Quote from: iceland2k14 on July 14, 2024, 11:27:53 AM

So instead of blind bruteforcing we could try to find the maximum likelihood range. This off course may not work for each of the remaining puzzle but if we see them together as a whole there seems to be a way of approach for many of them.
Privatekey being a composite number will have several factors. We are not interested in the Prime Factors but instead all the possible factors. Because once we have (somehow) a factor of the privatekey then the difficulty of that Key is reduced. Before thinking about how we can get a factor of the unknown Key, Lets analyze this concept in the already Found Keys first. There are some interesting observation. Some Keys are

what do you mean by "all the possible factors"?
this is what i found by factorizing the priv keys

Code:

0x1 : 1 : 1
0x3 : 3 : 3
0x7 : 7 : 7
0x8 : 8 : 2^3
0x15 : 21 : 3 * 7
0x31 : 49 : 7^2
0x4c : 76 : 2^2 * 19
0xe0 : 224 : 2^5 * 7
0x1d3 : 467 : 467
0x202 : 514 : 2 * 257
0x483 : 1155 : 3 * 5 * 7 * 11
0xa7b : 2683 : 2683
0x1460 : 5216 : 2^5 * 163
0x2930 : 10544 : 2^4 * 659
0x68f3 : 26867 : 67 * 401
0xc936 : 51510 : 2 * 3 * 5 * 17 * 101
0x1764f : 95823 : 3^4 * 7 * 13^2
0x3080d : 198669 : 3 * 47 * 1409
0x5749f : 357535 : 5 * 23 * 3109
0xd2c55 : 863317 : 7 * 13 * 53 * 179
0x1ba534 : 1811764 : 2^2 * 19 * 31 * 769
0x2de40f : 3007503 : 3^3 * 23 * 29 * 167
0x556e52 : 5598802 : 2 * 11 * 254491
0xdc2a04 : 14428676 : 2^2 * 19 * 189851
0x1fa5ee5 : 33185509 : 7 * 4740787
0x340326e : 54538862 : 2 * 7^2 * 556519
0x6ac3875 : 111949941 : 3 * 43 * 867829
0xd916ce8 : 227634408 : 2^3 * 3^3 * 1053863
0x17e2551e : 400708894 : 2 * 83 * 2413909
0x3d94cd64 : 1033162084 : 2^2 * 47 * 5495543
0x7d4fe747 : 2102388551 : 19^2 * 43 * 167 * 811
0xb862a62e : 3093472814 : 2 * 23 * 3001 * 22409
0x1a96ca8d8 : 7137437912 : 2^3 * 11 * 751 * 107999
0x34a65911d : 14133072157 : 19 * 41 * 131 * 138493
0x4aed21170 : 20112871792 : 2^4 * 13 * 96696499
0x9de820a7c : 42387769980 : 2^2 * 3^2 * 5 * 235487611
0x1757756a93 : 100251560595 : 3 * 5 * 6683437373
0x22382facd0 : 146971536592 : 2^4 * 60037 * 153001
0x4b5f8303e9 : 323724968937 : 3^2 * 138319 * 260047
0xe9ae4933d6 : 1003651412950 : 2 * 5^2 * 20073028259
0x153869acc5b : 1458252205147 : 23 * 63402269789
0x2a221c58d8f : 2895374552463 : 3^2 * 59 * 5452682773
0x6bd3b27c591 : 7409811047825 : 5^2 * 587 * 2903 * 173933
0xe02b35a358f : 15404761757071 : 2783789 * 5533739
0x122fca143c05 : 19996463086597 : 157 * 193 * 7477 * 88261
0x2ec18388d544 : 51408670348612 : 2^2 * 5839 * 2201090527
0x6cd610b53cba : 119666659114170 : 2 * 3^3 * 5 * 7 * 17 * 89 * 41847781
0xade6d7ce3b9b : 191206974700443 : 3 * 13 * 4902742941037
0x174176b015f4d : 409118905032525 : 3^2 * 5^2 * 23 * 197 * 1663 * 241313
0x22bd43c2e9354 : 611140496167764 : 2^2 * 3^2 * 12211 * 1390232159
0x75070a1a009d4 : 2058769515153876 : 2^2 * 3 * 7 * 43 * 53 * 197 * 2477 * 22039
0xefae164cb9e3c : 4216495639600700 : 2^2 * 5^2 * 53 * 795565215019
0x180788e47e326c : 6763683971478124 : 2^2 * 14359547 * 117755873
0x236fb6d5ad1f43 : 9974455244496707 : 7019 * 76123 * 18668011
0x6abe1f9b67e114 : 30045390491869460 : 2^2 * 5 * 19 * 79066817083867
0x9d18b63ac4ffdf : 44218742292676575 : 3^2 * 5^2 * 13 * 15117518732539
0x1eb25c90795d61c : 138245758910846492 : 2^2 * 23 * 1002377 * 1499107913
0x2c675b852189a21 : 199976667976342049 : 13 * 167 * 2511323 * 36678953
0x7496cbb87cab44f : 525070384258266191 : 307^2 * 5571097669559
0xfc07a1825367bbe : 1135041350219496382 : 2 * 13 * 31 * 71 * 269 * 587 * 3637 * 34537
0x13c96a3742f64906 : 1425787542618654982 : 2 * 13 * 54837982408409807
0x363d541eb611abee : 3908372542507822062 : 2 * 3 * 43 * 62922991 * 240750329
0x7cce5efdaccf6808 : 8993229949524469768 : 2^3 * 7 * 251 * 2383 * 268491108091
0xf7051f27b09112d4 : 17799667357578236628 : 2^2 * 3 * 19 * 3761 * 408229 * 50847529
0x1a838b13505b26867 : 30568377312064202855 : 5 * 67 * 5639 * 16181749866767

i don't understand how you found the "special" pattern you talked about