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Proth primes of the form k•2n+1, 300 < k < 2000
Overview
Automatically generated table from available Proth primes 300 < k < 2000.
Explanations
The colors used in the table are defined as:
- : k-value is reserved
- : k-value is not reserved
Primes table
There are 42 sequences:
| k | Type | Date | max n | Nash | # | Primes for n |
|---|---|---|---|---|---|---|
| 301 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1328 | 25 | 4, 184, 344, 352, 392, 1060, 2452, 7360, 9736, 10324, 21316, 22752, 27272, 27744, 28068, 55628, 72864, 88472, 95872, 124628, 218584, 424448, 517960, 880792, 1455620 | |
| 311 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1216 | 17 | 9, 29, 35, 105, 125, 131, 179, 359, 2735, 28199, 47349, 64485, 1094135, 1171199, 1323071, 2798459, 3037565 | |
| 319 | Low | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 667 | 18 | 2, 10, 18, 274, 314, 522, 562, 578, 594, 602, 930, 1074, 23826, 184554, 1923378, 2248914, 2290722, 3069362 |
| 345 | 315 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 4308 | 89 | 1, 2, 4, 8, 9, 11, 15, 18, 20, 24, 30, 40, 47, 87, 88, 150, 154, 166, 195, 264, 360, 412, 438, 546, 569, 621, 625, 778, 814, 1041, 1189, 1302, 1356, 1397, 1465, 1541, 1549, 1568, 3246, 6557, 6627, 9477, 10552, 12744, 13515, 14850, 15951, 18378, 18456, 27705, 27719, 27815, 30165, 32121, 41780, 43276, 48136, 49048, 62526, 79172, 87977, 103500, 144054, 155708, 161261, 180726, 181434, 194562, 213060, 261455, 441719, 442566, 459204, 525977, 613086, 633911, 808726, 838479, 958896, 1010394, 1039566, 1051282, 1335896, 1441905, 2042295, 2405701, 2792269, 3027769, 3532957 |
| 355 | Low | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 967 | 22 | 6, 12, 24, 34, 46, 138, 174, 816, 1164, 1668, 1704, 5334, 10126, 11340, 13818, 18564, 82968, 202986, 241368, 285492, 1482390, 3027372 |
| 373 | Low | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 868 | 25 | 2, 6, 14, 36, 62, 92, 122, 292, 758, 4436, 5526, 11066, 14076, 17036, 23618, 25412, 33692, 61358, 71018, 92156, 158476, 334026, 641606, 3036746, 3404702 |
| 389 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1097 | 20 | 11, 57, 59, 115, 299, 347, 715, 3845, 5157, 16945, 27949, 66379, 142649, 233985, 572625, 976169, 1186577, 1824385, 2916499, 3019025 | |
| 403 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2276 | 60 | 2, 4, 6, 14, 16, 32, 40, 74, 110, 134, 252, 280, 306, 356, 410, 692, 760, 1220, 1286, 1742, 2060, 2514, 3632, 7104, 7376, 10220, 10980, 18914, 20472, 20676, 22456, 24122, 40834, 42110, 44182, 44814, 45852, 60030, 67826, 68360, 87434, 94386, 158774, 180520, 201250, 237524, 238276, 316882, 457660, 688290, 732860, 817706, 992780, 1209326, 1337280, 1664194, 2012412, 2357572, 2894566, 3334410 | |
| 417 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 3454 | 75 | 2, 4, 7, 8, 11, 12, 15, 16, 19, 24, 28, 51, 59, 62, 63, 64, 75, 79, 132, 338, 355, 518, 692, 806, 1287, 1618, 1803, 2715, 2743, 2834, 3055, 3255, 3323, 4067, 5255, 6094, 6254, 6796, 7063, 7476, 7787, 8067, 10795, 13342, 14407, 22292, 23132, 27076, 30286, 50486, 54391, 78423, 97375, 130858, 133756, 162292, 170947, 234179, 239956, 276419, 305859, 351632, 435482, 506332, 642156, 828566, 1104563, 1439196, 1759055, 1943755, 2036482, 2284402, 2698652, 3026492, 3029342 |
| 435 | 315 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 4603 | 93 | 2, 4, 5, 7, 11, 18, 19, 33, 51, 68, 69, 82, 93, 99, 101, 113, 132, 138, 141, 198, 201, 255, 298, 522, 528, 533, 537, 547, 790, 903, 1032, 1195, 1365, 1612, 1725, 2223, 2343, 2398, 3740, 4138, 4315, 6285, 7161, 10401, 13444, 19922, 23030, 26104, 26922, 28617, 29297, 31543, 35370, 56818, 73111, 87221, 88708, 93319, 106800, 107174, 157397, 169192, 170218, 187785, 200455, 235444, 270243, 304661, 342582, 364178, 412858, 440433, 529247, 547893, 565591, 653451, 700257, 748240, 772448, 885602, 1096682, 1177574, 1183997, 1239504, 1402809, 1908579, 2327152, 2329948, 2378522, 2473905, 2831709, 2997453, 3041954 |
| 453 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2586 | 54 | 1, 10, 16, 18, 21, 33, 37, 48, 57, 66, 96, 108, 133, 198, 262, 480, 550, 673, 858, 988, 1065, 1576, 1737, 1756, 1920, 2362, 2860, 2917, 4666, 5988, 6598, 11206, 14326, 28317, 37158, 53617, 53896, 63925, 80022, 125992, 186325, 211897, 318880, 428428, 443212, 511288, 563253, 860497, 965572, 2367388, 2458461, 3056181, 3387048, 3461688 |
| 499 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1174 | 28 | 2, 18, 58, 94, 146, 362, 610, 714, 898, 994, 1514, 1718, 5742, 8278, 8374, 13610, 16306, 23798, 26314, 28854, 29222, 69358, 70646, 206986, 701434, 1150034, 1651814, 3066970 | |
| 511 | Low | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 383 | 6 | 8, 264, 1392, 317328, 495800, 1777488 |
| 513 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2665 | 62 | 2, 4, 5, 6, 9, 10, 12, 14, 17, 22, 26, 30, 33, 45, 66, 110, 116, 126, 153, 165, 174, 220, 230, 234, 294, 362, 404, 1576, 1625, 1640, 2540, 2936, 3525, 5470, 9736, 11004, 11110, 15652, 19965, 23244, 24341, 48386, 52234, 54021, 74264, 78604, 117992, 136476, 175370, 189156, 193212, 273482, 279213, 337140, 369969, 392925, 797084, 818964, 861512, 1820982, 2135642, 3092705 |
| 553 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 3105 | 79 | 2, 4, 6, 10, 22, 24, 30, 42, 46, 50, 56, 60, 64, 84, 182, 190, 202, 204, 214, 256, 322, 382, 384, 402, 768, 1100, 2236, 3424, 3470, 3514, 4170, 4398, 4712, 5196, 5708, 6944, 7146, 8182, 8370, 11648, 11792, 13090, 14844, 15206, 24216, 25518, 28494, 32556, 38722, 43068, 56362, 56804, 58080, 68712, 69870, 112944, 164944, 172118, 202064, 287146, 292460, 370040, 371716, 404754, 574760, 681652, 686506, 737048, 852760, 907328, 1058992, 1216046, 1344056, 1577344, 1902102, 2815596, 3066838, 3094072, 3532758 | |
| 555 | 315 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 4497 | 101 | 2, 3, 5, 6, 9, 14, 16, 17, 18, 20, 27, 33, 44, 48, 52, 60, 62, 65, 73, 84, 99, 112, 132, 184, 189, 217, 282, 360, 365, 412, 444, 553, 588, 739, 756, 1084, 1184, 1686, 1850, 2512, 2678, 5740, 6856, 8306, 8810, 11064, 12110, 12882, 12978, 14088, 16609, 16777, 18447, 18977, 20042, 23114, 25627, 27338, 32840, 33835, 36085, 36602, 78475, 82783, 82819, 98008, 108354, 116258, 125608, 134406, 139535, 151277, 202098, 210377, 266006, 288845, 316039, 343854, 356267, 414830, 461262, 591776, 660664, 750460, 1111663, 1174603, 1257047, 1363577, 1422674, 1593788, 1597517, 1629059, 1679952, 1813556, 1937595, 3016352, 3078792, 3325925, 3393389, 3502765, 3563328 |
| 615 | 315 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2908 | 62 | 1, 5, 7, 14, 23, 32, 37, 59, 65, 109, 115, 146, 199, 203, 209, 215, 389, 391, 557, 617, 709, 1049, 1574, 1763, 2273, 2497, 2734, 3389, 3743, 4867, 10982, 11372, 11878, 14989, 18254, 22249, 23039, 26174, 26894, 48179, 52663, 53806, 59153, 80318, 104407, 130664, 142097, 164797, 169022, 177953, 219197, 542783, 575972, 624752, 701305, 832925, 1041203, 1041857, 1298251, 1724209, 2235833, 3019445 |
| 629 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2596 | 68 | 1, 5, 7, 11, 17, 19, 29, 31, 43, 59, 61, 71, 83, 103, 125, 161, 257, 281, 445, 499, 619, 623, 637, 661, 787, 1027, 1573, 2267, 3521, 3587, 4043, 4571, 5915, 6485, 6509, 10487, 11669, 11843, 13007, 20809, 26681, 29131, 37915, 53779, 59789, 72331, 73651, 80857, 81595, 124871, 131345, 134873, 142511, 164297, 178621, 201187, 317369, 383299, 399503, 457877, 526211, 726049, 1043191, 1084915, 1469471, 1988579, 2857891, 3066827 | |
| 639 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 3560 | 85 | 1, 2, 3, 6, 13, 18, 22, 26, 27, 31, 34, 46, 50, 73, 119, 187, 190, 194, 199, 306, 326, 358, 393, 611, 663, 1298, 1314, 1329, 1567, 2067, 2146, 2186, 2591, 2689, 2706, 3138, 3330, 3483, 4509, 4714, 5602, 6679, 6699, 8877, 9409, 10046, 12767, 15154, 19234, 23341, 26631, 32594, 36107, 42922, 58642, 70187, 70342, 72718, 74423, 78731, 84026, 99090, 100426, 107602, 113391, 117607, 144059, 198039, 227574, 247677, 397790, 509058, 623113, 639554, 710709, 782159, 881991, 903407, 1310707, 1848903, 1880451, 1945473, 2740186, 3040438, 3635707 |
| 643 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1556 | 34 | 4, 10, 14, 40, 74, 124, 280, 346, 410, 604, 806, 2318, 3358, 4508, 4586, 5738, 7174, 13006, 26798, 36940, 38770, 39244, 51500, 59116, 157808, 237350, 318958, 368558, 371354, 782318, 1272644, 2078306, 3030650, 3501974 | |
| 677 | Low | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 759 | 13 | 3, 63, 127, 547, 823, 6663, 11767, 46035, 51235, 85695, 480447, 3063403, 3369115 |
| 699 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1894 | 48 | 1, 2, 5, 10, 13, 31, 38, 41, 85, 119, 125, 199, 202, 218, 263, 295, 311, 470, 674, 782, 1265, 1270, 2231, 2377, 7631, 7822, 13583, 14671, 22303, 46543, 61922, 63913, 75002, 142423, 185770, 420743, 431402, 467839, 570581, 877511, 907870, 1143143, 1200343, 1535678, 1674293, 2175031, 3023263, 3487253 |
| 745 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1430 | 31 | 6, 14, 108, 138, 194, 234, 408, 434, 504, 560, 924, 1356, 1760, 2190, 3204, 4104, 4688, 5096, 6408, 10196, 15660, 27668, 66510, 81060, 314118, 359604, 360726, 1253108, 2540726, 2761514, 3087428 | |
| 759 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2127 | 39 | 2, 3, 17, 29, 42, 78, 98, 179, 263, 327, 725, 755, 1107, 1517, 1547, 1590, 2490, 5079, 5378, 6378, 10542, 12803, 15725, 17417, 18690, 24905, 32933, 38195, 38739, 71570, 72173, 87063, 124247, 139427, 347099, 679127, 1319718, 1537049, 3015314 |
| 765 | 315 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 4734 | 87 | 1, 2, 3, 4, 5, 10, 12, 15, 18, 20, 22, 25, 40, 41, 50, 52, 67, 72, 77, 87, 90, 121, 135, 151, 168, 282, 288, 390, 408, 423, 445, 450, 471, 538, 572, 578, 777, 894, 921, 1188, 1382, 2251, 3861, 5217, 5775, 8337, 9568, 10347, 10500, 11570, 14413, 15561, 17862, 24728, 28041, 32211, 38824, 44508, 51550, 56028, 64722, 85119, 93355, 118330, 124000, 129751, 179985, 285088, 293794, 296373, 344115, 353165, 403590, 787971, 858453, 974997, 983445, 1006459, 1179540, 1346535, 1398051, 1635531, 1849609, 2106027, 2448660, 2735232, 3068511 |
| 789 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2515 | 44 | 1, 6, 9, 13, 21, 30, 57, 69, 105, 151, 171, 243, 978, 1251, 1611, 1779, 1909, 1914, 2307, 2397, 2589, 3103, 3199, 4975, 6390, 13173, 19519, 22713, 59593, 135393, 148647, 160375, 182263, 273075, 434965, 444439, 535627, 746301, 759679, 1114779, 1262973, 1367445, 1489887, 2670409 |
| 791 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1586 | 37 | 1, 3, 27, 31, 49, 81, 91, 105, 193, 243, 483, 577, 715, 889, 937, 2641, 4467, 6289, 10239, 17617, 22825, 29049, 29767, 31071, 56847, 65775, 82865, 116833, 265627, 272353, 286121, 630135, 752311, 1135983, 1885961, 3055695, 3323995 | |
| 801 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1434 | 32 | 5, 12, 23, 36, 41, 132, 288, 432, 743, 876, 1181, 1193, 1433, 1845, 2100, 2381, 11316, 12215, 13637, 17397, 17952, 20001, 23220, 87117, 116625, 128207, 448596, 469733, 474900, 485328, 912071, 3036045 |
| 869 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1804 | 38 | 5, 9, 15, 25, 29, 31, 41, 45, 61, 183, 257, 265, 481, 583, 713, 841, 933, 1095, 1143, 1709, 2383, 2559, 4397, 6233, 12013, 31793, 39679, 53671, 59997, 67165, 73845, 338197, 487791, 1000725, 1062609, 1364737, 1389895, 3030655 | |
| 875 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1864 | 37 | 3, 5, 13, 19, 21, 43, 47, 141, 173, 213, 253, 303, 453, 1815, 4623, 6623, 10779, 16467, 16685, 17711, 24711, 74559, 90347, 129279, 163927, 166795, 195343, 381471, 883743, 1017103, 1163883, 1591229, 1814911, 1818427, 2246363, 3018175, 3063847 | |
| 915 | 315 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2802 | 53 | 1, 3, 18, 22, 25, 37, 46, 55, 70, 91, 136, 186, 238, 438, 517, 652, 730, 1090, 1108, 1723, 2005, 2550, 2967, 3559, 3856, 3895, 6831, 9139, 11455, 11695, 13393, 16993, 21915, 23079, 23647, 28159, 48211, 58455, 75408, 95977, 100140, 110826, 134308, 143250, 155641, 847246, 1051477, 1686699, 1805031, 2064663, 2135151, 2375923, 3033775 |
| 933 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 3148 | 74 | 1, 2, 4, 13, 24, 30, 40, 42, 65, 153, 154, 161, 168, 226, 261, 286, 294, 421, 460, 521, 625, 714, 906, 997, 1174, 1482, 1585, 1804, 1961, 2616, 2845, 3304, 5268, 5764, 6546, 7068, 10133, 10782, 12000, 12102, 12721, 15865, 27216, 50088, 54825, 62102, 65976, 69177, 73570, 85117, 95173, 98385, 102057, 189398, 226416, 264264, 282846, 337677, 367230, 443740, 470094, 541668, 722277, 942033, 959214, 1336282, 1642574, 1786320, 1820068, 1868602, 2345893, 2567598, 2879973, 3091825 |
| 973 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2071 | 48 | 4, 6, 8, 12, 14, 16, 30, 32, 68, 70, 112, 134, 152, 184, 224, 278, 280, 320, 422, 676, 768, 1038, 1086, 1692, 2104, 2860, 5048, 10604, 28062, 31256, 34928, 52424, 55592, 104076, 132222, 486740, 588814, 612382, 753040, 923318, 1206088, 1267246, 2254320, 2511920, 2789516, 2923062, 2937046, 3069092 | |
| 1023 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 3931 | 82 | 2, 4, 9, 13, 14, 16, 32, 33, 81, 101, 124, 242, 272, 301, 380, 453, 469, 533, 612, 929, 1081, 1176, 1749, 1797, 1852, 2318, 2405, 3057, 3408, 3440, 4392, 5032, 6637, 9441, 9688, 11970, 13617, 15182, 15316, 17188, 19036, 33709, 34533, 34557, 34716, 37377, 38862, 43640, 47469, 63265, 109010, 111404, 131188, 132810, 183416, 203604, 216930, 253224, 270093, 287797, 289953, 301580, 358082, 367344, 490681, 550765, 611208, 620205, 641310, 681313, 797786, 868480, 943418, 1068402, 1138576, 1153248, 1177850, 1223814, 1426490, 2012570, 2398601, 2772512 |
| 1045 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2182 | 40 | 8, 10, 16, 20, 28, 44, 72, 106, 204, 216, 222, 288, 496, 706, 2300, 2626, 2668, 2844, 4506, 4576, 8844, 9302, 10048, 12392, 13376, 13712, 16808, 19454, 44988, 58776, 99676, 128862, 153354, 182346, 278020, 878392, 1233270, 1800784, 1955356, 3037988 | |
| 1065 | 315 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 4065 | 79 | 1, 2, 3, 4, 6, 14, 15, 21, 28, 30, 54, 56, 66, 70, 104, 126, 146, 174, 248, 266, 310, 334, 374, 435, 584, 642, 762, 914, 941, 1244, 1278, 1321, 1443, 2723, 3371, 5582, 6126, 6303, 7703, 9211, 9284, 11111, 11987, 15450, 21521, 28235, 35608,, 36326, 48964, 52346, 53716, 67034, 70690, 81222, 85988, 89130, 139358, 166193, 234488, 242373, 243903, 340231, 364285, 388808, 464242, 535328, 709627, 905518, 1006151, 1679402, 1698303, 1736222, 2113463, 2260193, 2441132, 2975442, 2994154, 3025527, 3447906 |
| 1105 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2102 | 41 | 2, 4, 8, 20, 28, 34, 40, 52, 62, 128, 136, 148, 220, 538, 790, 1478, 3118, 3184, 3386, 4376, 5986, 9170, 11584, 11870, 17446, 30458, 38954, 58556, 130684, 263320, 281308, 394832, 404584, 622142, 636002, 1065418, 1278476, 1314586, 2171956, 2213846, 3069884 | |
| 1139 | Low | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 682 | 12 | 9, 13, 91, 331, 529, 2641, 29169, 190753, 630055, 1450029, 2115949, 3079783 |
| 1149 | 3 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 2261 | 38 | 2, 7, 14, 26, 34, 82, 98, 166, 262, 263, 389, 538, 702, 823, 1697, 1838, 1995, 3283, 14338, 36743, 95199, 99034, 136214, 157598, 161738, 173515, 192166, 219654, 358385, 370878, 784805, 1141946, 1957223, 2336638, 2593359, 2839622, 3087514, 3481694 |
| 1165 | 2023-04-09 PrimeGrid Proth Prime Search (MR1) |
3,977,000 | 1454 | 22 | 6, 12, 38, 218, 282, 434, 462, 474, 614, 654, 1478, 2298, 3252, 14058, 16434, 18944, 63858, 150266, 360702, 704772, 1193202, 3060228 | |
| 1461 | 3 | 2021-08-09 PrimeGrid Proth Prime Search Extended (MR25) |
1,640,000 | 1347 | 31 | 3, 7, 12, 27, 36, 43, 51, 55, 75, 87, 301, 303, 847, 991, 1131, 1323, 1407, 2971, 4351, 5547, 6951, 20247, 35547, 39660, 41935, 51675, 116460, 127356, 497676, 827871, 3373383 |
| 1601 | 2021-08-09 PrimeGrid Proth Prime Search Extended (MR25) |
1,640,000 | 1503 | 35 | 1, 3, 15, 19, 21, 31, 45, 85, 91, 111, 225, 261, 331, 351, 631, 673, 691, 1435, 1503, 2643, 4485, 10281, 13765, 14697, 16581, 16647, 19617, 29895, 34395, 34515, 40005, 127927, 158805, 232431, 1644421 |
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