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Old 2022-06-22, 11:13   #1
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

344610 Posts
Default Smallest GFN divisors

Smallest k such that k*2^(n+1)+1 is prime and divides GFN(b,n) = b^(2^n)+1 (such prime factors must be == 1 mod 2^(n+1)), for 2<=b<=40, 1<=n<=40

search limit of k: 2^24

Code:
b: n = 1 to 40
2: 1, 2, 16, 2048, 10, 2142, 0, 0, 2368, 22262, 78, 14, 0, 0, 18528, 6300, 0, 26, 67258, 0, 1069378, 0, 10, 0, 387304, 572660, 564060, 0, 2240098, 298082, 0, 2958, 0, 0, 0, 20, 0, 12, 42, 0,
3: 1, 5, 1, 672605, 0, 0, 1, 24, 131233, 29, 193, 0, 0, 0, 1, 0, 0, 0, 13, 0, 37, 0, 0, 0, 0, 24, 0, 23, 72, 0, 1080, 24, 0, 1469, 0, 6630, 0, 12, 42, 0,
4: 4, 32, 4096, 20, 4284, 0, 0, 4736, 44524, 156, 28, 0, 0, 37056, 12600, 0, 52, 134516, 0, 2138756, 0, 20, 0, 774608, 1145320, 1128120, 0, 4480196, 596164, 0, 5916, 0, 0, 0, 40, 0, 24, 84, 0, 0,
5: 3, 39, 1, 81, 10, 6, 1, 3234, 19, 0, 367, 0, 10, 0, 1, 303, 3, 27, 7, 0, 0, 0, 10, 74, 4693852, 14922236, 0, 0, 0, 0, 0, 710, 0, 909, 0, 20, 0, 2465247, 267, 21,
6: 9, 162, 1, 11, 43, 0, 1, 36, 79, 183612, 0, 0, 0, 0, 1, 0, 0, 0, 13, 0, 12585474, 6969006, 2426623, 0, 37, 0, 193, 0, 0, 0, 0, 6682476, 42390, 0, 96, 336, 0, 0, 20136, 191,
7: 1, 150, 1, 11, 120307, 281, 1, 55991, 13, 6, 28, 1451, 0, 5, 1, 0, 247, 0, 67, 1036386, 1107, 0, 0, 0, 6748, 0, 0, 0, 0, 0, 10752, 333, 4684764, 6, 0, 0, 0, 0, 0, 155,
8: 1, 2, 6, 6, 10, 6, 0, 0, 2368, 6, 78, 14, 2424, 0, 18528, 6, 0, 26, 570, 0, 1752, 53430, 10, 0, 1110, 222, 12, 144, 5094, 13092, 0, 2958, 0, 6, 0, 20, 950988, 12, 42, 2418,
9: 10, 2, 1345210, 0, 0, 2, 48, 262466, 58, 386, 0, 0, 0, 2, 0, 0, 0, 26, 0, 74, 0, 0, 0, 0, 48, 0, 46, 144, 0, 2160, 48, 0, 2938, 0, 13260, 0, 24, 84, 0, 0,
10: 25, 9, 1, 11, 310, 9882899, 1, 21, 1479, 0, 0, 56021, 0, 0, 1, 63, 670, 1220, 67, 80, 0, 12123906, 0, 0, 0, 17, 0, 0, 49, 0, 0, 0, 0, 0, 40, 0, 287443, 0, 52731, 21,
11: 15, 915, 1, 1604, 3, 0, 60, 29669, 0, 859602, 412872, 0, 0, 5, 1, 1139069, 0, 0, 67, 0, 0, 0, 3183, 96, 0, 0, 13, 5601, 1695, 0, 43, 14897424, 0, 0, 3, 0, 0, 0, 0, 0,
12: 1, 11, 1, 4811, 12, 282, 1, 16121, 0, 3187781, 421, 5, 0, 5, 1, 3074610, 0, 11, 13, 0, 408, 0, 1967988, 0, 0, 2616, 0, 0, 49, 127182, 0, 0, 0, 0, 0, 0, 0, 12, 42, 120,
13: 1, 1785, 0, 83, 3, 2, 378, 0, 0, 0, 163, 5, 162, 5, 166723, 104, 0, 0, 0, 303, 0, 10482, 0, 14, 0, 17, 0, 522986, 3, 0, 0, 0, 0, 0, 213, 348140, 0, 0, 0, 0,
14: 49, 5, 1, 6, 117, 0, 1, 714, 0, 462165, 192, 14, 0, 29831, 1, 0, 4687, 0, 0, 120984, 0, 0, 0, 0, 0, 0, 1387, 6, 0, 99, 0, 495, 0, 0, 0, 0, 18343, 0, 42, 0,
15: 28, 2, 445, 8, 42, 1184, 12054120, 26, 603, 67802, 0, 5, 4, 0, 117, 125, 3, 0, 0, 0, 0, 0, 0, 0, 118, 2859, 0, 0, 0, 422, 0, 5914136, 16765, 7650, 0, 0, 0, 0, 0, 21,
16: 64, 8192, 40, 8568, 0, 0, 9472, 89048, 312, 56, 0, 0, 74112, 25200, 0, 104, 269032, 0, 4277512, 0, 40, 0, 1549216, 2290640, 2256240, 0, 8960392, 1192328, 0, 11832, 0, 0, 0, 80, 0, 48, 168, 0, 0, 695760,
17: 1, 5220, 1182, 8, 22, 6, 13, 0, 0, 0, 12831172, 509, 4, 542826, 0, 8094780, 1260, 0, 759955, 0, 0, 0, 0, 5, 0, 15884, 0, 0, 0, 0, 0, 0, 36252, 0, 0, 95675, 0, 5, 0, 0,
18: 1, 14, 6, 0, 3972, 2, 0, 2808, 0, 4954524, 3328, 0, 0, 2, 0, 11316, 4500330, 0, 0, 78, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12336, 578, 0, 0, 3769900, 0, 0, 12, 42, 0,
19: 45, 2, 942, 3, 2370, 282, 1, 45426, 2139823, 9, 15, 0, 0, 2, 18450, 225956, 199, 3188177, 0, 0, 0, 77, 83221, 0, 0, 107, 0, 0, 0, 0, 0, 24, 0, 12246954, 735, 0, 0, 0, 205, 141,
20: 100, 20000, 1, 3, 3, 0, 1, 0, 56272, 6, 0, 0, 39, 0, 1, 164, 0, 57, 0, 9371, 159, 0, 10, 0, 0, 2210, 0, 3464, 3, 39, 8437, 0, 0, 6, 0, 20, 0, 0, 97, 21,
21: 3, 12155, 3931, 38, 0, 2, 0, 74, 19, 6, 16, 0, 0, 0, 27, 164, 3144, 11, 530932, 0, 25, 0, 120, 0, 0, 0, 0, 0, 0, 0, 83896, 716, 0, 6, 0, 0, 0, 0, 42, 0,
22: 1, 9, 1, 14, 4, 221, 3, 74, 0, 1295, 0, 5, 9, 0, 1, 213, 3, 57, 88756, 0, 0, 0, 0, 5637483, 0, 0, 340, 0, 0, 0, 0, 0, 0, 0, 3291, 3830043, 0, 0, 0, 0,
23: 1, 17490, 1, 6, 4, 0, 0, 0, 0, 35052, 0, 88506, 0, 0, 1, 590849, 87, 8279, 913, 420, 3871740, 0, 0, 0, 45147, 0, 0, 0, 3, 0, 4512, 0, 0, 0, 0, 0, 0, 72, 295705, 3,
24: 144, 41472, 1, 6, 7, 4481, 1, 23, 540175, 6, 779821, 2779236, 1856473, 0, 1, 6, 12959832, 0, 13, 0, 0, 0, 0, 0, 535, 0, 12, 0, 72, 548039, 0, 0, 0, 6, 12265, 30, 24, 84, 389473, 82823,
25: 78, 2, 162, 20, 12, 2, 6468, 38, 0, 734, 0, 20, 0, 2, 606, 6, 54, 14, 0, 0, 0, 20, 148, 9387704, 0, 0, 0, 0, 0, 0, 1420, 0, 1818, 0, 40, 0, 4930494, 534, 42, 44,
26: 169, 2, 226, 3168, 2002107, 2, 3, 0, 0, 0, 0, 8, 0, 519, 18, 123, 0, 11, 120420, 0, 10051294, 0, 0, 11261, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0,
27: 1, 5, 1, 2400, 114, 2190, 1, 24, 50304, 29, 193, 3990, 0, 114, 1, 3797928, 0, 0, 13, 214548, 37, 0, 0, 324, 0, 24, 0, 23, 72, 0, 1080, 24, 7682544, 1469, 0, 6630, 144, 12, 42, 0,
28: 1, 76832, 1, 3, 120858, 74, 1, 0, 544, 56, 10, 0, 0, 206, 1, 0, 0, 358316, 0, 0, 0, 0, 0, 4425, 92947, 275, 0, 1798848, 0, 0, 2085642, 4211, 236082, 0, 1461, 0, 0, 84, 77023, 0,
29: 105, 44205, 1, 0, 3, 2, 42, 836, 57, 0, 2061, 0, 9, 0, 1, 503, 21264, 0, 0, 105303, 0, 0, 4598716, 0, 0, 0, 0, 0, 0, 399200, 0, 6326, 0, 0, 81, 30, 0, 0, 42, 3,
30: 4, 30, 21, 3, 0, 24242, 0, 0, 85, 186, 0, 127376, 4, 824, 55, 0, 0, 0, 0, 181044, 33, 0, 67068, 0, 7, 0, 1042, 123, 0, 0, 0, 231, 0, 0, 1599171, 1055, 63, 1377, 0, 21,
31: 3, 51, 1, 59, 75, 2, 0, 0, 25, 56, 0, 0, 73, 149, 1, 0, 0, 487646, 1693030, 17805, 1225, 119, 126430, 0, 3590008, 0, 0, 17270, 0, 0, 0, 333, 13419, 6, 0, 0, 85, 0, 6, 0,
32: 1, 2, 16, 2048, 10, 2142, 0, 0, 60, 20, 78, 14, 10, 27540, 18528, 6300, 0, 26, 3060, 0, 1069378, 0, 10, 54410, 387304, 572660, 564060, 0, 850, 298082, 0, 2958, 0, 60, 9352830, 20, 0, 12, 42, 0,
33: 1, 12, 0, 18, 3, 26, 1, 117078, 754, 32, 268473, 398, 7, 266, 0, 4422768, 528, 0, 25, 17615, 0, 0, 0, 0, 7, 24, 0, 0, 13109542, 0, 0, 16042895, 5912607, 0, 3, 1974, 0, 114, 912793, 1236060,
34: 3, 167042, 2965, 3, 0, 58415, 0, 1508, 172, 611, 0, 0, 4, 0, 18, 6, 147, 0, 0, 63599, 0, 0, 157, 5, 0, 0, 478, 65, 3, 0, 2333125, 0, 12, 6231261, 0, 3264, 352, 5, 0, 15170525,
35: 153, 93789, 7, 18, 3, 0, 3, 0, 49, 13884, 10, 21390, 0, 2, 21, 0, 1926507, 41, 1567, 879968, 1107, 0, 0, 0, 0, 29, 0, 0, 3, 545, 1017, 0, 247, 0, 0, 0, 0, 206, 6, 21,
36: 324, 2, 22, 86, 0, 2, 72, 158, 367224, 0, 0, 0, 0, 2, 0, 0, 0, 26, 0, 0, 13938012, 4853246, 0, 74, 0, 386, 0, 0, 0, 0, 13364952, 84780, 0, 192, 672, 0, 0, 40272, 382, 0,
37: 1, 11, 1, 173958, 7, 0, 1, 156, 0, 29, 940, 0, 0, 2, 0, 185940, 28023, 0, 13, 0, 2268, 0, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 85, 5435, 3803373, 99,
38: 1, 5, 33693, 46728, 0, 6, 1, 21, 148, 0, 40, 6006, 6138195, 2, 408457, 8169, 262, 0, 0, 11, 0, 342, 0, 0, 47833, 0, 13, 0, 0, 0, 157621, 0, 0, 0, 0, 0, 1380, 0, 88410, 0,
39: 190, 144590, 1, 44, 3, 3914187, 1, 0, 691900, 65, 78, 0, 0, 0, 1, 0, 0, 0, 13, 80, 0, 0, 42658, 0, 0, 0, 23230, 0, 3, 0, 0, 0, 0, 0, 2163, 0, 10, 0, 88, 0,
40: 400, 96, 1, 270, 2877073, 3429, 1, 971, 13, 0, 56997, 0, 8525922, 0, 1, 303, 3, 2870, 0, 0, 0, 20, 28, 51, 0, 23426, 0, 0, 0, 0, 0, 170, 0, 80, 0, 0, 0, 0, 0, 21,

Last fiddled with by sweety439 on 2022-06-22 at 11:13
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