pbies (OP)
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February 06, 2024, 08:08:13 AM |
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I have written Python script to find all divisors of puzzle's integer private keys: #!/usr/bin/env python3
def get_divisors(n): divisors = [] for i in range(1, n+1): if n % i == 0: divisors.append(i) return divisors
i=[ 1, 3, 7, 8, 21, 49, 76, 224, 467, 514, 1155, 2683, 5216, 10544, 26867, 51510, 95823, 198669, 357535, 863317, 1811764, 3007503, 5598802, 14428676, 33185509, 54538862, 111949941, 227634408, 400708894, 1033162084, 2102388551, 3093472814, 7137437912, 14133072157, 20112871792, 42387769980, 100251560595, 146971536592, 323724968937, 1003651412950, 1458252205147, 2895374552463, 7409811047825, 15404761757071, 19996463086597, 51408670348612, 119666659114170, 191206974700443, 409118905032525, 611140496167764, 2058769515153876, 4216495639600700, 6763683971478124, 9974455244496707, 30045390491869460, 44218742292676575, 138245758910846492, 199976667976342049, 525070384258266191, 1135041350219496382, 1425787542618654982, 3908372542507822062, 8993229949524469768, 30568377312064202855 ]
for j in i: print(str(j)+'='+str(get_divisors(j)))
I get: 1=[1] 3=[1, 3] 7=[1, 7] 8=[1, 2, 4, 8] 21=[1, 3, 7, 21] 49=[1, 7, 49] 76=[1, 2, 4, 19, 38, 76] 224=[1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224] 467=[1, 467] 514=[1, 2, 257, 514] 1155=[1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155] 2683=[1, 2683] 5216=[1, 2, 4, 8, 16, 32, 163, 326, 652, 1304, 2608, 5216] 10544=[1, 2, 4, 8, 16, 659, 1318, 2636, 5272, 10544] 26867=[1, 67, 401, 26867] 51510=[1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 101, 102, 170, 202, 255, 303, 505, 510, 606, 1010, 1515, 1717, 3030, 3434, 5151, 8585, 10302, 17170, 25755, 51510] 95823=[1, 3, 7, 9, 13, 21, 27, 39, 63, 81, 91, 117, 169, 189, 273, 351, 507, 567, 819, 1053, 1183, 1521, 2457, 3549, 4563, 7371, 10647, 13689, 31941, 95823] 198669=[1, 3, 47, 141, 1409, 4227, 66223, 198669] 357535=[1, 5, 23, 115, 3109, 15545, 71507, 357535] 863317=[1, 7, 13, 53, 91, 179, 371, 689, 1253, 2327, 4823, 9487, 16289, 66409, 123331, 863317] 1811764=[1, 2, 4, 19, 31, 38, 62, 76, 124, 589, 769, 1178, 1538, 2356, 3076, 14611, 23839, 29222, 47678, 58444, 95356, 452941, 905882, 1811764] 3007503=[1, 3, 9, 23, 27, 29, 69, 87, 167, 207, 261, 501, 621, 667, 783, 1503, 2001, 3841, 4509, 4843, 6003, 11523, 14529, 18009, 34569, 43587, 103707, 111389, 130761, 334167, 1002501, 3007503] 5598802=[1, 2, 11, 22, 254491, 508982, 2799401, 5598802] 14428676=[1, 2, 4, 19, 38, 76, 189851, 379702, 759404, 3607169, 7214338, 14428676] 33185509=[1, 7, 4740787, 33185509] 54538862=[1, 2, 7, 14, 49, 98, 556519, 1113038, 3895633, 7791266, 27269431, 54538862] 111949941=[1, 3, 43, 129, 867829, 2603487, 37316647, 111949941] 227634408=[1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216, 1053863, 2107726, 3161589, 4215452, 6323178, 8430904, 9484767, 12646356, 18969534, 25292712, 28454301, 37939068, 56908602, 75878136, 113817204, 227634408] 400708894=[1, 2, 83, 166, 2413909, 4827818, 200354447, 400708894] 1033162084=[1, 2, 4, 47, 94, 188, 5495543, 10991086, 21982172, 258290521, 516581042, 1033162084] 2102388551=[1, 19, 43, 167, 361, 811, 817, 3173, 7181, 15409, 15523, 34873, 60287, 135437, 136439, 292771, 662587, 2573303, 2592341, 5823791, 12589153, 48892757, 110652029, 2102388551] ...
Maybe some look into divisors could give us something?
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