Bitcoin puzzle transaction ~32 BTC prize to who solves it

[AzizLeBG]

Pure math is reasoning

What do you know about math?  if you know how to solve a key by using pure math,  then this is for you if you know things.
We have 4 points and 4 scalar, 3 points are unknown but they do relate to all 4 scalar keys. Can you point out a hint as to how we can solve any of the 3 points?

Here are our 3 points

Code:

P1=
03f4bef7834ec36e40f1c007a4c27c2f7d2ded709fda3333fdd5801625736ed152
P2=
03389523df912b20e7f5b2223f50a3e074551d3859487701d9e6297b950c9a78ea
P3=
032b0d9abd02f210631ca0fdf138a19c6725f6b67f2dba6c22bf181c73e81abd08

Here are 4 scalar

Code:

A1=
0x1c16e0f93f27c98dfa5
A2=
0x3f6feeff01e9e8d265
A3=
0x181fe2094f092b00d40
A4=
0x200ddfe92f46681b20a

P1+P2= A4, P2-P1= P3, P3-A4= P2*2, P1-A4/2= P3/2.
Here is the trick, A1, A2 and A3 point to different public keys,  however if we subtract A1-1 from P1, subtract A2-1 from P2 and add the results,  we would get 2, which means P1 and P2 are close they are also close to P3 because half of A4 subtracted from P1 equals half of P3.  This is pure math,  but how can we solve any of the 3 points while we only have A4 and why A1, A2 and A3 behave similar to our 3 points?  They are in close range with each other but where are they exactly?

Pure math is reasoning

What do you know about math?  if you know how to solve a key by using pure math,  then this is for you if you know things.
We have 4 points and 4 scalar, 3 points are unknown but they do relate to all 4 scalar keys. Can you point out a hint as to how we can solve any of the 3 points?

Here are our 3 points

Code:

P1=
03f4bef7834ec36e40f1c007a4c27c2f7d2ded709fda3333fdd5801625736ed152
P2=
03389523df912b20e7f5b2223f50a3e074551d3859487701d9e6297b950c9a78ea
P3=
032b0d9abd02f210631ca0fdf138a19c6725f6b67f2dba6c22bf181c73e81abd08

Here are 4 scalar

Code:

A1=
0x1c16e0f93f27c98dfa5
A2=
0x3f6feeff01e9e8d265
A3=
0x181fe2094f092b00d40
A4=
0x200ddfe92f46681b20a

P1+P2= A4, P2-P1= P3, P3-A4= P2*2, P1-A4/2= P3/2.
Here is the trick, A1, A2 and A3 point to different public keys,  however if we subtract A1-1 from P1, subtract A2-1 from P2 and add the results,  we would get 2, which means P1 and P2 are close they are also close to P3 because half of A4 subtracted from P1 equals half of P3.  This is pure math,  but how can we solve any of the 3 points while we only have A4 and why A1, A2 and A3 behave similar to our 3 points?  They are in close range with each other but where are they exactly?

It seems you're dealing with elliptic curve cryptography (ECC) where you have points on a curve and scalar multiplication operations. From your provided information, you have points P1, P2, and P3, as well as scalars A1, A2, A3, and A4.

Your hint suggests that A1, A2, and A3 are related to P1, P2, and P3 respectively, in a way that when you subtract 1 from each scalar and subtract that from its corresponding point, adding the results gives you 2. This indicates that P1, P2, and P3 are likely related to A1-1, A2-1, and A3-1 respectively in some manner.

The relationship between P1, P2, and P3 is also given in terms of scalar operations involving A4. From the relationships provided:

P1 + P2 = A4:

If you add point P1 and point P2 together on the elliptic curve, you get the point A4.
P2 - P1 = P3:

If you subtract point P1 from point P2 on the elliptic curve, you get the point P3.
P3 - A4 = 2P2:

If you subtract point A4 from point P3 on the elliptic curve, you get twice the value of point P2.
P1 - (A4 / 2) = (P3 / 2):

If you subtract half of the value of A4 from point P1 on the elliptic curve, you get half of point P3.
 
Given only A4 and these relationships, it's possible to find the coordinates of at least one of the points P1, P2, or P3 by performing scalar operations with A4.

To find the exact coordinates of the points P1, P2, and P3, you can use scalar multiplication operations on a known base point on the elliptic curve, which is usually provided in ECC. By performing scalar multiplication operations with A4 and using the provided relationships, you can compute the coordinates of at least one of the points. Once you have the coordinates of one point, you can use the relationships between the points to deduce the coordinates of the others.

[1715286094]

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[1715286094]

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[1715286094]

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[citb0in]

What do you know about math?  if you know how to solve a key by using pure math,  then this is for you if you know things.
...,  however if we subtract A1-1 from P1, subtract A2-1 from P2 and add the results,  we would get 2, which means P1 and P2 are close they are also close to P3 because half of A4 subtracted from P1 equals half of P3.  This is pure math, ...

...
If you subtract point P1 from point P2 on the elliptic curve, you get the point P3.
P3 - A4 = 2P2:

If you subtract point A4 from point P3 on the elliptic curve, you get twice the value of point P2.
P1 - (A4 / 2) = (P3 / 2):

If you subtract half of the value of A4 from point P1 on the elliptic curve, you get half of point P3.
 
...

@Digaran: are you not tired creating new accounts and talk to yourself? Why not substracting yourself from this thread?
stop acting like God or Satoshi Nakamoto, you are neither a Satoshi nor a Nakamoto but universes away from it. Please stop spamming the thread with nonsense. Two more users on the ignore list...

[satashi_nokamato]

you can compute the coordinates of at least one of the points

Thanks for the reply,  all I need now is to figure out which one from P1 and P2 is inverse,  definitely one of them is negative,  given that I know the original range from where I started my calculations,  it should be easy to work out the nearest point to one of the above points.
I understand that P1 could be a number like 600, then P2 could be a number like 50, having just 550 as their distance is enough on it's own if I can guess which one is my known scalar to solve one of the points.

[cujo10226]

How about binary Tetris any pattern from the binary notations of the pks?

https://i.ibb.co/c6m2fTq/Screenshot-2024-03-03-at-13-11-49.png


https://i.ibb.co/8xJKNt0/Screenshot-2024-03-03-at-13-11-29.png


https://i.ibb.co/ySsySq7/Screenshot-2024-03-03-at-13-11-03.png

[isellkarma]

COMP MODE    : COMPRESSED
COIN TYPE    : BITCOIN
SEARCH MODE  : Single Address
DEVICE       : GPU
CPU THREAD   : 0
GPU IDS      : 0
GPU GRIDSIZE : 256x256
SSE          : YES
RKEY         : 5 Mkeys
MAX FOUND    : 65536
BTC ADDRESS  : 13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so
OUTPUT FILE  : Found.txt

Start Time   : Sun Mar  3 09:55:18 2024
Base Key     : Randomly changes on every 5 Mkeys
Global start : 20000000000000000 (66 bit)
Global end   : 3FFFFFFFFFFFFFFFF (66 bit)
Global range : 1FFFFFFFFFFFFFFFF (65 bit)

Can someone answer me one question? I'm having trouble understanding how RKEY works (I'm new). My guess is that it has a Base key then goes from there and tries 5m keys and then changes the base key to a random one within the range and goes through another 5m keys? Correct?

[WanderingPhilospher]

COMP MODE    : COMPRESSED
COIN TYPE    : BITCOIN
SEARCH MODE  : Single Address
DEVICE       : GPU
CPU THREAD   : 0
GPU IDS      : 0
GPU GRIDSIZE : 256x256
SSE          : YES
RKEY         : 5 Mkeys
MAX FOUND    : 65536
BTC ADDRESS  : 13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so
OUTPUT FILE  : Found.txt

Start Time   : Sun Mar  3 09:55:18 2024
Base Key     : Randomly changes on every 5 Mkeys
Global start : 20000000000000000 (66 bit)
Global end   : 3FFFFFFFFFFFFFFFF (66 bit)
Global range : 1FFFFFFFFFFFFFFFF (65 bit)

Can someone answer me one question? I'm having trouble understanding how RKEY works (I'm new). My guess is that it has a Base key then goes from there and tries 5m keys and then changes the base key to a random one within the range and goes through another 5m keys? Correct?

No, this looks like key-hunt cuda, therefore, there is no basekey.

The program generates x amount of random points within the given range, based on your GPU grid size.

In your example, 256x256 is your grid size so the program generates 65,536 random points. Now, from there the program starts adding to each random point, in a sequential manner, until the RKEY number is reached. Once the RKEY number is reached, the program generates 65,536 new random points, and repeats the process. In your example, 5 MKeys is the rekey number.

So from each random point, the program will check 76 sequential points from each random point, before a rekey. 5,000,000 / 65,536 = 76.

Make sense?

[isellkarma]

COMP MODE    : COMPRESSED
COIN TYPE    : BITCOIN
SEARCH MODE  : Single Address
DEVICE       : GPU
CPU THREAD   : 0
GPU IDS      : 0
GPU GRIDSIZE : 256x256
SSE          : YES
RKEY         : 5 Mkeys
MAX FOUND    : 65536
BTC ADDRESS  : 13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so
OUTPUT FILE  : Found.txt

Start Time   : Sun Mar  3 09:55:18 2024
Base Key     : Randomly changes on every 5 Mkeys
Global start : 20000000000000000 (66 bit)
Global end   : 3FFFFFFFFFFFFFFFF (66 bit)
Global range : 1FFFFFFFFFFFFFFFF (65 bit)

Can someone answer me one question? I'm having trouble understanding how RKEY works (I'm new). My guess is that it has a Base key then goes from there and tries 5m keys and then changes the base key to a random one within the range and goes through another 5m keys? Correct?

No, this looks like key-hunt cuda, therefore, there is no basekey.

The program generates x amount of random points within the given range, based on your GPU grid size.

In your example, 256x256 is your grid size so the program generates 65,536 random points. Now, from there the program starts adding to each random point, in a sequential manner, until the RKEY number is reached. Once the RKEY number is reached, the program generates 65,536 new random points, and repeats the process. In your example, 5 MKeys is the rekey number.

So from each random point, the program will check 76 sequential points from each random point, before a rekey. 5,000,000 / 65,536 = 76.

Make sense?

Yes. Thank you!

[pbies]

I believe there is a formula that can solve all puzzles at once.  I'm not kidding.
Logarithms and polynomials are in play. But I can't prove it. It's a matter of belief for now.

The complexity is great. Maybe lifetime won't be enough

I also think that too.

Maybe some HD wallet with some specific parameters...

There should be an algorithm.

[ccinet]

The concept of a logarithm was invented just a few centuries ago and immediately changed engineering as we know it.

You can even do regression analysis
https://i.ibb.co/jJYVpd6/Figure-1.png

I'm lost between the size of the numbers and the precision required here . . .

There is no pattern. But it's not random either according to the polynomial analysis. There is an exact math formula for making this puzzle with some script, errors = ZERO.  With high decimal precision (mp.dps = 20 at least)
And the formula is in the creator's mind.

Viewing it at that level of precision, it obviously corresponds to a regression line corresponding to 2^n.
The problem comes when inferring where the private address falls in the range 2^n-1 -2^n when n>50, in this case if a random pattern exists here it will be very difficult to find it in the range.
However, a prediction with linear regression can give us a clue that could be +15% -15% or 30% of the predicted value, which in the case of the range for bit 66 and greater is still an astronomical number.

[mckemo]

there is no pattern.
i can exactly tell you why:

The creator of the puzzle posted already, that he created a wallet and masked the keys to match in the key range with 0
Therefore 256 adresses have been generated and he just put as many 000 to fit in. So it is kinda random.
No rythm, no nothing involved.

[AndrewWeb]

there is no pattern.
i can exactly tell you why:

The creator of the puzzle posted already, that he created a wallet and masked the keys to match in the key range with 0
Therefore 256 adresses have been generated and he just put as many 000 to fit in. So it is kinda random.
No rythm, no nothing involved.

Not even something unintentional ?

[ccinet]

there is no pattern.
i can exactly tell you why:

The creator of the puzzle posted already, that he created a wallet and masked the keys to match in the key range with 0
Therefore 256 adresses have been generated and he just put as many 000 to fit in. So it is kinda random.
No rythm, no nothing involved.

I partially agree that the directions are random, but when generating the prediction using linear regression the prediction does not seem to behave as random. If that were the case, my results should be close to a 50 average difference and this does not seem to be the case as the average comes out to 27,81. See the Differ column

#Puzzle       Real address                        %Range        Predict address                             %Range      Differ
-----------------------------------------------------------------------------------------------------------------------------
3       ::      7                         ::      100.0 %       6                                ::         66.67 %     33.33
4       ::      8                         ::      0.0 %         15                               ::         100.0 %     100.0
5       ::      21                        ::      33.33 %       16                               ::         0.0 %       33.33
6       ::      49                        ::      54.84 %       40                               ::         25.81 %     29.03
7       ::      76                        ::      19.05 %       96                               ::         50.79 %     31.75
8       ::      224                       ::      75.59 %       158                              ::         23.62 %     51.97
9       ::      467                       ::      82.75 %       426                              ::         66.67 %     16.08
10      ::      514                       ::      0.39 %        925                              ::         80.82 %     80.43
11      ::      1155                      ::      12.81 %       1183                             ::         15.54 %      2.74
12      ::      2683                      ::      31.02 %       2299                             ::         12.26 %     18.76
13      ::      5216                      ::      27.35 %       5194                             ::         26.81 %      0.54
14      ::      10544                     ::      28.71 %       10422                            ::         27.23 %      1.49
15      ::      26867                     ::      63.99 %       21037                            ::         28.4 %      35.59
16      ::      51510                     ::      57.2 %        51310                            ::         56.59 %      0.61
17      ::      95823                     ::      46.21 %       103183                           ::         57.45 %     11.23
18      ::      198669                    ::      51.57 %       195056                           ::         48.82 %      2.76
19      ::      357535                    ::      36.39 %       395765                           ::         50.97 %     14.58
20      ::      863317                    ::      64.66 %       731909                           ::         39.6 %      25.06
21      ::      1811764                   ::      72.78 %       1667578                          ::         59.03 %     13.75
22      ::      3007503                   ::      43.41 %       3562229                          ::         69.86 %     26.45
23      ::      5598802                   ::      33.49 %       6269961                          ::         49.49 %     16.0
24      ::      14428676                  ::      72.0 %        11491816                         ::         36.99 %     35.01
25      ::      33185509                  ::      97.8 %        27504184                         ::         63.94 %     33.86
26      ::      54538862                  ::      62.54 %       63833934                         ::         90.24 %     27.7
27      ::      111949941                 ::      66.82 %       113495584                        ::         69.12 %      2.3
28      ::      227634408                 ::      69.6 %        224580693                        ::         67.33 %      2.28
29      ::      400708894                 ::      49.28 %       453804297                        ::         69.06 %     19.78
30      ::      1033162084                ::      92.44 %       825924623                        ::         53.84 %     38.6
31      ::      2102388551                ::      95.8 %        1969361098                       ::         83.41 %     12.39
32      ::      3093472814                ::      44.05 %       4145832285                       ::         93.06 %     49.0
33      ::      7137437912                ::      66.18 %       6682030526                       ::         55.58 %     10.6
34      ::      14133072157               ::      64.53 %       14049401668                      ::         63.56 %      0.97
35      ::      20112871792               ::      17.07 %       28221647532                      ::         64.27 %     47.2
36      ::      42387769980               ::      23.36 %       44022721150                      ::         28.12 %      4.76
37      ::      100251560595              ::      45.89 %       85412760887                      ::         24.29 %     21.59
38      ::      146971536592              ::      6.94 %        193364673951                     ::         40.69 %     33.76
39      ::      323724968937              ::      17.77 %       315876858626                     ::         14.92 %      2.86
40      ::      1003651412950             ::      82.56 %       643143861650                     ::         16.99 %     65.58
41      ::      1458252205147             ::      32.63 %       1836301474982                    ::         67.01 %     34.38
42      ::      2895374552463             ::      31.67 %       3099961081281                    ::         40.97 %      9.3
43      ::      7409811047825             ::      68.48 %       5887202929472                    ::         33.86 %     34.62
44      ::      15404761757071            ::      75.13 %       14093166703784                   ::         60.22 %     14.91
45      ::      19996463086597            ::      13.67 %       30201532176581                   ::         71.68 %     58.01
46      ::      51408670348612            ::      46.11 %       44884294010167                   ::         27.57 %     18.54
47      ::      119666659114170           ::      70.06 %       99617204420010                   ::         41.56 %     28.49
48      ::      191206974700443           ::      35.86 %       229750447356991                  ::         63.25 %     27.39
49      ::      409118905032525           ::      45.35 %       401043185877867                  ::         42.48 %      2.87
50      ::      611140496167764           ::      8.56 %        814161270555782                  ::         44.62 %     36.06
51      ::      2058769515153876          ::      82.86 %       1319345329097142                 ::         17.18 %     65.67
52      ::      4216495639600700          ::      87.25 %       3760945352862053                 ::         67.02 %     20.23
53      ::      6763683971478124          ::      50.18 %       8219929160770636                 ::         82.52 %     32.34
54      ::      9974455244496707          ::      10.74 %       14236430186441562                ::         58.06 %     47.32
55      ::      30045390491869460         ::      66.79 %       21991831924581256                ::         22.08 %     44.71
56      ::      44218742292676575         ::      22.73 %       56172595859062496                ::         55.91 %     33.18
57      ::      138245758910846492        ::      91.85 %       94220023057453888                ::         30.76 %     61.1
58      ::      199976667976342049        ::      38.76 %       255212325192053440               ::         77.09 %     38.33
59      ::      525070384258266191        ::      82.17 %       426892909478600768               ::         48.11 %     34.06
60      ::      1135041350219496382       ::      96.9 %        1002629087575579392              ::         73.93 %     22.97
61      ::      1425787542618654982       ::      23.67 %       2206900063121315328              ::         91.42 %     67.75
62      ::      3908372542507822062       ::      69.5 %        3230525871167049216              ::         40.1 %      29.4
63      ::      8993229949524469768       ::      95.01 %       7484438930281590784              ::         62.29 %     32.72
64      ::      17799667357578236628      ::      92.98 %       17258083624034758656             ::         87.11 %      5.87
65      ::      30568377312064202855      ::      65.71 %       35350867246359666688             ::         91.64 %     25.93

[kTimesG]

1 to 0 ratio so far for random unknowns is 1027 to 1053.
#66 adds 65 more bits, so 2145 total.
Let's assume # 66 adds 65 more zeros and no 1s. Ratio would be 1027 to 1118.
Confidence interval for [1027 ... 1118] successes in 2045 trials with p = 1/2 is 95%.
In other words, even if puzzle 66 is full of zeros and the fixed 1, it's still in the 95% expectation range, so it would only be an anomaly from other perspectives.
If confidence range would be really low, we can suspect that the unknowns don't follow a uniform chance to appear, so there is manipulation (e.g. a hidden pattern).

Unfortunately naturally occurring randomness looks like patterns, until you simulate 10.000 times and you realize each one has completely different results over time. Sometimes the cumulative/average/whatever probabilities will go down, sometimes they will jump all over the place, intersect, don't intersect, swap places, dance with each other, or go into opposite extremes (and then return to the other side, or maybe not). An yes, this happens when you use a maximum entropy source, e.g. actual unpredictable noise. It will behave "strange" each time.

So yeah, there is a pattern, it's called randomness. What can we do about it? Let's pretend to assume that the 1 and 0 frequencies should approach an uniform distribution (central limit theorem). This will only happen when we have an infinite number of samples. Until that point, anything is possible within the confidence range, because of binomial distribution of limited number of samples. So #66 can be full of 0, full of 1, or any other combination, and it would still be completely normal within 95% accuracy.

Otherwise, filling out randomness on top of randomness by any pattern or set of patterns has the problem that it can be done in 2^n ways.
Even if assuming that we need to have an equal amount of 0 and 1 still means to check comb(65, 32) possibilities, which is a ***load of candidates itself, as it's the peak of the distribution.

Tell that to the linear regression

[Baskentliia]

Hello everyone, why do you think Puzzle 66 has not been found yet?
In April 2023, the reward was increased 10 times, but it still has not been found. What do you think is the reason?
Although many amateur people from all over the world searched, it could not be found.
Doesn't anyone have a chance?
Or is puzzle 66 somewhere outside this range?
What are your thoughts?

[albert0bsd]

Hello everyone, why do you think Puzzle 66 has not been found yet?
In April 2023, the reward was increased 10 times, but it still has not been found. What do you think is the reason?
Although many amateur people from all over the world searched, it could not be found.
Doesn't anyone have a chance?
Or is puzzle 66 somewhere outside this range?
What are your thoughts?

it was not found because the 66 bit space is absurdly big for regular brute force

It is simple, every extra bit increate the difficulty by a factor of TWO

Puzzle 63 1NpYjtLira16LfGbGwZJ5JbDPh3ai9bjf4 was redeem in June 2019
Puzzle 64 16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN was reddem in September 2022

Puzzle 66 range is 4 times bigger than puzzle 64 make your own stimations

Puzzle 65 doesn't count because it was solved with the publickey with kangaro

Or is puzzle 66 somewhere outside this range?

No, all solved puzzles were in their respectives ranges, so please STOP spreading this shit.

[citb0in]

are you kidding ?

[shelby0930]

can anyone tell me if the puzzle 130 starts from 2 or 3 ?  since the range is 0x200000000000000000000000000000000 and 0x3ffffffffffffffffffffffffffffffff can anyone tell me if its private key starts from 2 or 3 ?

[citb0in]

can anyone tell me if the puzzle 130 starts from 2 or 3 ?  since the range is 0x200000000000000000000000000000000 and 0x3ffffffffffffffffffffffffffffffff can anyone tell me if its private key starts from 2 or 3 ?

it starts with 3. Good luck

[shelby0930]

can anyone tell me if the puzzle 130 starts from 2 or 3 ?  since the range is 0x200000000000000000000000000000000 and 0x3ffffffffffffffffffffffffffffffff can anyone tell me if its private key starts from 2 or 3 ?

it starts with 3. Good luck

how do you say this ? is there a certain way to know if it starts from 3 ?

[albert0bsd]

how do you say this ? is there a certain way to know if it starts from 3 ?

There is not correct answer until the puzzle its solved it can be 2 or 3
Look:

Code:

>>> hex(2**129)
'0x200000000000000000000000000000000'
>>> hex(2**130)
'0x400000000000000000000000000000000'