>> (p.1)
    Author Topic: Puzzle's divisors  (Read 202 times)
    pbies (OP)
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    February 06, 2024, 08:08:13 AM
     #1

    I have written Python script to find all divisors of puzzle's integer private keys:

    Code:
    #!/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:

    Code:
    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?

    BTC: bc1qmrexlspd24kevspp42uvjg7sjwm8xcf9w86h5k
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