Bitcoin puzzle transaction ~32 BTC prize to who solves it

[tyz]

50 addresses have been cleaned out so far. The integers for the first 24 private keys have been posted.
Could anyone post the pvks for 25 to 50?

[1713993807]

1713993807

[1713993807]

1713993807

[1713993807]

1713993807

[vlom]

thats why i still like this forum. topics like this are a pleasure to follow.

keep going and solve this.

[Bulista]

All of this story tell us something.

We now know that someone out there is able to crack aprox. 2^50 private keys in about 1 year.

(in a worst case scenario, also assuming that the one who cracked the 50 addresses brute forced all the possible addresses sequential)

As time goes by this capability will increase, it may take decades and decades or centuries but eventually it will be possible to crack 2^256 pvks.

The transaction referenced in this thread is a good reference to test how far the mankind cracking capabilities are.

As of now, we can enjoy the safety of bitcoin for a long long time

2^1   2   
2^2   4   
2^3   8   
2^4   16   
2^5   32   
2^6   64   
2^7   128   
2^8   256   
2^9   512   
2^10   1024   
2^11   2048   
2^12   4096   
2^13   8192   
2^14   16384   
2^15   32768   
2^16   65536   
2^17   131072   
2^18   262144   
2^19   524288   
2^20   1048576   
2^21   2097152   
2^22   4194304   
2^23   8388608   
2^24   16777216   
2^25   33554432   
2^26   67108864   
2^27   134217728   
2^28   268435456   
2^29   536870912   
2^30   1073741824   
2^31   2147483648   
2^32   4294967296   
2^33   8589934592   
2^34   17179869184   
2^35   34359738368   
2^36   68719476736   
2^37   137438953472   
2^38   274877906944   
2^39   549755813888   
2^40   1099511627776   
2^41   2199023255552   
2^42   4398046511104   
2^43   8796093022208   
2^44   17592186044416   
2^45   35184372088832   
2^46   70368744177664   
2^47   140737488355328   
2^48   281474976710656   
2^49   562949953421312   
2^50   1125899906842620   <- This is aprox. the number of bitcoins private keys someone is able to crack in about 1 year
2^51   2251799813685250   
2^52   4503599627370500   
2^53   9007199254740990   
2^54   18014398509482000   
2^55   36028797018964000   
2^56   72057594037927900   
2^57   144115188075856000   
2^58   288230376151712000   
2^59   576460752303423000   
2^60   1152921504606850000   
2^61   2305843009213690000   
2^62   4611686018427390000   
2^63   9223372036854780000   
2^64   18446744073709600000   
2^65   36893488147419100000   
2^66   73786976294838200000   
2^67   147573952589676000000   
2^68   295147905179353000000   
2^69   590295810358706000000   
2^70   1180591620717410000000   
2^71   2361183241434820000000   
2^72   4722366482869650000000   
2^73   9444732965739290000000   
2^74   18889465931478600000000   
2^75   37778931862957200000000   
2^76   75557863725914300000000   
2^77   151115727451829000000000   
2^78   302231454903657000000000   
2^79   604462909807315000000000   
2^80   1208925819614630000000000   
2^81   2417851639229260000000000   
2^82   4835703278458520000000000   
2^83   9671406556917030000000000   
2^84   19342813113834100000000000   
2^85   38685626227668100000000000   
2^86   77371252455336300000000000   
2^87   154742504910673000000000000   
2^88   309485009821345000000000000   
2^89   618970019642690000000000000   
2^90   1237940039285380000000000000   
2^91   2475880078570760000000000000   
2^92   4951760157141520000000000000   
2^93   9903520314283040000000000000   
2^94   19807040628566100000000000000   
2^95   39614081257132200000000000000   
2^96   79228162514264300000000000000   
2^97   158456325028529000000000000000   
2^98   316912650057057000000000000000   
2^99   633825300114115000000000000000   
2^100   1267650600228230000000000000000   
2^101   2535301200456460000000000000000   
2^102   5070602400912920000000000000000   
2^103   10141204801825800000000000000000   
2^104   20282409603651700000000000000000   
2^105   40564819207303300000000000000000   
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2^108   324518553658427000000000000000000   
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2^116   83076749736557200000000000000000000   
2^117   166153499473114000000000000000000000   
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2^142   5575186299632660000000000000000000000000000   
2^143   11150372599265300000000000000000000000000000   
2^144   22300745198530600000000000000000000000000000   
2^145   44601490397061200000000000000000000000000000   
2^146   89202980794122500000000000000000000000000000   
2^147   178405961588245000000000000000000000000000000   
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2^149   713623846352980000000000000000000000000000000   
2^150   1427247692705960000000000000000000000000000000   
2^151   2854495385411920000000000000000000000000000000   
2^152   5708990770823840000000000000000000000000000000   
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2^156   91343852333181400000000000000000000000000000000   
2^157   182687704666363000000000000000000000000000000000   
2^158   365375409332726000000000000000000000000000000000   
2^159   730750818665451000000000000000000000000000000000   
2^160   1461501637330900000000000000000000000000000000000   
2^161   2923003274661810000000000000000000000000000000000   
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2^168   374144419156711000000000000000000000000000000000000   
2^169   748288838313422000000000000000000000000000000000000   
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2^171   2993155353253690000000000000000000000000000000000000   
2^172   5986310706507380000000000000000000000000000000000000   
2^173   11972621413014800000000000000000000000000000000000000   
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2^176   95780971304118100000000000000000000000000000000000000   
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2^178   383123885216472000000000000000000000000000000000000000   
2^179   766247770432944000000000000000000000000000000000000000   
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2^181   3064991081731780000000000000000000000000000000000000000   
2^182   6129982163463560000000000000000000000000000000000000000   
2^183   12259964326927100000000000000000000000000000000000000000   
2^184   24519928653854200000000000000000000000000000000000000000   
2^185   49039857307708400000000000000000000000000000000000000000   
2^186   98079714615416900000000000000000000000000000000000000000   
2^187   196159429230834000000000000000000000000000000000000000000   
2^188   392318858461668000000000000000000000000000000000000000000   
2^189   784637716923335000000000000000000000000000000000000000000   
2^190   1569275433846670000000000000000000000000000000000000000000   
2^191   3138550867693340000000000000000000000000000000000000000000   
2^192   6277101735386680000000000000000000000000000000000000000000   
2^193   12554203470773400000000000000000000000000000000000000000000   
2^194   25108406941546700000000000000000000000000000000000000000000   
2^195   50216813883093400000000000000000000000000000000000000000000   
2^196   100433627766187000000000000000000000000000000000000000000000   
2^197   200867255532374000000000000000000000000000000000000000000000   
2^198   401734511064748000000000000000000000000000000000000000000000   
2^199   803469022129495000000000000000000000000000000000000000000000   
2^200   1606938044258990000000000000000000000000000000000000000000000   
2^201   3213876088517980000000000000000000000000000000000000000000000   
2^202   6427752177035960000000000000000000000000000000000000000000000   
2^203   12855504354071900000000000000000000000000000000000000000000000   
2^204   25711008708143800000000000000000000000000000000000000000000000   
2^205   51422017416287700000000000000000000000000000000000000000000000   
2^206   102844034832575000000000000000000000000000000000000000000000000   
2^207   205688069665151000000000000000000000000000000000000000000000000   
2^208   411376139330302000000000000000000000000000000000000000000000000   
2^209   822752278660603000000000000000000000000000000000000000000000000   
2^210   1645504557321210000000000000000000000000000000000000000000000000   
2^211   3291009114642410000000000000000000000000000000000000000000000000   
2^212   6582018229284820000000000000000000000000000000000000000000000000   
2^213   13164036458569600000000000000000000000000000000000000000000000000   
2^214   26328072917139300000000000000000000000000000000000000000000000000   
2^215   52656145834278600000000000000000000000000000000000000000000000000   
2^216   105312291668557000000000000000000000000000000000000000000000000000   
2^217   210624583337114000000000000000000000000000000000000000000000000000   
2^218   421249166674229000000000000000000000000000000000000000000000000000   
2^219   842498333348457000000000000000000000000000000000000000000000000000   
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2^231   3450873173395280000000000000000000000000000000000000000000000000000000   
2^232   6901746346790560000000000000000000000000000000000000000000000000000000   
2^233   13803492693581100000000000000000000000000000000000000000000000000000000   
2^234   27606985387162300000000000000000000000000000000000000000000000000000000   
2^235   55213970774324500000000000000000000000000000000000000000000000000000000   
2^236   110427941548649000000000000000000000000000000000000000000000000000000000   
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2^240   1766847064778380000000000000000000000000000000000000000000000000000000000   
2^241   3533694129556770000000000000000000000000000000000000000000000000000000000   
2^242   7067388259113540000000000000000000000000000000000000000000000000000000000   
2^243   14134776518227100000000000000000000000000000000000000000000000000000000000   
2^244   28269553036454100000000000000000000000000000000000000000000000000000000000   
2^245   56539106072908300000000000000000000000000000000000000000000000000000000000   
2^246   113078212145817000000000000000000000000000000000000000000000000000000000000   
2^247   226156424291633000000000000000000000000000000000000000000000000000000000000   
2^248   452312848583266000000000000000000000000000000000000000000000000000000000000   
2^249   904625697166533000000000000000000000000000000000000000000000000000000000000   
2^250   1809251394333070000000000000000000000000000000000000000000000000000000000000   
2^251   3618502788666130000000000000000000000000000000000000000000000000000000000000   
2^252   7237005577332260000000000000000000000000000000000000000000000000000000000000   
2^253   14474011154664500000000000000000000000000000000000000000000000000000000000000   
2^254   28948022309329000000000000000000000000000000000000000000000000000000000000000   
2^255   57896044618658100000000000000000000000000000000000000000000000000000000000000   
2^256   115792089237316000000000000000000000000000000000000000000000000000000000000000   <- And this is how safe bitcoin is.

[Bulista]

they seem to be always close to the double of the previous value, excluding the first few values.

There may, or may not be an actual pattern to the values, but that "close to the double of the previous value" would occur if you simply chose a completely random number from a set with 1 additional binary digit at each level.

Effectively each new private key would be a number of binary digits equivalent to the number of milibitcoins stored at the address with the first digit being a 1.

Let us assume that there is some sort of mathematical formula to solve this puzzle.

That's the only way we will ever be able to solve this puzzle during our lifetime.

I strongly recommend to all the mathematical experts out there to have a look at this sequence, maybe they are able to find something.

[Bulista]

50 addresses have been cleaned out so far. The integers for the first 24 private keys have been posted.
Could anyone post the pvks for 25 to 50?

Probably only two guys know that (who cracked and who owns), and they are probably not among us in this forum.

[calkob]

All of this story tell us something.


(in a worst case scenario, also assuming that the one who cracked the 50 addresses brute forced all the possible addresses sequential)

As time goes by this capability will increase, it may take decades and decades or centuries but eventually it will be possible to crack 2^256 pvks

are you serious it may take decades?  seriously  and the way technology is improving you think that in decades from now we will be relaying on tech from 2009.  wise up if the 20 years the tech to break bitcoin has improved so will the tech to have improved bitcoin security.

Like antonantonopolus says the inventioin is out of the box, it cant be put back in. "worst case senario bitcoin breaks and tomorrow we start a new crypto with all the failures of bitcoiin sorted"..... YES  and yes those who new about crypto get in at the bottom.........

[DannyHamilton]

- snip -
it may take decades and decades or centuries but eventually it will be possible to crack 2^256 pvks.
- snip -

It's impossible to say whether or not any future mathematicians will be able to discover any weaknesses in the ECDSA algorithm with the secp256k1 curve.

It will not, however, ever be possible to brute-force attempt 2²⁵⁶ possibilities.

2^160   1461501637330900000000000000000000000000000000000

2¹⁶⁰ is the security level of version 1 bitcoin addresses.

2^256   115792089237316000000000000000000000000000000000000000000000000000000000000000   <- And this is how safe bitcoin is.

Nope.

That's how secure an ECDSA public key is, but version 1 bitcoin addresses use a 160 bit hash of that public key, so the security is reduced to 2¹⁶⁰.

[justspare]

Any info on who published this puzzle and what's their goal? Also, how would one go on about calculating those pvk decimal values and covert them to the private keys?

I don't know why but I'm smelling a big scam. Because a newbie that offer more than 12 000€ to solve a following of numbers this is strange...

The OP is not offering anything

Why would anyone pay such a high amount for this? They must have some kind of goal behind it, no one just does that for no reason.
Of course the OP is not offering anything. Why would he? He probably doesn't even know what to do with it when someone cracks it. I don't either.
This will take a very long time to crack, thats probably the reason why the reward is so high.

[NorrisK]

- snip -
it may take decades and decades or centuries but eventually it will be possible to crack 2^256 pvks.
- snip -

It's impossible to say whether or not any future mathematicians will be able to discover any weaknesses in the ECDSA algorithm with the secp256k1 curve.

It will not, however, ever be possible to brute-force attempt 2²⁵⁶ possibilities.

2^160   1461501637330900000000000000000000000000000000000

2¹⁶⁰ is the security level of version 1 bitcoin addresses.

2^256   115792089237316000000000000000000000000000000000000000000000000000000000000000   <- And this is how safe bitcoin is.

Nope.

That's how secure an ECDSA public key is, but version 1 bitcoin addresses use a 160 bit hash of that public key, so the security is reduced to 2¹⁶⁰.

So a version 1 bitcoin address has a security level of 2¹⁶⁰, but how to make sure you have a security of 2²⁵⁶? From when on was the version 1 bitcoin address abandoned and we are sure to enjoy increased security?

Maybe I'm understanding this wrong and everybody is using version 1 addresses, but I would rather know for sure I'm using the safest keys possible.

[Bulista]

-snip-

It will not, however, ever be possible to brute-force attempt 2²⁵⁶ possibilities.

-snip-

2^256   115792089237316000000000000000000000000000000000000000000000000000000000000000   <- And this is how safe bitcoin is.

Nope.

That's how secure an ECDSA public key is, but version 1 bitcoin addresses use a 160 bit hash of that public key, so the security is reduced to 2¹⁶⁰.

Effectively yes.

My analogy was based on the fact that there are 2^256 private keys.

With regards to the future, we never know what will be possible tomorrow.

I believe somehow there will be some kind of evolution in computation that will make all the current encryption algorithms useless, but surely not during our life time.

I know its hard to believe, but if back in 1700 you'd tell Isaac Newton that one day mankind would have something called computers at home doing millions of instructions per second using his formulas, it would also be hard to believe.

[BurtW]

After some analysis I believe the underlying sequence is probably random.  It may have been a PRNG instead of a RNG but that would not help us much.  It would be great if we had all 50 actual values to work with.

Code:

  BTC   Actual      Range of Values                        Location
Value  Value       Low                    High            in Range
-----  ----------  -------------------------------------  ---------
0.001  1           0                      1               100.0000%
0.002  3           2                      3               100.0000%
0.003  7           4                      7               100.0000%
0.004  8           8                      15                0.0000%
0.005  21          16                     31               33.3333%
0.006  49          32                     63               54.8387%
0.007  76          64                     127              19.0476%
0.008  224         128                    255              75.5906%
0.009  467         256                    511              82.7451%
0.010  514         512                    1,023             0.3914%
0.011  1,155       1,024                  2,047            12.8055%
0.012  2,683       2,048                  4,095            31.0210%
0.013  5,216       4,096                  8,191            27.3504%
0.014  10,544      8,192                  16,383           28.7144%
0.015  26,867      16,384                 32,767           63.9871%
0.016  51,510      32,768                 65,535           57.1978%
0.017  95,823      65,536                 131,071          46.2150%
0.018  198,669     131,072                262,143          51.5728%
0.019  357,535     262,144                524,287          36.3889%
0.020  863,317     524,288                1,048,575        64.6648%
0.021  1,811,764   1,048,576              2,097,151        72.7833%
0.022  3,007,503   2,097,152              4,194,303        43.4089%
0.023  5,598,802   4,194,304              8,388,607        33.4858%
0.024  14,428,676  8,388,608              16,777,215       72.0032%
0.025              16,777,216             33,554,431
0.026              33,554,432             67,108,863
0.027              67,108,864             134,217,727
0.028              134,217,728            268,435,455
0.029              268,435,456            536,870,911
0.030              536,870,912            1,073,741,823
0.031              1,073,741,824          2,147,483,647
0.032              2,147,483,648          4,294,967,295
0.033              4,294,967,296          8,589,934,591
0.034              8,589,934,592          17,179,869,183
0.035              17,179,869,184         34,359,738,367
0.036              34,359,738,368         68,719,476,735
0.037              68,719,476,736         137,438,953,471
0.038              137,438,953,472        274,877,906,943
0.039              274,877,906,944        549,755,813,887
0.040              549,755,813,888        1,099,511,627,775
0.041              1,099,511,627,776      2,199,023,255,551
0.042              2,199,023,255,552      4,398,046,511,103
0.043              4,398,046,511,104      8,796,093,022,207
0.044              8,796,093,022,208      17,592,186,044,415
0.045              17,592,186,044,416     35,184,372,088,831
0.046              35,184,372,088,832     70,368,744,177,663
0.047              70,368,744,177,664     140,737,488,355,327
0.048              140,737,488,355,328    281,474,976,710,655
0.049              281,474,976,710,656    562,949,953,421,311
0.050              562,949,953,421,312    1,125,899,906,842,620
0.051              1,125,899,906,842,620  2,251,799,813,685,250
0.052              2,251,799,813,685,250  4,503,599,627,370,490

[BurtW]

With regards to the future, we never know what will be possible tomorrow.

Not exactly true.  With respect to brute forcing a private key we know it will never be possible because we can calculate how much energy it would take for a theoretical best possible computer from a thermodynamics point of view to do the task of just counting from 1 to 2¹⁶⁰ or 2²⁵⁶.

Since any possible actual computer will be less efficient than the best possible computer we know it will take any possible actual computer more energy than the theoretical machine - which is already too much energy.

Carefully reread the description next to the picture of the sun that is posted every single time this question is posed.

In your previous thread it was posted here:

https://bitcointalk.org/index.php?topic=1305887.msg13377953#msg13377953

[BurtW]

So a version 1 bitcoin address has a security level of 2¹⁶⁰, but how to make sure you have a security of 2²⁵⁶? From when on was the version 1 bitcoin address abandoned and we are sure to enjoy increased security?

Maybe I'm understanding this wrong and everybody is using version 1 addresses, but I would rather know for sure I'm using the safest keys possible.

Even though the security of Bitcoin is reduced to "only" 2¹⁶⁰ by the selected second hashing algorithm it is actually more secure in other ways due to the selection of two different hashing algorithms in the public key to Bitcoin address step since both algorithms need to be broken in order to break that step.

Every step of the way everything possible was done to ensure that Bitcoin was secure.  For example Bitcoin is one of the only systems in existence that uses the secp256k1 curve instead of the secp256r1 curve that is used by almost everyone else.  But this was a very wise decision in light of recent leaks about the NSA and their underhanded practices with respect to the cryptography they produce or help produce.

secp256r1 was designed by the NSA, secp256k1 was not.

[Amph]

With regards to the future, we never know what will be possible tomorrow.

Not exactly true.  With respect to brute forcing a private key we know it will never be possible because we can calculate how much energy it would take for a theoretical best possible computer from a thermodynamics point of view to do the task of just counting from 1 to 2¹⁶⁰ or 2²⁵⁶.

Since any possible actual computer will be less efficient than the best possible computer we know it will take any possible actual computer more energy than the theoretical machine - which is already too much energy.

Carefully reread the description next to the picture of the sun that is posted every single time this question is posed.

In your previous thread it was posted here:

https://bitcointalk.org/index.php?topic=1305887.msg13377953#msg13377953

mmh, "never" is a strong statement, you can't be sure about a very distant future. 1-10 thousand years or more, maybe the laws that we know today will be reviewed, because new things will be discovered in the unknown universe

even satoshi said that if something will broke sha256 in the future, it will be a completely new thing, not imaginable today

[Bulista]

After some analysis I believe the underlying sequence is probably random.  It may have been a PRNG instead of a RNG but that would not help us much.  It would be great if we had all 50 actual values to work with.

Code:

  BTC   Actual      Range of Values                        Location
Value  Value       Low                    High            in Range
-----  ----------  -------------------------------------  ---------
0.001  1           0                      1               100.0000%
0.002  3           2                      3               100.0000%
0.003  7           4                      7               100.0000%
0.004  8           8                      15                0.0000%
0.005  21          16                     31               33.3333%
0.006  49          32                     63               54.8387%
0.007  76          64                     127              19.0476%
0.008  224         128                    255              75.5906%
0.009  467         256                    511              82.7451%
0.010  514         512                    1,023             0.3914%
0.011  1,155       1,024                  2,047            12.8055%
0.012  2,683       2,048                  4,095            31.0210%
0.013  5,216       4,096                  8,191            27.3504%
0.014  10,544      8,192                  16,383           28.7144%
0.015  26,867      16,384                 32,767           63.9871%
0.016  51,510      32,768                 65,535           57.1978%
0.017  95,823      65,536                 131,071          46.2150%
0.018  198,669     131,072                262,143          51.5728%
0.019  357,535     262,144                524,287          36.3889%
0.020  863,317     524,288                1,048,575        64.6648%
0.021  1,811,764   1,048,576              2,097,151        72.7833%
0.022  3,007,503   2,097,152              4,194,303        43.4089%
0.023  5,598,802   4,194,304              8,388,607        33.4858%
0.024  14,428,676  8,388,608              16,777,215       72.0032%
0.025              16,777,216             33,554,431
0.026              33,554,432             67,108,863
0.027              67,108,864             134,217,727
0.028              134,217,728            268,435,455
0.029              268,435,456            536,870,911
0.030              536,870,912            1,073,741,823
0.031              1,073,741,824          2,147,483,647
0.032              2,147,483,648          4,294,967,295
0.033              4,294,967,296          8,589,934,591
0.034              8,589,934,592          17,179,869,183
0.035              17,179,869,184         34,359,738,367
0.036              34,359,738,368         68,719,476,735
0.037              68,719,476,736         137,438,953,471
0.038              137,438,953,472        274,877,906,943
0.039              274,877,906,944        549,755,813,887
0.040              549,755,813,888        1,099,511,627,775
0.041              1,099,511,627,776      2,199,023,255,551
0.042              2,199,023,255,552      4,398,046,511,103
0.043              4,398,046,511,104      8,796,093,022,207
0.044              8,796,093,022,208      17,592,186,044,415
0.045              17,592,186,044,416     35,184,372,088,831
0.046              35,184,372,088,832     70,368,744,177,663
0.047              70,368,744,177,664     140,737,488,355,327
0.048              140,737,488,355,328    281,474,976,710,655
0.049              281,474,976,710,656    562,949,953,421,311
0.050              562,949,953,421,312    1,125,899,906,842,620
0.051              1,125,899,906,842,620  2,251,799,813,685,250
0.052              2,251,799,813,685,250  4,503,599,627,370,490

Very good info, thanks.

I also got to similar conclusion, doesn't look like this will be solvable without years of brute force.

It would be great if the guy that cracked the #50 shows up here and tell us the results.

With regards to the future, we never know what will be possible tomorrow.

Not exactly true.  With respect to brute forcing a private key we know it will never be possible because we can calculate how much energy it would take for a theoretical best possible computer from a thermodynamics point of view to do the task of just counting from 1 to 2¹⁶⁰ or 2²⁵⁶.

Since any possible actual computer will be less efficient than the best possible computer we know it will take any possible actual computer more energy than the theoretical machine - which is already too much energy.

Carefully reread the description next to the picture of the sun that is posted every single time this question is posed.

In your previous thread it was posted here:

https://bitcointalk.org/index.php?topic=1305887.msg13377953#msg13377953

mmh, "never" is a strong statement, you can't be sure about a very distant future. 1-10 thousand years or more, maybe the laws that we know today will be reviewed, because new things will be discovered in the unknown universe

even satoshi said that if something will broke sha256 in the future, it will be a completely new thing, not imaginable today

Exactly, was going to reply similar post.

There are many laws in the universe that we still don't know, finding them can completely rewrite everything.

Just look at all the quantum field and you will see how many unanswered questions are there.

Off topic but interesting:

https://www.youtube.com/watch?v=DfPeprQ7oGc

[BurtW]

I am comfortable in my use of "never" since it is based on the most fundamental laws of thermodynamics.

At any rate if a computer ever does simply count from 1 to 2²⁵⁶ look dig me up so you can tell me "I told you so".

[Bulista]

I am comfortable in my use of "never" since it is based on the most fundamental laws of thermodynamics.

At any rate if a computer ever does simply count from 1 to 2²⁵⁶ look dig me up so you can tell me "I told you so".

We all will be long gone when that happens to tell you "I told you so" 

About the puzzle, the final verdict is that it is unsolvable without brute force, same opinion all?

[tyz]

I made some research and I believe that the numbers are results of a polynomial (ring) function.

It also seems that someone already got into this in February 2015. Probably the guy who cashed out the first addresses.
http://pastebin.com/erN0F1ce

-673909/1307674368000*x^15 + 5004253/87178291200*x^14 - 151337/52254720*x^13 + 9320029/106444800*x^12 - 25409989753/14370048000*x^11 + 2192506957/87091200*x^10 - 19011117413/73156608*x^9 + 1200887962891/609638400*x^8 - 3585932821063/326592000*x^7 + 647416874047/14515200*x^6 - 18586394742863/143700480*x^5 + 30899291755337/119750400*x^4 - 274137631043849/825552000*x^3 + 36933161067083/151351200*x^2 - 87781079/1155*x

If you put for x the values 0 to 15, you will get exactly the first 16 numbers.

1
3
7
8
21
49
76
224
467
514
1155
2683
5216
10544
26867
51510

When you put x = 17 then you got -1514935. This is probably because the formula is not complete. There is x^16 to x^256 missing.
The callange is to find out what formula generates the -673909/1307674368000, 5004253/87178291200,... values.

[calkob]

Good luck with this, cause i havn't got a baldy what the heck yous are talking about.   

[ATguy]

I made some research and I believe that the numbers are results of a polynomial (ring) function.

It also seems that someone already got into this in February 2015. Probably the guy who cashed out the first addresses.
http://pastebin.com/erN0F1ce

-673909/1307674368000*x^15 + 5004253/87178291200*x^14 - 151337/52254720*x^13 + 9320029/106444800*x^12 - 25409989753/14370048000*x^11 + 2192506957/87091200*x^10 - 19011117413/73156608*x^9 + 1200887962891/609638400*x^8 - 3585932821063/326592000*x^7 + 647416874047/14515200*x^6 - 18586394742863/143700480*x^5 + 30899291755337/119750400*x^4 - 274137631043849/825552000*x^3 + 36933161067083/151351200*x^2 - 87781079/1155*x

If you put for x the values 0 to 15, you will get exactly the first 16 numbers.

1
3
7
8
21
49
76
224
467
514
1155
2683
5216
10544
26867
51510

When you put x = 17 then you got -1514935. This is probably because the formula is not complete. There is x^16 to x^256 missing.
The callange is to find out what formula generates the -673909/1307674368000, 5004253/87178291200,... values.

Nice finding, so it is puzzle afterall and not just bruteforcing the x random bits. It also explain why the adresses are redeemed in bundles at the same time...