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Williams primes of the form (b-1)•bn-1

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Primes table

b Date max n # Primes for nTemplate:Williams prime dpl.defaultTemplate:Williams prime dpl.defaultTemplate:Williams prime dpl.defaultTemplate:Williams prime dpl.default
2 2024-10-31
GIMPS 		124,817,431 52 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161, 74207281, 77232917, 82589933, 136279841
3 2024-08-01 2,000,000 38 1, 2, 3, 7, 8, 12, 20, 23, 27, 35, 56, 62, 68, 131, 222, 384, 387, 579, 644, 1772, 3751, 5270, 6335, 8544, 9204, 12312, 18806, 21114, 49340, 75551, 90012, 128295, 143552, 147488, 1010743, 1063844, 1360104, 2834778
4 2024-10-13
PrimeGrid 		11,010,905 40 1, 2, 3, 9, 17, 19, 32, 38, 47, 103, 108, 153, 162, 229, 235, 637, 1638, 2102, 2567, 6338, 7449, 12845, 20814, 40165, 61815, 77965, 117380, 207420, 351019, 496350, 600523, 1156367, 2117707, 5742009, 5865925, 5947859, 8874017, 9462494, 10464378, 11051688
5 2024-08-30 1,000,000 25 1, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339, 2033, 6583, 15393, 282989, 498483, 504221, 754611, 864751, 1132659, 1292915, 1330541, 3189669, 6181673
6 2023-11-21 1,000,000 29 1, 2, 6, 7, 11, 23, 33, 48, 68, 79, 116, 151, 205, 1016, 1332, 1448, 3481, 3566, 3665, 11233, 13363, 29166, 44358, 58530, 191706, 386450, 605168, 616879, 1204077
7 2015-11-13 200,000 21 1, 2, 7, 18, 55, 69, 87, 119, 141, 189, 249, 354, 1586, 2135, 2865, 2930, 4214, 7167, 67485, 74402, 79326
8 2024-06-13 4,000,000 12 3, 7, 15, 59, 6127, 8703, 11619, 23403, 124299, 1743223, 3537579, 4095347
9 2016-02-02 200,000 17 1, 2, 5, 25, 85, 92, 97, 649, 2017, 2978, 3577, 4985, 17978, 21365, 66002, 95305, 142199
10 2024-09-30 600,000 22 1, 3, 7, 19, 29, 37, 93, 935, 8415, 9631, 11143, 41475, 41917, 48051, 107663, 212903, 223871, 260253, 364521, 383643, 1009567, 1762063
11 2024-09-17 300,000 13 1, 3, 37, 119, 255, 355, 371, 497, 1759, 34863, 50719, 147709, 263893
12 2024-08-28 200,000 16 1, 2, 21, 25, 33, 54, 78, 235, 1566, 2273, 2310, 4121, 7775, 42249, 105974, 138961
13 2024-10-03 200,000 16 2, 7, 11, 36, 164, 216, 302, 311, 455, 738, 1107, 2244, 3326, 4878, 8067, 46466
14 2024-10-12 200,000 14 1, 3, 5, 27, 35, 165, 209, 2351, 11277, 21807, 25453, 52443, 63069, 117693
15 2024-10-12 200,000 5 14, 33, 43, 20885, 30323
16 2024-09-02 1,750,000 10 1, 20, 29, 43, 56, 251, 25985, 27031, 142195, 164066
17 2024-10-24 200,000 10 1, 3, 71, 139, 265, 793, 1729, 18069, 80585, 150569
18 2024-10-24 200,000 14 2, 6, 26, 79, 91, 96, 416, 554, 1910, 4968, 53979, 55532, 106760, 139928
19 2024-11-04 200,000 10 6, 9, 20, 43, 174, 273, 428, 1388, 35423, 76364
20 2024-09-09 100,000 7 1, 219, 223, 3659, 31029, 43921, 73113
21 2024-09-09 100,000 16 1, 2, 7, 24, 31, 60, 230, 307, 750, 1131, 1665, 1827, 8673, 27775, 39257, 99102
22 2024-11-04 200,000 14 1, 2, 5, 19, 141, 302, 337, 4746, 5759, 16530, 31301, 45025, 73549, 98449
23 2024-09-15
Richard Kapek 		400,000 8 55, 103, 115, 131, 535, 1183, 9683, 149027
24 2024-09-14 100,000 9 12, 18, 63, 153, 221, 1256, 13116, 15593, 30932
25 2024-11-04 200,000 19 1, 5, 7, 30, 75, 371, 383, 609, 819, 855, 7130, 7827, 9368, 33614, 83133, 107006, 153267, 166679, 196256
26 2024-09-23 100,000 4 133, 205, 215, 1649
27 2024-09-23 100,000 17 1, 3, 5, 13, 15, 31, 55, 151, 259, 479, 734, 1775, 2078, 6159, 6393, 9013, 33499
28 2024-11-04 200,000 5 20, 1091, 5747, 6770, 25598
29 2024-09-25 100,000 7 1, 7, 11, 57, 69, 235, 16487
30 2018-03-17 25,000 11 2, 83, 566, 938, 1934, 2323, 3032, 7889, 8353, 9899, 11785
31 2018-03-17 25,000 13 1, 5, 27, 41, 48, 177, 398, 536, 608, 618, 13728, 14393, 14949
32 2024-09-24
Michael Curtis, Ryan Propper 		670,000 13 1, 7, 23, 41, 47, 693, 16331, 30053, 54823, 81221, 133257, 651837, 1817617
33 2019-04-20 10,000 7 2, 3, 146, 1543, 1592, 2247, 3087
34 2019-04-20 10,000 4 15, 25, 99, 188
35 2019-04-20 10,000 9 3, 5, 7, 13, 31, 69, 341, 437, 485
36 2024-10-03 25,000 10 1, 9, 11, 15, 27, 145, 417, 762, 2693, 21365
37 2019-04-20 10,000 5 7, 325, 439, 3769, 8537
38 2011-07-12 142,000 1 136211
39 2019-04-20 10,000 10 1, 3, 5, 8, 90, 272, 290, 767, 2775, 6809
40 2019-04-20 10,000 6 1, 19, 218, 767, 2607, 7075
41 2019-04-20 10,000 3 7, 295, 1573
42 2019-04-20 10,000 12 1, 3, 6, 9, 11, 47, 61, 105, 263, 517, 5225, 5783
43 2019-04-20 10,000 5 7, 39, 71, 639, 4590
44 2019-04-20 10,000 5 7, 17, 43, 731, 1751
45 2019-04-20 10,000 9 1, 13, 72, 83, 132, 144, 1473, 1901, 4412
46 2019-04-21 10,000 12 1, 2, 3, 9, 12, 24, 68, 108, 476, 619, 839, 1561
47 2019-04-21 10,000 7 1, 9, 15, 45, 211, 1633, 1933
48 2019-04-21 10,000 8 2, 3, 14, 48, 215, 324, 518, 2439
49 2024-10-03 25,000 12 1, 5, 18, 21, 35, 84, 121, 189, 2610, 4281, 4579, 12101
50 2019-04-21 10,000 7 25, 37, 39, 47, 99, 245, 1589
51 2019-04-21 10,000 5 1, 31, 170, 557, 3644
52 2019-04-21 10,000 10 5, 13, 19, 425, 585, 1833, 2130, 3617, 4999, 8447
53 2019-04-21 10,000 3 3, 251, 4567
54 2019-04-21 10,000 9 1, 5, 14, 321, 427, 620, 902, 1461, 1555
55 2019-04-21 10,000 9 1, 15, 44, 71, 98, 147, 225, 242, 4837
56 2019-04-21 10,000 4 1, 25, 77, 297
57 2019-04-21 10,000 5 1, 2, 3, 18, 367
58 2019-04-21 10,000 3 2, 14, 1076
59 2024-10-26
Richard Kapek 		300,000 4 3, 15, 493, 2183
60 2019-04-21 10,000 3 1, 5, 13
61 2019-04-21 10,000 10 1, 2, 7, 25, 132, 216, 439, 482, 581, 1081
62 2019-04-18 10,000 3 899, 2185, 5641
63 2019-04-21 10,000 8 3, 30, 36, 79, 527, 1002, 2687, 8967
64 2021-03-21 833,333 10 11, 21, 119, 1677, 3939, 18759, 19151, 20629, 36449, 101784
65 2024-10-11 100,000 7 1, 7, 619, 785, 1649, 2845, 10537
66 2024-10-11 100,000 13 1, 2, 17, 71, 145, 149, 228, 996, 2898, 3072, 5375, 5954, 32939
67 2024-10-14 100,000 13 1, 2, 18, 54, 63, 203, 863, 1146, 8821, 8855, 24771, 27249, 53637
68 2024-10-18 100,000 3 63, 119, 139
69 2024-10-18 100,000 9 1, 6, 39, 193, 307, 3258, 4166, 16365, 19249
70 2024-10-14 100,000 11 13, 18, 19, 110, 189, 354, 380, 689, 3233, 17657, 36773
71 2024-10-24 100,000 6 1, 59, 93, 2093, 5485, 42931
72 2024-10-24 100,000 4 25, 373, 4010, 7343
73 2024-09-29 25,000 6 8, 12, 98, 204, 231, 536
74 2024-10-03 25,000 5 3, 7, 19, 187, 337
75 2024-10-03 25,000 13 2, 6, 30, 78, 572, 852, 956, 2118, 2874, 9109, 10724, 10897, 23425
76 2024-09-29 25,000 9 7, 18, 37, 51, 66, 83, 246, 263, 10621
77 2024-10-03 25,000 4 1, 7, 69, 1935
78 2024-10-03 25,000 5 44, 228, 2463, 2496, 13550
79 2024-09-29 25,000 6 2, 68, 145, 398, 2663, 8287
80 2024-10-03 25,000 2 11, 889
81 2024-10-03 25,000 10 3, 5, 18, 54, 203, 252, 417, 458, 704, 3090
82 2024-09-29 25,000 1 81
83 2008-08-22 29,000 1 21495
84 2024-10-03 25,000 4 1, 86, 1122, 5629
85 2024-09-29 25,000 9 2, 6, 15, 18, 38, 48, 78, 155, 6505
86 2024-10-03 25,000 5 1, 23, 25, 49, 143
87 2024-10-03 25,000 11 1, 2, 6, 11, 13, 95, 119, 2187, 2967, 6717, 17049
88 2018-04-08 25,000 5 3, 163, 366, 522, 4571
89 2024-10-03 25,000 5 25, 37, 529, 531, 15759
90 2024-10-01 25,000 9 1, 2, 6, 8, 42, 188, 193, 1385, 1871
91 2024-09-29 25,000 3 519, 2598, 5088
92 2024-10-01 25,000 4 77, 613, 7013, 10665
93 2018-04-08 25,000 2 476, 908
94 2024-09-29 25,000 16 1, 2, 6, 18, 25, 73, 205, 408, 540, 855, 966, 2341, 3159, 3461, 10025, 17300
95 2024-10-01 25,000 5 1, 49, 197, 4709, 7189
96 2024-10-01 25,000 7 2, 3, 14, 105, 573, 1280, 2028
97 2024-09-29 25,000 7 1, 23, 25, 102, 165, 511, 1129
98 2024-10-01 25,000 2 4983, 10267
99 2024-10-01 25,000 11 2, 9, 15, 39, 49, 111, 207, 299, 6933, 7419, 11313
100 2024-09-29 200,000 9 2, 17, 35, 41, 359, 1247, 4262, 26041, 69835
101 2024-09-29 25,000 7 1, 3, 5, 27, 99, 383, 3769
102 2024-09-29 25,000 10 1, 6, 17, 31, 53, 117, 537, 839, 1653, 19943
103 2024-09-29 25,000 4 3, 20, 163, 224
104 2024-09-29 25,000 8 1, 9, 15, 23, 1029, 1695, 12409, 14629
105 2024-09-29 25,000 11 3, 33, 60, 141, 289, 429, 788, 842, 6048, 13928, 18089
106 2024-09-29 25,000 11 2, 11, 17, 20, 66, 139, 725, 4079, 7069, 7242, 10490
107 2018-04-08 25,000 6 37, 103, 319, 583, 605, 5317
108 2024-09-29 25,000 2 410, 3187
109 2024-09-29 25,000 8 6, 77, 111, 308, 695, 1899, 2232, 7088
110 2024-09-29 25,000 5 5, 3533, 7511, 7881, 14349
113 2012-10-01 290,000 1 286643
128 2024-04-19 2,450,000 0
158 2018-04-15 25,000 4 127, 263, 323, 6119
188 2008-07-17 20,000 1 13507
233 2014-10-02 250,000 0
256 2024-11-13
No Prime Left Behind 		350,000 5 3, 5, 61, 56268, 74010
268 2022-10-31 500,000 0
293 2013-11-07 200,000 0
383 2013-09-19 200,000 0
401 2013-09-04 103,679 1 103669
417 2011-08-04 21,250 1 21002
458 2011-08-06 50,000 1 46899
478 2013 200,000 0
488 2013-12-02 200,000 0
491 2006-08-31 10,000 7 1, 5, 9, 75, 109, 2171, 3575
492 2006-08-31 10,000 5 29, 283, 1829, 3283, 4223
493 2006-08-31 10,000 6 2, 15, 67, 2199, 4055, 8103
494 2011-08-09 22,000 1 21579
495 2006-08-31 10,000 7 1, 12, 39, 201, 530, 4434, 6767
496 2006-08-31 10,000 5 1, 6, 186, 281, 517
497 2006-08-31 10,000 5 1, 3, 5, 61, 89
498 2006-08-31 10,000 4 2, 8, 26, 906
499 2006-08-31 10,000 2 32, 67
500 2006-08-31 10,000 3 1, 11, 173
512 2024-03-09
No Prime Left Behind 		313,333 5 1, 85, 1659, 4193, 102039
518 2013-09-23 131,000 1 129371
527 2011-08-22 67,000 1 65821
533 2013-12-03 200,000 0
554 2014 200,000 0
602 2011-08-28 22,000 1 17643
608 2011-08-29 37,000 1 36227
638 2011-09-06 76,000 1 74527
663 2011-09-13 75,000 1 47556
665 2014-05-22 200,000 0
698 2011-09-13 200,000 0
758 2011-09-17 50,563 1 50563
779 2014-06-11 200,000 0
833 2011-09-20 16,400 1 12219
863 2011-10-25 200,000 0
878 2014-04-22 200,000 0
918 2011-09-12 10,000 1 9756
932 2014-08-20 200,000 0
938 2011-10-25 51,500 1 50007
941 2014-08-15 200,000 0
950 2011-09-15 20,000 1 16247
1010 2021-05-24 300,000 0
1012 2011-11-02 33,700 1 32693
1024 2014-10-22 190,000 7 1, 7, 38, 74, 89, 115963, 149203
1034 2014-04-08 150,000 0
1088 2012-07-09 41,000 1 29579
1108 2012-07-10 26,000 1 15647
1115 2012-07-11 4,000 1 3629
1142 2014-07-11 15,000 1 9501
1145 2012-09-18 100,000 0
1160 2012-09-20 31,000 1 24303
1163 2012-09-20 5,000 1 3967
1164 2012-10-31 100,000 0
1199 2012-12-03 100,000 0
1253 2012-12-20 100,000 0
1268 2012-12-21 30,000 1 13735
1283 2024-08-21 200,000 0
1290 2019-06-03 5,500 1 5377
1328 2013-01-17 100,000 0
1353 2013-02-17 100,000 0
1388 2013-02-21 52,000 1 49063
1430 2013-03-25 100,000 0
1444 2013-03-25 39,000 1 26345
1489 2013-05-23 100,000 0
1493 2013-05-28 100,000 0
1522 2013-06-18 100,000 0
1558 2013-06 11,000 2 4931, 10944
1559 2013-05-29 21,000 1 20055
1568 2013-05-30 17,000 1 14759
1632 2013-05-30 12,200 1 12169
1653 2013-06-05 55,000 1 21102
1658 2013-06-13 100,000 0
1676 2013-06-13 34,000 1 29309
1683 2013-08-16 100,000 0
1696 2013-06-18 15,700 1 15488
1733 2013-08-07 100,000 0
1738 2013-08-07 100,000 0
1745 2013-08-05 100,000 0
1748 2013-07-08 48,000 1 24095
1772 2013-07-05 33,000 1 13163
1793 2013-07-08 52,000 1 45859
1801 2019-06-05 34,000 1 23089
1808 2013-07-29 100,000 0
1813 2013-07-18 46,800 1 46159
1820 2013-07-18 12,000 1 7051
1826 2013-07-17 6,600 1 6443
1873 2013-08-11 61,000 1 60619
1893 2013-07-24 26,000 2 18264, 21084
1898 2013-07-18 5,000 1 4447
1901 2013-07-18 5,700 1 4177
1913 2013-08-16 100,000 0
1922 2013-08-05 38,000 1 36597
1928 2013-08-21 100,000 0
1940 2013-08-11 62,000 1 55679
1948 2013-08-29 100,000 0
1967 2013-07-24 18,800 1 16993
1970 2013-07-25 27,000 1 13387
1988 2013-09-12 100,000 0
2018 2013-09-12 200,000 0
2036 2013-07-26 13,000 1 12831
2048 2015-05-18 100,000 3 7, 139, 143

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