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Proth primes of the form k•2n+1, 10,000 ≤ k ≤ 100,000
Overview
Automatically generated table from available Proth primes 10,000 < k < 100,000.
Explanations
The colors used in the table are defined as:
- : k-value is reserved
- : k-value is not reserved
Primes table
There are 48 sequences:
| k | Type | Date | max n | Nash | # | Primes for n |
|---|---|---|---|---|---|---|
| 10001 | 2018-04-05 | 1,000,000 | 1114 | 30 | 7, 27, 33, 55, 61, 67, 85, 91, 103, 133, 159, 187, 223, 375, 727, 1179, 1933, 4267, 40915, 104887, 109213, 129183, 227169, 255391, 317107, 354861, 374461, 462753, 960399, 2172615 | |
| 10003 | 2019-07-21 | 400,000 | 2157 | 45 | 2, 4, 6, 14, 18, 28, 42, 44, 50, 64, 74, 78, 96, 174, 212, 288, 352, 596, 642, 686, 712, 796, 1084, 1826, 3632, 3670, 4338, 4594, 5830, 7222, 8962, 12276, 15044, 15590, 22834, 31876, 34676, 37532, 77478, 96670, 177394, 384864, 479254, 528030, 1468292 | |
| 10223 | Low | 2017 | 31,278,077 | 207 | 1 | 31172165 |
| 12321 | 3 | 2020-06-15 | 300,000 | 2495 | 46 | 4, 24, 29, 47, 61, 63, 67, 69, 87, 101, 129, 143, 153, 249, 252, 333, 408, 561, 616, 732, 929, 1349, 3467, 6156, 6919, 9244, 14413, 17128, 20059, 20169, 20512, 23479, 24076, 26208, 27189, 34113, 37648, 43893, 45537, 63107, 79527, 88752, 118701, 122844, 164961, 218753 |
| 12743 | Low | 2020-06-09 | 100,000 | 416 | 3 | 9, 41205, 49113 |
| 15735 | 315 | 2020-10-11 | 50,000 | 2954 | 35 | 4, 7, 10, 94, 95, 98, 110, 128, 136, 200, 215, 334, 559, 676, 740, 856, 935, 1159, 1463, 1468, 1763, 1795, 3274, 4037, 4162, 6139, 6857, 9893, 10228, 14915, 18815, 22903, 28555, 29278, 36490 |
| 19683 | 3 | 2019-10-12 | 4,000,000 | 1802 | 32 | 1, 5, 8, 32, 50, 400, 536, 592, 676, 866, 1157, 1300, 1661, 1730, 2440, 7046, 9698, 16180, 16226, 22330, 26990, 206005, 238780, 278941, 366665, 485845, 493846, 901745, 1797997, 1868828, 2033900, 2265896 |
| 21181 | Low | 2024-11-12 PrimeGrid Seventeen or Bust (MR16) |
42,252,000 | 169 | 0 | |
| 22249 | Low | 2020-04-10 | 500,000 | 284 | 2 | 2, 408602 |
| 22699 | Low | 2024-11-12 PrimeGrid Seventeen or Bust (MR16) |
42,252,000 | 69 | 0 | |
| 23451 | 3 | 2024-06-22 | 100,000 | 1223 | 17 | 43, 75, 147, 163, 197, 203, 709, 973, 1503, 20635, 32333, 36045, 42623, 67103, 186837, 215203, 3739388 |
| 23873 | Low | 2020-04-08 | 136,733 | 282 | 2 | 5, 136733 |
| 23971 | Low | 2020-10-06 | 10,000,000 | 108 | 1 | 8 |
| 24737 | Low | 2024-11-12 PrimeGrid Seventeen or Bust (MR16) |
42,252,000 | 174 | 0 | |
| 27697 | 2024-06-04 | 50,000 | 1193 | 17 | 4, 6, 12, 46, 166, 286, 582, 756, 1132, 1924, 2188, 6454, 7036, 9414, 16774, 25168, 48222 | |
| 28831 | Low | 2020-04-09 | 204,580 | 225 | 2 | 4, 204580 |
| 30985 | 2024-09-24 | 400,000 | 1783 | 29 | 2, 8, 20, 72, 74, 146, 150, 200, 212, 674, 812, 830, 1068, 2630, 3554, 6620, 8856, 11262, 21450, 30548, 53630, 54132, 114074, 114608, 130328, 131166, 176688, 177296, 191706 | |
| 32247 | 3 | 2022-03-04 | 100,000 | 1736 | 23 | 10, 18, 40, 94, 114, 190, 234, 240, 300, 538, 922, 1224, 6514, 8740, 13438, 19692, 23764, 43894, 48862, 49774, 60148, 75202, 75780 |
| 33505 | Low | 2024-10-29 (Blue8thNote) |
110,000 | 843 | 16 | 92, 108, 248, 342, 698, 2282, 3974, 8948, 12504, 22808, 29748, 42384, 57602, 62418, 101676, 174002 |
| 35461 | Low | 2020-04-08 | 129,820 | 202 | 2 | 4, 129820 |
| 39527 | Low | 2020-04-08 | 143,055 | 141 | 2 | 15, 143055 |
| 42717 | 3Low | 2024-06-22 | 100,000 | 893 | 7 | 39, 51, 59, 4671, 5931, 13479, 905792 |
| 44243 | Low | 2020-04-17 | 440,969 | 237 | 2 | 9, 440969 |
| 45323 | Low | 2020-10-17 CRUS Even Sierpiński (MR12) |
10,000,000 | 266 | 1 | 1 |
| 48495 | 315 | 2024-08-22 (Alex_soldier) |
1,200,000 | 3088 | 51 | 11, 13, 29, 40, 43, 49, 50, 70, 73, 82, 106, 125, 163, 251, 269, 349, 401, 479, 527, 614, 920, 1180, 2105, 2789, 3263, 3581, 4690, 6503, 8470, 10582, 12361, 14690, 16702, 20102, 23341, 28379, 44686, 81371, 81443, 87370, 105287, 109625, 112484, 113482, 115156, 137894, 138056, 142984, 189373, 569842, 805655 |
| 50777 | Low | 2020-10-06 | 10,000,000 | 166 | 1 | 11 |
| 50873 | Low | 2020-10-17 CRUS Even Sierpiński (MR12) |
10,000,000 | 410 | 1 | 1 |
| 53133 | 3 | 2022-03-04 | 50,000 | 1475 | 18 | 14, 26, 44, 72, 144, 146, 204, 222, 404, 642, 716, 1116, 1178, 5846, 16292, 21224, 24788, 42542 |
| 54953 | Low | 2020-04-19 | 622,065 | 220 | 2 | 9, 622065 |
| 55459 | Low | 2024-11-12 PrimeGrid Seventeen or Bust (MR16) |
42,252,000 | 242 | 0 | |
| 57377 | Low | 2020-04-09 | 447,439 | 155 | 2 | 7, 447439 |
| 60357 | 3 | 2024-06-22 | 100,000 | 2209 | 34 | 2, 6, 8, 14, 18, 24, 26, 80, 218, 270, 378, 410, 450, 572, 774, 1712, 2660, 2712, 2994, 3500, 4040, 4326, 7766, 8832, 13406, 15578, 31524, 39830, 47186, 48948, 49124, 66804, 95954, 1676907 |
| 60849 | 3 | 2024-06-22 | 100,000 | 1368 | 22 | 9, 129, 147, 181, 225, 337, 549, 597, 1177, 1327, 2685, 11019, 18397, 19539, 66889, 77959, 90405, 95647, 97497, 246691, 390015, 3067914 |
| 66741 | 3Low | 2020-07-05 | 50,000 | 811 | 9 | 5, 51, 95, 117, 237, 357, 2231, 3767, 6837 |
| 67275 | 315 | 2020-10-08 | 1,000 | 3481 | 25 | 3, 4, 7, 9, 13, 15, 22, 33, 36, 37, 49, 64, 69, 72, 78, 93, 102, 109, 145, 211, 216, 277, 325, 348, 457 |
| 67607 | Low | 2024-11-12 PrimeGrid Seventeen or Bust (MR16) |
42,252,000 | 56 | 0 | |
| 68221 | Low | 2020-04-09 | 200,944 | 326 | 2 | 16, 200944 |
| 68633 | Low | 2020-06-02 | 2,715,609 | 250 | 2 | 9, 2715609 |
| 71657 | Low | 2020-05-01 | 1,146,175 | 327 | 2 | 15, 1146175 |
| 76877 | Low | 2020-10-06 | 10,000,000 | 96 | 1 | 11 |
| 77297 | Low | 2020-04-08 | 118,499 | 257 | 2 | 3, 118499 |
| 77777 | Low | 2023-05-28 (Alex_soldier) |
2,100,000 | 374 | 6 | 15, 103, 223, 1063, 34087, 2013487 |
| 78557 | Low | 1962 | 0 | 0 | 0 | No primes possible! |
| 79309 | Low | 2024-11-12 PrimeGrid Prime Sierpiński Problem (MR18) |
33,582,000 | 56 | 0 | |
| 79817 | Low | 2024-11-12 PrimeGrid Prime Sierpiński Problem (MR18) |
33,582,000 | 146 | 0 | |
| 84363 | 3 | 2024-06-22 | 100,000 | 1624 | 28 | 2, 4, 16, 20, 26, 34, 38, 328, 346, 610, 628, 656, 700, 800, 866, 1160, 1198, 1334, 1654, 2558, 4462, 6032, 9044, 9796, 11782, 43534, 87308, 2222321 |
| 85287 | 3 | 2024-06-22 | 100,000 | 1630 | 20 | 14, 22, 26, 58, 182, 190, 274, 416, 524, 1426, 1790, 5440, 5536, 10682, 13958, 15656, 20906, 34784, 52390, 1890011 |
| 95283 | 3 | 2020-07-05 | 50,000 | 1489 | 27 | 4, 14, 22, 28, 34, 148, 230, 274, 304, 352, 446, 616, 652, 1214, 1796, 2632, 4516, 4888, 4918, 7852, 9314, 13096, 17908, 25124, 25828, 29912, 40228 |
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