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		2024-04-30	5,000,000	1328	26	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, 3284232
311		2024-04-30	5,000,000	1216	19	9, 29, 35, 105, 125, 131, 179, 359, 2735, 28199, 47349, 64485, 1094135, 1171199, 1323071, 2798459, 3037565, 3270759, 3282455
319	Low	2024-04-30	5,000,000	667	18	2, 10, 18, 274, 314, 522, 562, 578, 594, 602, 930, 1074, 23826, 184554, 1923378, 2248914, 2290722, 3069362
345	315	2024-04-30	5,000,000	4308	92	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, 3779921, 3817949, 4173969
355	Low	2024-04-30	5,000,000	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	2024-04-30	5,000,000	868	26	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, 4487274
389		2024-04-30	5,000,000	1097	20	11, 57, 59, 115, 299, 347, 715, 3845, 5157, 16945, 27949, 66379, 142649, 233985, 572625, 976169, 1186577, 1824385, 2916499, 3019025
403		2024-02-29	4,500,000	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	2024-02-29	4,500,000	3454	81	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, 3136187, 3160443, 3248255, 3895404, 4003224, 4473466
435	315	2024-02-29	4,500,000	4603	95	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, 4216447, 4292968
453	3	2024-02-29	4,500,000	2586	55	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, 3303073, 3387048, 3461688
499		2024-02-29	4,500,000	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	2024-02-29	4,500,000	383	6	8, 264, 1392, 317328, 495800, 1777488
513	3	2024-02-29	4,500,000	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		2024-02-29	4,500,000	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	2024-02-29	4,500,000	4497	102	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, 3916875
615	315	2023-04-30	4,000,000	2908	64	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, 3738023, 3844151
629		2023-04-30	4,000,000	2596	70	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, 2892961, 3066827, 3731479
639	3	2023-04-30	4,000,000	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		2023-04-30	4,000,000	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	2023-04-30	4,000,000	759	13	3, 63, 127, 547, 823, 6663, 11767, 46035, 51235, 85695, 480447, 3063403, 3369115
699	3	2023-04-30	4,000,000	1894	49	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, 3974045
745		2022-07-31	3,640,000	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	2022-07-31	3,640,000	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	2022-07-31	3,640,000	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	2022-07-31	3,640,000	2515	45	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, 3183463
791		2022-07-31	3,640,000	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	2022-07-31	3,640,000	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		2022-07-31	3,640,000	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		2022-07-31	3,640,000	1864	38	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, 3256589
915	315	2022-07-31	3,640,000	2802	54	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, 3141942
933	3	2022-07-31	3,640,000	3148	76	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, 3231438, 3270993
973		2022-07-31	3,640,000	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	2022-07-31	3,640,000	3931	83	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, 3214745
1045		2022-07-31	3,640,000	2182	41	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, 3273488
1065	315	2022-07-31	3,640,000	4065	80	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, 3143667, 3447906
1105		2022-07-31	3,640,000	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	2022-07-31	3,640,000	682	12	9, 13, 91, 331, 529, 2641, 29169, 190753, 630055, 1450029, 2115949, 3079783
1149	3	2022-07-31	3,640,000	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		2022-07-31	3,640,000	1454	23	6, 12, 38, 218, 282, 434, 462, 474, 614, 654, 1478, 2298, 3252, 14058, 16434, 18944, 63858, 150266, 360702, 704772, 1193202, 3060228, 3207702
1461	3	2024-05-14 PrimeGrid Proth Prime Search Extended (MR25)	1,960,000	1347	32	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, 3448423
1601		2024-05-14 PrimeGrid Proth Prime Search Extended (MR25)	1,960,000	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

Proth primes

Miscellaneous

Proth prime Sierpiński problem Least n (k≤12)

Tables

1-300 300-2000 2000-4000 4000-6000 6000-8000 8000-10000 104-105 105-106 106-107 107-108 108-109 109-1010 1010-∞

Categories

1-300 300-2000 2000-4000 4000-6000 6000-8000 8000-10000 104-105 105-106 106-107 107-108 108-109 109-1010 1010-∞

Others

3k 15k 2145k 2805k 0 primes 100+ primes Sierpiński numbers Missing ranges

Other categories

Low weight