep statistics hash drop-down sets for each individual character (for the first character out of 40 for the second out of 40, etc.) here 1 step means the distribution from 1 to 256 between 16 characters. the next step they mix and so on once they start repeating (both individual numbers and all sets, there is not a linear distribution of 16 for each of the 256 steps but so)

in the example above, where two "f", "f" matched 200, similarly the entire hash160 hex 40key should match.
19  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: August 04, 2021, 05:54:03 PM
collision test for pz 20

2^20 1048576, 20 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum | 863317

(24!/12!/12!)/2^20 2,578884124755859375
1048576 2^20
2704156 step
2 collisions, finds only 1 for some reason

(28!/14!/14!)/2^20 38,25817108154296875
1048576 2^20
40116600 step
38 collisions, why is it 43...

step 565214   seed 0000011001110101101110001110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 1269043  seed 0000101111000101110001110011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 1816300  seed 0000111100111010110010100101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 2886941  seed 0001011011010100110001100111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 3376293  seed 0001100111100010001011111100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 4307993  seed 0001111100011000111000110110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 5007146  seed 0010010010001011010111001111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 5488783  seed 0010011101100101001111110000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 6365709  seed 0010110010111101010100101001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 7330410  seed 0011001010001111010100011101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 8876578  seed 0011101100101011000110011001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 8937380  seed 0011101110000010110101011100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 9402193  seed 0011111000110001011110011000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 9785819  seed 0100000110000011101011011111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 10747091 seed 0100011110110000101110110010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 11895627 seed 0100111010000100011101011101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 11905033 seed 0100111010010000011001111101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 12211211 seed 0101000010010111100111010101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 12277674 seed 0101000011111100111001000110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 14709359 seed 0101111011001011001111000000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 15764971 seed 0110010101111111101000100000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 15843680 seed 0110010111100110101001011000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 15900143 seed 0110011000111110010011000110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 17155504 seed 0110110101001000010110111010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 17858310 seed 0111000110101101110010010010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 21522266 seed 1000101000111001001110001111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 23500878 seed 1001010110110010100110000111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 23833593 seed 1001011110000011100111000011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 24985276 seed 1001111000011011000101111000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 25327445 seed 1010000010101101110011010011 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 26246246 seed 1010010111101001010111000001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 26556823 seed 1010011110011010110001101000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 28067683 seed 1011000010101110001101110010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 28359337 seed 1011001001000000110011111101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 28899884 seed 1011010100111100010011110000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 32201625 seed 1100101000111000110100110110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 32409102 seed 1100101101001110011100110000 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 33586060 seed 1101001001100011001100001111 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 33958451 seed 1101010001111011000100100101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 36614769 seed 1110010101010100011111000100 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 36700341 seed 1110010111010100010111000010 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 36918609 seed 1110011100101011000010100110 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 37574368 seed 1110101100111010100010010001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum



Quote
import random
from bit import Key

list = ["1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum"] # pz 20 > dec 863317

def lexico_permute_string(s):
    a = sorted(s)
    n = len(a) - 1
    while True:
        yield ''.join(a)
        for j in range(n-1, -1, -1):
            if a[j] < a[j + 1]:
                break
        else:
            return
        v = a[j]
        for k in range(n, j, -1):
            if v < a[k]:
                break
        a[j], a[k] = a[k], a[j]
        a[j+1:] = a[j+1:][::-1]

a1="1"*14
a2="0"*14
a3=a1+a2 # seed str
    
s = a3 # seed str 000000000000000111111111111111
sv = lexico_permute_string(s)

count0 = 0

for line1 in sv:
        
    s = line1#[0:30]
        
    count0 += 1
    random.seed(s)

    Nn = "0","1"

    RRR = [] #func()

    for RR in range(20): # "bit" set
        DDD = random.choice(Nn)
        RRR.append(DDD)

    d = ''.join(RRR)
    b = int(d,2)
    if b >= 1:
        key = Key.from_int(b)
        addr = key.address
        if addr in list:
            print ("found...........","seed step from 000000000000111111111111 to 111111111111000000000000","step",count0,"seed",s,"bit",d,"dec",b,addr)
            #s1 = str(b)
            #s2 = addr
            #f=open("a.txt","a")
            #f.write(s1)
            #f.write(s2)      
            #f.close()
            pass
        else:
            pass
            #print ("step",count0,"seed",s,"bit",d,"dec",b,addr) #print (X,sv,len(sv),dd,len(dd),b,addr)

print("pz end")
input() #"pause"
 

for 64 ...

(188!/94!/94!)/2^64 1235956206315626091331338051467874028
18446744073709551616 2^64
22799367824217315491046998779230288685596678611381812000
1235956206315626091331338051467874028 collisions
                                    
(168!/84!/84!)/2^64 1246690648845973918331482456337
18446744073709551616 2^64
22997383338348585032434609379579328145757058837400 168!/84!/84!
1246690648845973918331482456337 collisions
                              
(148!/74!/74!)/2^64 1266470970702566355349691
18446744073709551616 2^64
23362265873332749085315221863910685052043000 148!/74!/74!
1266470970702566355349691 collisions
                        
(128!/64!/64!)/2^64 1298394228608800905,709 collisions
18446744073709551616 2^64
23951146041928082866135587776380551750 128!/64!/64!  
1298394228608800905 collisions
                  
(100!/50!/50!)/2^64 5469330747,064212325444
18446744073709551616 2^64
100891344545564193334812497256 100!/50!/50!
5469330747 collisions
          
(80!/40!/40!)/2^64 5827,977463326783892683
18446744073709551616 2^64
107507208733336176461620 80!/40!/40!
5827 collisions

(70!/35!/35!)/2^64 6,081630306594410506193
18446744073709551616 2^64
112186277816662845432 70!/35!/35!
6 collisions

(68!/34!/34!)/2^64 1,542442469063799766063
18446744073709551616 2^64
28453041475240576740 68!/34!/34!
1 collisions

the best option? (128!/64!/64!)/2^64

because 1 (68!/34!/34!)/2^64 may not exist, how to search 6? (70!/35!/35!)/2^64

112186277816662845432/6 = 18697712969443807572 (~ 2^64)

take the first step randomly and add to it 5 times dec 2^64...

or looking for "mathematical expectation" yeah monkeys are writing a book

it is not clear why because 256 bits can be different

bit to character sampling ratio

1111 11111111 1111111111111111 11111111111111111111111111111111...

Quote
import random

def lexico_permute_string(s):
    a = sorted(s)
    n = len(a) - 1
    while True:
        yield ''.join(a)
        for j in range(n-1, -1, -1):
            if a[j] < a[j + 1]:
                break
        else:
            return
        v = a[j]
        for k in range(n, j, -1):
            if v < a[k]:
                break
        a[j], a[k] = a[k], a[j]
        a[j+1:] = a[j+1:][::-1]

a1="1"*300
a2="0"*300
a3=a1+a2
    
s = a3#"11100000000" #000000000000000111111111111111
sv = lexico_permute_string(s)

count0 = 0
count1 = 0
count2 = 0
count3 = 0
count4 = 0    
for line1 in sv:
        
    s = line1#[0:30]
        
    count0 += 1
    random.seed(s)

    Nn = "0","1"

    RRR = [] #func()

    for RR in range(256): # len bit set
        DDD = random.choice(Nn)
        RRR.append(DDD)

    d = ''.join(RRR)

    v1 = d[0:4]
    v2 = d[0:8]
    v3 = d[0:16]
    v4 = d[0:32]
    if v1 == "1111":
        count1 += 1
        #print(count0,count1,v1,s)
        if v2 == "11111111":
            count2 += 1
            #print(count0,count1,count2,v1,v2,s)
            if v3 == "1111111111111111":
                count3 += 1
                print(count0,count1,count2,count3,v1,v2,v3,s)
                #print("")
                if v4 == "11111111111111111111111111111111":
                    count4 += 1
                    print(count0,count1,count2,count3,count4,v1,v2,v3,v4,s)
                    #print("")
              

 

***

or take for each puzzle the same ratio of collisions to length (as far as possible), look at the graphs for the distribution of collisions and search in possible areas... although there is a freaking random and there is not much sense from this.
20  Bitcoin / Bitcoin Discussion / Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it on: July 28, 2021, 06:59:46 AM
@Andzhig And if we increase one more character of address 16jY7qLJn & 'x' then most binaries are started from '111'

few examples -

16jY7qLJnxLQQRYPX5BLuCtcBs6tvXz8BE   1110000000100110101001101101010100100011010011001000100000110110000   7013536A91A6441B0
16jY7qLJnX9uchnyf26t3QJnsUf78Xdikb   1110010000101000111010000001111110010000001011001101111011100000   E428E81F902CDEE0
16jY7qLJnX9eX8j612s8fnbn6uzR48xjua   1110100000001101111010110011001110101001011001111010000010001111   E80DEB33A967A08F
16jY7qLJnx2EZZumnYFke3GutCrRnHKs1M   111010110100110101001101101010111010101000110011101011001010110000   3AD3536AEA8CEB2B0
16jY7qLJnx2ixrxCnTLSraerkgyB3YYAiT   1110110111111001110011010110000000110101011011011100110000011001   EDF9CD60356DCC19
16jY7qLJnxHBp3dqwV2kzYq1LucfZzgxsH   1110111010111001101010110011001101001101111100100111011100001101   EEB9AB334DF2770D
16jY7qLJnX2cZXJ78wV1ef42e7cLAZJ1Vn   1111111000101000011001011100011011011011111111101100001110000011   FE2865C6DBFEC383


Could this also be some logic?

it is difficult to say that experiments are needed, but soon there is none. otherwise it's too easy.

16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN base58 , 58 characters 123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz "x" we know. 2 after "x" and 24 after

how many possible addresses after "x" 2×58×58×58×58×58×58×58×58×58×58×58×58×58×58×58×58×58×58×58×58×58×58×58×58 = 4200508241814704971052461011661183822856192 (2^141)

***

Quote
How many characters are in the private key in binary?

we have 64 bit address 2^64 , 64 characters 1 and 0 randomly located (which are not known to us)

***

collisions and with such spreads slip

__1111111111_1100000000_0_0_00', ',_, >', 6, '001111111111011000000001010100 1111111100000000
1_111_111111_11000000_0_0_0000', ',_, >', 6, '101110111111011000000101010000 0000000011111111
11_1111_111111_000000_00_0_000', ',_, >', 6, '110111101111110000000100101000 1111111111111111
1111_1_1111_1110000_000_0_0000', ',_, >', 6, '111101011110111000010001010000 0000000011111111
11111_111_111_1_0_0000_0000000', ',_, >', 6, '111110111011101101000010000000 1111111111111111
111111111_1_11_000000_0_0_0000', ',_, >', 6, '111111111010110000000101010000 0000000011111111

000000000_000___1111111111__11', ',_, >', 6, '000000000100011011111111110011 0000000000000000
00000000__000_0111_1111111_11_', ',_, >', 6, '000000001100010111011111110110 1111111100000000
0000000_000_0_0111111111__111_', ',_, >', 6, '000000010001010111111111001110 1111111100000000
00000_0_0000_00111111_111_111_', ',_, >', 6, '000001010000100111111011101110 0000000011111111
0000_000000000_111111_11111_11', ',_, >', 4, '000010000000001111111011111011 0000000000000000
0000_0000_0_0001_111_1111_1111', ',_, >', 6, '000010000101000101110111101111 0000000000000000
0_000000_00000_111111_11111__1', ',_, >', 6, '010000001000001111111011111001 1111111100000000
_00_0000000_00011_1111111_1_11', ',_, >', 6, '100100000001000110111111101011 1111111111111111

i.e. 3 there 3 here (and 2 1 times)

but the whole enumeration of their 4 parts is too long

111111111111000 all permut 455 000000000000111 all permut 455, (15x15 = 30 seed, 455x455 = 207025) 207025×207025×207025×207025 = 1836923935996687890625 step

but can this be repeated when seed 78 len (1 seed for 64).

39 x 39 - 78
000000000000000000000000000000000000111 all permut 9139  111111111111111111111111111111111111000 all permut 9139, 9139 x 9139 = 83521321

still need to see if instead of 16 to 8, take (8x8) whether the chance of random catching increases.

***

1 by 2 ran empy, by 3 runs...

000000000000000000000000000100000001010101111011111111111111111111111111111110 78 1101011100110011010001001001010010000011111101100110011111110010 64 15506813346626562034 14rydssuUnBn2bDeDRwjRxn546iuYq5s8n
000000000000000000000000000100000001010101111011111111111111111111111111111011 78 1110110010100000011011001101111010011011010110010100100010100111 64 17050747892569557159 13kzS77Upy2EqPtSybbGmoYzZMXtAGtkVm
000000000000000000000000000100000001010101111011111111111111111111111111110111 78 1011000001001110010110100111110101011101010011101101111100000101 64 12704191093341609733 1FEDNb3vX4pkfHboWWuodggQdRSW5jA3ey
000000000000000000000000000100000001010101111011111111111111111111111111101111 78 1010111101000001100001001110101111000001100011001011011100110110 64 12628520978222987062 152M84nqWb66tJpueESC2XaFUCPq9HcsW4
000000000000000000000000000100000001010101111011111111111111111111111111011111 78 1101011101001100001101011101101001101000011001100000101100011011 64 15513834028555176731 15gV7VfkWFg9LdLcaYE2iL7q1t923uM7Dc
000000000000000000000000000100000001010101111011111111111111111111111011111111 78 1111100011010101010100010001000001001000110110101000110100010101 64 17930326621829106965 1NMJUq3TfTzW3846bC9kijhF1r77K7UhWY
000000000000000000000000000100000001010101111011111111111111111111101111111111 78 1110111101110101001100010100110001010001111100100011111101100110 64 17254751751202029414 1NYCF4WV6aD1Mz9VmFs9jXTjb8CFgzV7G4
000000000000000000000000000100000001010101111011111111111111111110111111111111 78 1110111000101011001001001111111011101010110010101111000101100101 64 17161851482304868709 1BDBLPttExoSwJDw7LbNWAsZ1JKdkLwwmE
000000000000000000000000000100000001010101111011111111111111111101111111111111 78 1011000001001101110100111011000011000110110110100110010100111010 64 12704042880085943610 13uodKaP1yYG2qUGrdUFTLDnZoTPV3GDqY
000000000000000000000000000100000001010101111011111111111111111011111111111111 78 1011000110110111101001100111001001101000100000011111100000100111 64 12805887075761125415 1En1yWAp8bP8s5Wsi3LnRVx9tfN2ABtNV5
000000000000000000000000000100000001010101111011111111111111101111111111111111 78 1100010001000110101010110011011011101100110111011010111111100111 64 14143179932194156519 1BuXVR46gQXHbo1n4UpUajbpHsE3oYYfsM
000000000000000000000000000100000001010101111011111111111111011111111111111111 78 1001110011100000001100010100100011101111111010110100101101110100 64 11304089254032526196 1HAo6Xq4N4nsS2r3ESt7Gzxs68EK6sqKZM
000000000000000000000000000100000001010101111011111111111110111111111111111111 78 1100001110111000110010011000111001111101101110000101011111000100 64 14103243846942480324 1KVPGV3irrQK2fXy9xbB5k44GehXhAhmM9
000000000000000000000000000100000001010101111011111111111101111111111111111111 78 1001110111110111101110011001100100010011000111010000011001110110 64 11382770650304022134 1GB6gXhhUFhhebYEARknDXCFgk5XzXaaBb
000000000000000000000000000100000001010101111011111111101111111111111111111111 78 1110000101111010110101101100110100000000111110100010101001111000 64 16247534781665520248 1Gkuxy1DhJYzHxCxNrmYQxmGCHj8c4KWVt
000000000000000000000000000100000001010101111011111110111111111111111111111111 78 1100011011001110000111101000100001100011000011000110000101110101 64 14325421035838267765 1GuL9fLofPMNNeT7rqmUezpDAKKuBgvL1T
000000000000000000000000000100000001010101111011111011111111111111111111111111 78 1010001111101100100001011111000011001100000111001100001100110110 64 11811963191949050678 1Cq9nGaqmP8bUUBKBFQqkC5nQ1Q2tpuoNF
000000000000000000000000000100000001010101111011110111111111111111111111111111 78 1110100011101110101011100111101110101110000011111011101110000001 64 16784544707480894337 1FBSMs5GU6pkd5QSCXYecRqbxvAhpZuL5C
000000000000000000000000000100000001010101111011101111111111111111111111111111 78 1001111101001000000110000110010111100110000000100001101011000011 64 11477450476283370179 1CAPXky8N3AqJwgKnv1vN9McC112ZZdw8m
000000000000000000000000000100000001010101111010111111111111111111111111111111 78 1000011001100111100100010011111101011101011000111111000111110001 64 9684869225019339249 1LUHZkGEBqXVtaN5MuFnvUrdEHf5B928jY
000000000000000000000000000100000001010101111001111111111111111111111111111111 78 1011001110001111001110100001101110101100111100011100001000111000 64 12938624144998777400 1MJxoDoa9kYFn4pdKeAi7gA83ZoPqvic9x
000000000000000000000000000100000001010101110111111111111111111111111111111101 78 1011010110100010010011110000010010111011001100100110101011001011 64 13088110348831189707 1JXNK2J6trmBQRMHDKgB8K8FYe7XPaneHa
000000000000000000000000000100000001010101110111111111111111111111111111111011 78 1001100010001010100001100000001000101110101000101010011010110010 64 10991745184481584818 12RXgtZZpaKXs2fX6whvs2ojceDRRyDZwP
000000000000000000000000000100000001010101110111111111111111111111111111110111 78 1100011110010010111100000011101010111010110010100010101111011110 64 14380820695179996126 1D2pcWu62Y3SJfejsgHXEKtNsAtvZGNtWK
000000000000000000000000000100000001010101110111111111111111111111111111101111 78 1010000011000101010011101111000111001000101100101111000000001101 64 11584752416841723917 1DX6NzYW2grMLGCUft1LBbFxm39nqEA9Ae
000000000000000000000000000100000001010101110111111111111111111111111110111111 78 1011000101010010010001111101000100010010101011100010011100111010 64 12777354056090658618 1N3Ku5oR3C88xVgm6VVquNs7JfnSk2xvZk
000000000000000000000000000100000001010101110111111111111111111111111101111111 78 1000010011001011110100110010011010001001101100110111111100011100 64 9568973995751210780 1NwpUf69nR9CTuNcWgKFXY7EuewSqTAtTS
000000000000000000000000000100000001010101110111111111111111111111111011111111 78 1101001001100011101001100110111010001001011110001010101001111100 64 15160143764342221436 19wQikrohsLzKDnwX8F4Ag6NCTxQ2fEpGE
000000000000000000000000000100000001010101110111111111111111111110111111111111 78 1000001111100101011101100100100000001010100111001100000111101000 64 9504132640423068136 1GmLqntzgCukjzF7xTzfjXLN8oDunwChkk
000000000000000000000000000100000001010101110111111111111111111101111111111111 78 1011011100101001000011011101000011111001011100010000110011111110 64 13198095374175243518 18zhvaSdwVmcAhorEYtfpHTGG8wB8jdWKV
000000000000000000000000000100000001010101110111111111111111110111111111111111 78 1001101111000001000000110011011111011101111110100011100001000110 64 11223255284866234438 19mCEpHUanT1J7hDbdyMgqCZUHLWeSb5xU
000000000000000000000000000100000001010101110111111111111111101111111111111111 78 1111001000011010100011100111011110011101001000001110101000000101 64 17445412750961469957 18VcFdKicFFqjKAXWRqd8zGXi43S4Rq2NM
000000000000000000000000000100000001010101110111111111111111011111111111111111 78 1000111001111000000010111100000111001111010111010001000011011000 64 10265968277626622168 1cTZzdVCNg8NG4a9xoQXgkWD4muJkppGa
000000000000000000000000000100000001010101110111111111111110111111111111111111 78 1001001001011111111110100101000110110001011001100000001011001110 64 10547424081100538574 1PZgpSVPtZDen8bBAMSrJ5gxcqUyFAqsQ4
000000000000000000000000000100000001010101110111111110111111111111111111111111 78 1000000000110101101000110110111101111010110001010101111100110111 64 9238469909816893239 19osC5SyTMdPY18sbjLuYuT44HppxXT28k
000000000000000000000000000100000001010101110111011111111111111111111111111111 78 1001111100000011000110001000001101001100110001110000100001101011 64 11458028829168568427 1HqH8xuq3WqsJxTE7QAu6iBDsPENzMJt6H
000000000000000000000000000100000001010101110101111111111111111111111111111111 78 1111000111100111110011001111011100111011001010111100011111001011 64 17431126244982507467 1BUVWY4UkZ39ZSZmiwe9fAPTwvZ3n6osK7
000000000000000000000000000100000001010101110011111111111111111111111111111111 78 1111111110111001001101110011011100111010000011000000000011001001 64 18426820060699689161 1Eqc7UPgWRPJidsvt3EhKZ6jNWkfdMFKrN

Quote
from os import system
system("title "+__file__)
import random
from bit import Key


def Permute(string):
    if len(string) == 0:
        return ['']
    prevList = Permute(string[1:len(string)])
    nextList = []
    for i in range(0,len(prevList)):
        for j in range(0,len(string)):
            newString = prevList[0:j]+string[0]+prevList[j:len(string)-1]
            if newString not in nextList:
                nextList.append(newString)
    return nextList

def Permute2(string2):
    if len(string2) == 0:
        return ['']
    prevList = Permute(string2[1:len(string2)])
    nextList = []
    for i in range(0,len(prevList)):
        for j in range(0,len(string2)):
            newString = prevList[0:j]+string2[0]+prevList[j:len(string2)-1]
            if newString not in nextList:
                nextList.append(newString)
    return nextList


list = ["16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN"]


for X in range(0,1,1):
    
    random.seed() # seed initiation () random or (X)
    
    string = "000000000000000000000000000000000000111" # initiation seed len
    sv = Permute(string) #''.join(random.sample(s,len(s)))
    string2 ="111111111111111111111111111111111111000" # initiation seed len
    sv2 = Permute2(string2)    
    for elem in sv:
        for elem1 in sv2:
            sv3 = elem+elem1
            
  
            random.seed(sv3) #string

            Nn = "0","1" #"0","1"
            RRR = []

            for RR in range(64): # pz bit range
                DDD = random.choice(Nn)
                RRR.append(DDD)

            d = ''.join(RRR)
            #print(d,len(d))
            
                
            b = int(d,2)
            if b >= 9223372036854775807:
                key = Key.from_int(b)
                addr = key.address
                if addr in list:
                    print ("found!!!",b,addr)
                    s1 = str(b)
                    s2 = addr
                    f=open("a.txt","a")
                    f.write(s1)
                    f.write(s2)      
                    f.close()
                    pass
                else:
                    #print (X,"seed mask len",len(string),string,",","64 bit pz",dd,",",b,addr)
                    print(sv3,len(sv3),d,len(d),b,addr) #print (X,sv,len(sv),dd,len(dd),b,addr)


***

can be 32 more out of 46

11111111111111111111000
00000000000000000000111 23+23 (1771×1771 = 3136441)

11111111111111110000000000000000 x2 32

3136441×3136441 = 9837262146481 steps ,for a long time

and it is problematic to analyze in a few hours only 3 seeds found

    steps                         32 bits                                                       seed
169382696 11111111111111110000000000000000 0110111111111111111110000000000000000100011010
244507506 11111111111111110000000000000000 1111000111111111111111100000000000000001100100
244854754 11111111111111110000000000000000 1111001001010111111111111111100000000000000000

***

crap may be if "111111111111000 all permut 455 000000000000111 all permut 455, (15x15 = 30 seed, 455x455 = 207025)" 207025 everyone crawls here from surplus (16 bit, from 000000000000000 to 1111111111111111) 65536 i.e. 455^2 > 2^16. and to get for 64 bits it is necessary to have more "000000000000000000000000000000000000111 all permut 9139  111111111111111111111111111111111111000 all permut 9139, 9139 x 9139 = 83521321" 9139^2 need such a number so that it is also more than a 64-bit puzzle. and these are huge numbers something around this 25000000000^2 = 625000000000000000000. but maybe it doesn't work that way.

***

all permutations are considered factorial

256!/128!/128! = 5768658823449206338089748357862286887740211701975162032608436567264518750790 2^251

30!/15!/15! = 155117520, all 4 by 4 permut 155117520^4 578953136014989894775911260160000 and they have 1000^4 provided that we all 4 pebble.

578953136014989894775911260160000
1000000000000

partially which also got here

"collisions and with such spreads slip"
__1111111111_1100000000_0_0_00', ',_, >', 6, '001111111111011000000001010100 1111111100000000
1_111_111111_11000000_0_0_0000', ',_, >', 6, '101110111111011000000101010000 0000000011111111
11_1111_111111_000000_00_0_000', ',_, >', 6, '110111101111110000000100101000 1111111111111111
1111_1_1111_1110000_000_0_0000', ',_, >', 6, '111101011110111000010001010000 0000000011111111
11111_111_111_1_0_0000_0000000', ',_, >', 6, '111110111011101101000010000000 1111111111111111
111111111_1_11_000000_0_0_0000', ',_, >', 6, '111111111010110000000101010000 0000000011111111

000000000_000___1111111111__11', ',_, >', 6, '000000000100011011111111110011 0000000000000000
00000000__000_0111_1111111_11_', ',_, >', 6, '000000001100010111011111110110 1111111100000000
0000000_000_0_0111111111__111_', ',_, >', 6, '000000010001010111111111001110 1111111100000000
00000_0_0000_00111111_111_111_', ',_, >', 6, '000001010000100111111011101110 0000000011111111
0000_000000000_111111_11111_11', ',_, >', 4, '000010000000001111111011111011 0000000000000000
0000_0000_0_0001_111_1111_1111', ',_, >', 6, '000010000101000101110111101111 0000000000000000
0_000000_00000_111111_11111__1', ',_, >', 6, '010000001000001111111011111001 1111111100000000
_00_0000000_00011_1111111_1_11', ',_, >', 6, '100100000001000110111111101011 1111111111111111


apparently because here "455x455 = 207025" < 65536 (2^16 all bit)

but if we take

84!/42!/42! 1678910486211891090247320 < 18446744073709551616 2^64 the puzzle fits here but will he end up in the desired area

42!/39!/3! = 11480, 11480x11480 (42+42= seed 84 > 64 bit) = 131790400 , 131790400 vs 18446744073709551616

option to increase the ratio to repeat the experience with 16 of 30

4000!/3997!/3!)^2 = 113607203534224000000 (207025 < 65536, 6 len vs 5 len) 21 len vs 20
or
(42!/28!/14!)^2 = 2794203818390077646400 (207025 < 65536, 6 len vs 5 len) 22 len vs 20

probably this is how it works... but maybe not)))

***

how many fits 4 out of 30

2^4 = 16 (from 0000 to 1111)

for each about 31000 seeds 30, and for all 16 approximately  16x31000 = 499114  (although if 30!/15!/15! = 155117520, 155117520 / 65536 = ~2366 should be for 16, x4 from 30, and 155117520/16 =9694845 for 4 x16 from 30)

if all 16 iterate over 1×2×3×4×56×7×8×9×10×11×12×13×14×15×16 = 39055874457600

a chance for good luck? 31000^16 = 727423121747185263828481000000000000000000000000000000000000000000000000

how to guess 16 parts in correct sequence from 31000^16 or 8 random to take the rest 8 to rearrange all combinations... with the same success, can simply duplicate everything from 0000 to 1111 and randomly choose))

blablabla
000000000000101111111111111001 0000
000000000000111111101011111011 0011
000000000001011101110111111110 1111
000000000001011101111110111101 0011
000000000001011111111011010111 0011
000000000001101001111111111101 0111
000000000001101011010111111111 1111
000000000001101111111111101100 1010
000000000001110011111011111011 0111
000000000001111100111011110111 0100
000000000001111111010111101110 0111
000000000001111111101111011001 1100
000000000010010111111101111110 0010
000000000010011101101111101111 1000
000000000010011111111011110011 0101
000000000010011111111100011111 0001
000000000010101110011111101111 1010
000000000010101110111001111111 1101
000000000010101111011101011111 0101
000000000010110110111110011111 1110
000000000010111100111111101101 1001
000000000010111111110100111101 1000
000000000011001011101110111111 1111
000000000011001011111111110110 0000
000000000011001110110111111011 0011
000000000011001110111110111101 0100
000000000011010011110101111111 0110
000000000011010111110111110110 0111
000000000011011010111001111111 0111
000000000011011010111110101111 1110
000000000011011101111011111100 1010
000000000011011101111110100111 0000
000000000011100011110111111101 1101
000000000011100101011011111111 1100
000000000011100110111111100111 0101
000000000011100111011101111011 0011
000000000011101001111111011110 0001
000000000011101010111101111101 1100
000000000011101011011101110111 1010
000000000011101101001111011111 0011
000000000011101101111111011100 0100
000000000011101110010111111011 1001
000000000011101110111011011110 0010
000000000011101110111101111100 0110
...
111111111100000000100111001000 1000
111111111100000001000000111010 1100
111111111100000001101000101000 1010
111111111100000001110000011000 1101
111111111100000010110010100000 1110
111111111100000100000100011100 0011
111111111100000100011000101000 1001
111111111100000100100100100001 0101
111111111100000101001000100010 0100
111111111100000101100100000001 1000
111111111100000110000100000110 1110
111111111100000110001100001000 1011
111111111100000110010100000001 0111
111111111100010000001100101000 0110
111111111100010011000000001001 1010
111111111100010011011000000000 1100
111111111100100001000001101000 0001
111111111100100010001000101000 1001
111111111100100110000100000100 0100
111111111100101000000100001100 1011
111111111100101000010010001000 0110
111111111100110000000100010100 1101
111111111101000001010000000110 1011
111111111101000010100100100000 0100
111111111101001000000000101100 1001
111111111101001000000010000011 1111
111111111101001000010010000001 1001
111111111101010000000010100100 1100
111111111110000000000100011100 0001
111111111110000000100001010100 0111
111111111110000001011010000000 0100
111111111110001000000110000001 1110
111111111110001010100010000000 0101
111111111110001100000000000011 0010
111111111110001110000000000100 1100
111111111110010000000000110001 1010
111111111110010000000010100100 1111
111111111110010000000100100001 1101
111111111110010011000000001000 0000
111111111111000000010001000010 0010
111111111111000001001000000010 1101
111111111111010010000010000000 1101


if not all 16 mix, then you need to guess 1 of the first 4 of 16 or just randomly beat all

in general, need to read Knuth's books, maybe there are some ideas...

and where "collisions" can be hidden

2^256 115792089237316195423570985008687907853269984665640564039457584007913129639936

280!/140!/140! 9254907226247087987824475869322170638984082742378874048534193150547106114131047 0440

300!/150!/150! 9375970277282745279319375443906408487923265570008135892047235271297517002183959 1675861424

600!300!/300! 600!/300!/300! 1351079419961942685144748779785045303972339454491934799259657217864741504080057 1696195048019827446981867333413136583724904390049076115159169530842704853694762 1976068789875968372656

65536!/32768!/32768!
6244451173709303839677735352736393808643926541430499952680244622304945024766277 7348251162415824434780833837869384615282491294253208186955690035235723070374467 4547331888238220028526071339188932518445883598263647876265467953874357843495195 2609291609751497259993259479390478830808924706942831021289260260274393594628484 5056896441270822212678895027372103914835658926543702135628990076488623868794509 1676041618986416584638240808113954858472321471228586928680407543030967081765605 5178073758957566613950687127038106584702532827680236501469260459526532972322245 7536423165518869006613233189617798562895781407747174750816140765117697238954400 0806284820988697277572181641368961081836496386013323385876280777020741824583294 0943627001064661727429599359224342815252518781202737797364649728386951411824995 2697857412291840197060142937787086514872614873117782753233929638085189306956633 5298714746876887058731821784595021357020768468301863908134826821764883742939355 1961704296048433347886148467375682317158459509192681335206391557812557340167584 0269845825325683896422234765075057614000395790045419995130894297966109932242925 0722160109241751756684865945983483884785875298631514063541613431202490323118412 3811246712095786897201651895766340378689843615323696697711789471017752066851747 6579073191467928423660555245869228576060405089735108103438699903219872786478608 0876560141311964969191570679496861478328596867536933134288866775792542625471786 1006024196039040785562214879850927924931403108762574519617145396029843070879526 9466790425482345125350690157357218473809567340636481289139633498415671867263639 8228066459889242946718197150793742060169613916749074824702391043501866264397460 7115428127603209487738958889196749783739042431621693157692404199837103708655989 9423983679353489127299174965402802532948561431977724870913964228120436365678597 6708140032340144230602290043540120952109151341981784322206484856082161650678411 4287274444913314050683463977234965591832114948844483158231720543864565722917256 8171404585792517641292933668504363860030951629985663000486219176214724742099051 6503710393613325647934942114299502595393632368802711150430057638139195487055452 2758446617798591394343391777313433835959852349559231805798461886409983764253042 9000517854226216328271022394434250772626807274287316949283568995031582667489458 6454651577123016722863434127233600245731629132901900402818790989706383170556203 6712520998074699060506426454664882562536053268393738879207937123122726879425991 4679792109181326479247614466303643013944127126443645085777262553879422568235639 2671544966999060986167305651013917834551295029450913949643835132830176343526752 1602215541438157717100313235321009127938122473998423197984739809346409730754287 7359338043604163727907869527036631661990403945682254367828136269511010335694208 2599027283413201384355430433534394905767658643729733568929071523757442069286246 1389498985141177936623655228718785683453323046829094861034619526634307003689436 1046096287843211464194302145985485527178930297993254947070524308964891713727428 3810158985858950127139366258118836629009311676983714092549117897421711225062835 3155289289633517777785508303170501999042341964824891257173416128138024143622867 4588283053953458459799380663048558976940415090485165209557260386983258038607655 2711373196821546688677311114097903886623233945355300552022845261926960461417644 7857606646918960544104167750054154902382083916925333869634028593607127565931607 7532218679940622790683146829703922622845851487423206680269112526578060799496003 8457559288867056763811481063822530900257027278441721621038501094026099974322840 5818130403932450642607696713971785728340998897093295807057081967311151909218817 3276707112268189706820195839872396610239060119842444683983660230336949551082594 2121916043204834281653924782437102266179368317481447977361503064739023250712240 4087334178294246355714099311367769655266431882414925743099900435650660307631056 7261427501989070964315695722034484896339719731353725801324298557301891779199796 9407508987480499863926998969216602695400700234393530241420466378805328142751592 0836429448587697876553093510774480791173803218861586074046305466955377402536514 7969098349884445031107632486398687330876394117455566664456846988353979166861660 2168322042775095812414800477947039015496832246902175004497324885784943877455480 4856020917686537888031907080190153246259716204031521011714753857134930326088089 1191134624459130659702431621823305276269590940610608062018399543299045702835499 1408710179744056281921292456248327927303695815182272728539322287308581069902228 6608819380318539114052534122453791597341196608792893908747771677165083955970327 3377453234181668039182785172382461272432987501949573618991542560257793180373318 6512006279662570034036422064292632970758859466498449972822334992922531121270232 7529704374028809174181717841593296819398550834797540715446846827236451222212067 2928879424422590607319012479963399043037016285225021272690831818614497103262501 2924853263058026865823571386421678424400915297719713185356231634997413654534345 4020287353855140684729006513805911471032301232721733251297669424833978780780640 7540817363599694802040042685908343884272005693646916852875835752961578679538692 2964651578129420921200526686887858990339452039836197158356638611618918796043744 5353881155405077495225991221301385359086968733735512270984824249476165954394806 1167750177610768693682609896679539917894515483870119153587421146987628007848151 7444446760418685780463440864483903850586250497223934318872796590377227164387909 3448349808037691921411651139041925885617020545441852728159406841462834090553630 3031271004428296336747286943939713348408485702947410337079131131329540726330724 3651096713701035806298642628470050779609206896342924457929499346973984911195100 8835415121080456977077782614671491546851628220164745151297222053286151249249048 2452343215441193636197986337803145450308568697988813896580373137718114450340189 4362612009945938364778657657333452792981683257500261507585272301504002195323428 4557891216169179358980034187010355394282963131337280104259317910912136102105604 8110455036107900131917611532377049605509880514816910416918542204324039173376225 3286488497108518986843037562813217073462202155852979324379220164532761969607798 8360953962219826862667919486881774665269105535630839444363767329525361377352878 8978815366231073151775322648085533291216219753027064758575444982103812736038404 2483305659694253939386267220871236945921311991888946104796945211592321158452872 2515954024233499684935588876541582125894974310591293248502240787334513485611255 1448132405009785208423367173450305465337688539559954565101159419765518273757074 6190130590898435832661812030320211683361472661390955517057524995577986560805386 0413494808398017434625373525174062228849253429869199698171910459179081127293881 2157912070411936650708934674533021837672644322590878807869539839941326704253093 5674639608594177856421522573245025164517324200066676578802403181032285288360694 6838579854722117159532164317092910745623922820821371340935216845132236038877665 7339418352276371684732436040321486657454388471939734084055758840535689131401651 7566673597351592980501750088559487724231387085963290339234918565001279513497675 0745036467376845179652017489466681764834338205566597214757966498864643507590301 6355111454405801057048032213775608223565327591367505087053980715569689515924870 7127233585220122572564796423067413932406675963079912410446565916168531236895779 8202727487715873679448199538835880601907354785712434134222808844571085910906499 0605047193313196378507049458543261063152155663268828565042264874128508179820866 5504332647457478752915376222250294253389734679623684267420691296098397586033317 6705577789676081841932654774537190372433541186239292847055037023502702232255870 6822968832060288251318439778826040182598858941920509914605048444622695138860877 1783425028084590953531345860000846283315312118203367999365673920409797877311032 2240279307855389977178577070047757444915398364355769670636329865970871844286799 4289002252782206060135096225911169402856615061098429267693603300206460733815318 8059246268661594895404105683963757323404136999878894676091029266484589308183395 3564282003370961593805061960886289318422037872535360029856738385677062674618175 3684318163299191377272021763233804350252330033819693119617938570635739374269085 0859884884609391965080584643737117940970456455374274665897980284526405758385358 0105661045949664643573809578908382655130075583942936415490897900898242601263339 7812631685346496468635114465918082247690413768547453319080049763916599426408179 5129871186730042486829776731810692564739599642285665911671321178155248524331441 1255807190498834709714446684555265549278032073199340637878479508267953956104169 5650403098933406767289952281867066972784457102058004869779474548714208815469973 6281276005682918310880313730846974765628433748039683625904154949205215237141500 6659591368186278626512117671667394607293575179564347988569355764803954546466941 1398561051557351917596382757288663999393873584398879214931725840445008255223919 3153013701993248427542479041182761822114273672116952646985292306125006160548687 7669711408825779579550268416207135766855369847493790803139998286911151172045224 5777839402549358447623411684719782087088940813527343761776240467314041923398777 6506410387665967645870782861692016097117488956266659289628763891694594814376094 8109685198650658113457434573361848746993545490084456864739793775920118050483997 6789916374540606482780908899044816969836558859091176241857742983087511493156520 8525445997696705585793948806706089127033911116118444489242826649424233546968779 5640498660765879891104094228756254396657143949991067997845544592751343358816678 2348027502850728183554275144839645910635079125209137019705922435780609242089233 5490238765846832840362051483491990778138538844417212451656239764460749091800410 0241225892338070704310472009856590092615157278718459512995907729091443167368432 5134425576833897053750999228408161185557344762605198173794559213050171007480479 1001981221807061249014009351834912840224944024493130779240675094729399467655289 7529506204287870735562383464347600439721184281702813181306189323342894117951931 4325628742715505876594735342366147065258554990342811991211128088903917418529892 3301888543886960119961776826916735148327005901964038776036107316595553217852644 3476705657296301122611421362719615107869366260176246107858937030521799156230696 7092907443770954668983815232983765289262441348650605406460713654819544319094195 7990990624499042032320223722876289547657506363127031356326687981678987200372736 0770377251590258571328868733257660906033881846506489622904132393195184169404109 4377853025584561224260622612319756726683055168484809809387802826809391865173025 7945591535873779977231529847452656019901621705178625268991249822154601912374013 7154968938420320948405805714965755371078409671455638975218379998917640436707618 8681942675795825722846648375909627081741770280239948089919943443011764542437966 9611910720964275659425642257816884674573888013893091922506812783156727721951364 5257203698271015668175729149756949615453627103126219752780605958929376282595388 5032440094709153676482677165344253896068507563794940023230122099574323858101707 2570638148874735932810469233330972002317534726941519125649637666763620593257555 2802013394057045075157710792960615959121895242708435936065181343607878987441938 5655280834775645798472734097704637039533870041496371720488837433422650649335827 5371193144219381208174409661775833038322297682715125848168967111372860342179508 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1244847267231538753091535114812935922237572277246427770915848136234726946522964 2078874235893895838449951601815802327666952501956682635154917401313486877535689 5051514941873389530455430681479734480256174344142780947544192259464704239345761 5601042532302193891544319484551953698313254917964906522194131080913735962221900 9270135127956422700444996034706878829595876337587399113528151221484310339651969 0706970210982147196992421863868691600364222311506435015959980780297122481446433 2141918276849889008977461303807488090411862932833148905782888568497592921787244 1553355052010969069565075404057221920036010562005449568813877888079124769636221 9348161496531155026976529276021527916040665229743274290178727697374929074137857 2492032102947426897596336763682153349730754782258386716752288182408290534582610 4241411830721680711989755394616053020447403489830408035867621408322007807260783 7464564080712578137963222422256384238818738413419896706280486114787878469760287 6573138419904391216774170956196251985515026868429189603016811088332328853934618 5158497960049066647729843574376759140925609326714817792151729387351364769118371 1710439370397069478045886777967376729199441316921478878974773943341707704697649 2616954254680796135215948550812913828522302411217088506637071746100007202182358 5114824966333677561115985450847355372116949330800978107383794787109962765468892 2796299889301486091270920630015243432410927922263684015460897037542910495686438 0928265625218248874449839379265532544661237605748251709756266596450840222616406 2570367153491509500866931587256638179446682749881747535628012796468062508698161 7254266721638598668812438002837082173233219843036829767637642663015651220571258 3333956436466949532618689789656520037552479595010730617740131650473459920599765 5207733263734536758803439170867032666161617840065527811136501323037626190548296 5837357257175827758628167265745516473572310523810054154911913556500531628534991 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5473031344532990715282895178258703229802746869935715993993326472742609243935989 9779810396391634871124747847851932796566286644729957224060326119857428758882035 0177206933283748581550916765228905592114017045336446274065947381912614446281006 7378399454639949542972383027154809890579644982044032492913268449414677690492107 6485574488587168191402762722491605020116201882923508240164393522829963771162912 2242800563279525606082168491459028145966658847893585099423621625917760206917247 5626452155975603705630235327738138242410691838381305120382512661502996135980431 6539367358098566150767806513518744245412665457500982615686747298500669515564717 4709638705314055982991570154738733936726844065720429748166601468071403913137256 5947409310042437572161393134647015994341909774486375414393481658130903102139157 2090894891488948011836268218440122912221919423551780592951803812335583525049371 2623410811045834716123979430168179365958613571509923667834923999890510139917094 0880905337387215436411627100547320991729730176911741387440617429807537638582298 6372095943075849358458791346133606381524011675241845080070138114770710672691089 6126491462898236851542169694661390231514014317922125142841841116199007367163624 7291637589468206011752010542550327269844347328892648660605995908630238827458747 5057549202872247241165092614595773471018609838922743784821637915774052170919453 4198012069859175795469519042107762080176370013133378082294542343852792412975624 9674407413645080359359104330108082856186772309839157759339197424534779278691292 4321071341100726062261684895004918806983404547460421189841201777432565267579415 8697738109256702509161280100955400038257604895744457291726076483436948301199847 8353533338734041756531416761265581804225457614433475269485977882197049869273368 3541986022710933145549909892456662325323420834723394183503882302294410893459873 9876414679523272327734810790136757735637294078163960853162109606016805967447679 0582570386343934845080124797659401709130579147039280407998759787902057592965547 8582937634578619751617710800726630557672478820381448129261203144066677335978913 0234413007237888073093318241914748739185546777280391099214158739185703403304995 1706491512630050114473113409569724488925083508684026371029313911523234222539669 3210968043611546302789334169384913173868224038140509375477916768053538002499680 8316002360142472578168489672443312094244237509385497975324662979624958181784357 6623336283867220867066956273104710086093850921377148690097981381786526258069723 1625597784158870765637811512612853325836992803770217252742015781501028753944295 9002621590394396621832133457855856489800575805611396297166196809301807867266190 2430894395662876725284176467075983553129068777176049450227823561954841348527867 6281689346770392381930033821328990934223201310725494100390927267583852007423808 6819069237891244710113660587196051868245342662877337534067611730491604096157035 0036794017284915247385720218004738305365598463158178381585122062137530152478737 5653186030673408489000147956634333900868671077157071849168106655621416780300759 7171705332401490575928467860191381228081262425952980998990337608689949047653112 6667259838330166326212928861143676396324732799203143249448954754997830206199314 2185188970986155163081455895222829479159483973682479422088999618728941584958548 0095010188820499631314574533565275538259261573473445232070673462746741441121728 9631778279135621909992198926459412370981765804138429449700861927408303669276022 5925593308433621961621744916321388403761291486400802954688905492281068006042683 7046008580042479868333140932317247339384992861799072109304090116202837778082975 1316646372073797493669750197485249952987735100352566658599758167586697057829286 9761657458799043829229539937366757581685426142964536866604502679454690051670354 5691523639714898960397775150944076237536601433281924431004953910474960706736223 7732596737481277100634850062654607918225721859000158655352316249488157653643894 6606372028220197015316239583528121934587597328045069273933689966874011867257067 6733729331608151899989646255160166488546208960556973235897050352490671107448591 4440675800707191124789192326507330077249237733260082767078570128436108125237227 1443969420582666229855359231399763088537617648375701867559234890795965719388521 7163315348210402464215481905945670589293529242503320703787242251821853985899188 9512815680103932319763515980764846569542231100329444778593302003414523100058620 5963810587290960912971650716517907073396007736249504411615371691043857316871426 6483349410368906128887060764124797835607270563333647531743803884503128088200802 4412266579349646633089008260789631840097698442447700550

***

example, total permutations of 1>10 and 0>10 = 20 11111111110000000000 = 20!/10!/10! 184756
means for each of 4 (2^4) 184756/2^4 = 11547 collisions
184756
11547

we can take this number of all permutations and use them as the initiating seed and they are almost completely enough to sort out all the permutations.

this is a search option in a larger number smaller

numbers can of course be converted into strings (str) it will not change the essence.

from 11547 collisions for "0000" (from 2^4 bit) from count 20!/10!/10! = 184756 (from 0 to 184756)

it is interesting that even secondary seeds repeat themselves initiated by different numbers first seed.

            seed 2                seed 1  4 bit                    
('00000110101010111101', 10580, '0000')
('00000110101010111101', 28894, '0000')
('00000110101010111101', 59931, '0000')
('00000110101010111101', 148666, '0000')

('01101000111110010100', 29195, '0000')
('01101000111110010100', 41692, '0000')
('01101000111110010100', 141462, '0000')
('01101000111110010100', 176562, '0000')

('01101001011001011010', 50482, '0000')
('01101001011001011010', 57288, '0000')
('01101001011001011010', 177912, '0000')
('01101001011001011010', 178529, '0000')

('01110011001011001010', 35976, '0000')
('01110011001011001010', 47548, '0000')
('01110011001011001010', 58853, '0000')
('01110011001011001010', 113112, '0000')
('01110011001011001010', 139744, '0000')

***

or filter the initiating seed by 4 > "1"

('00000001001111110111', 111185, '0010')
('00000011010100111111', 111017, '0010')
('00000011100111011110', 116511, '0110')
('00000011110001111101', 112811, '0011')
('00000011111101100101', 111451, '0011')
('00000100101111011011', 101119, '1001')
('00000101001110111011', 118181, '0110')
('00000101101101101101', 130111, '0100')
('00000101111010111001', 118611, '0000')
('00000110001110111110', 111417, '1001')
...
('11111100010000010101', 111189, '0000')
('11111100010101000100', 119116, '1010')
('11111101001010100000', 111166, '0011')
('11111101101000000100', 111671, '0101')
('11111110000101000010', 118141, '1100')
('11111110001001010000', 118118, '0101')
('11111110010001000001', 171181, '0000')

~800 can calculate similar techniques for attack pz

***

there are how many collisions

180!/90!/90! = 91012248672832285155575331798825309656983959185522800

91012248672832285155575331798825309656983959185522800/ pz 64 2^64 = 4933783886693786561852355929668775 collisions

91012248672832285155575331798825309656983959185522800/pz 160 2^160 = 62273 collisions

600!/300!/300!

1351079419961942685144748779785045303972339454491934799259657217864741504080057 1696195048019827446981867333413136583724904390049076115159169530842704853694762 1976068789875968372656

9244460529167650795540731674161791846040585150874740675211703275797841931797666 8404488686921898322882212568056295459139633654182256 2^160 collisions
7324216211615967328305946861026949927023153844181547075253885258466971658764981 4215996027965475907402114296086782480287591076169589308698251700422304548067593 59 2^64 collisions
1166814960211057090384486027721779669646648766821734965205742389473249903857269 571929430822183654654146 2^256 collisions    

how to catch them? for 1 pz 64 7324216211615967328305946861026949927023153844181547075253885258466971658764981 4215996027965475907402114296086782480287591076169589308698251700422304548067593 59 collisions from 600!/300!/300!  

is the probability of generating a collision in this way identical to the probability of guessing 64 puzzles by random?

in this way it is easier to fork "Isaacdelly/Plutus" to search for everything at once than just 1 64 pz

because of working with strings, the larger the string, the slower it works

65536!/32768!/32768! barely creeps

20000!/!10000/10000!  6019 len num, 6017 > 2, 2 > 4, 6019!/6017!/2! = 18111171, 6685588 ran in total in a day  

6685588 dec init seed > 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 2222222222222222222222222222222222222222222222222222222222222222222222222222222 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***
algorithm, due to "Narayana Pandita" for permutations, the algorithm is normal and can write to the file immediately without loading memory (little who wants to experiment)

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