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Proth primes of the form k•2n+1, k < 300
Overview
Automatically generated table from available Proth primes k < 300.
Explanations
The colors used in the table are defined as:
- : k-value is reserved
- : k-value is not reserved
Primes table
There are 41 sequences:
| k | Type | Date | max n | Nash | # | Primes for n |
|---|---|---|---|---|---|---|
| 1 | Low | 2010-10-01 FermatSearch |
8,589,934,591 | 39 | 5 | 1, 2, 4, 8, 16 |
| 3 | 3 | 2024-10-13 PrimeGrid 321 Prime Search (MR22) |
22,021,811 | 2132 | 50 | 1, 2, 5, 6, 8, 12, 18, 30, 36, 41, 66, 189, 201, 209, 276, 353, 408, 438, 534, 2208, 2816, 3168, 3189, 3912, 20909, 34350, 42294, 42665, 44685, 48150, 54792, 55182, 59973, 80190, 157169, 213321, 303093, 362765, 382449, 709968, 801978, 916773, 1832496, 2145353, 2291610, 2478785, 5082306, 7033641, 10829346, 16408818 |
| 5 | Low | 2024-09-06 Ryan Propper |
9,000,000 | 891 | 25 | 1, 3, 7, 13, 15, 25, 39, 55, 75, 85, 127, 1947, 3313, 4687, 5947, 13165, 23473, 26607, 125413, 209787, 240937, 819739, 1282755, 1320487, 1777515 |
| 7 | 2022-07-21 | 9,000,000 | 2144 | 43 | 2, 4, 6, 14, 20, 26, 50, 52, 92, 120, 174, 180, 190, 290, 320, 390, 432, 616, 830, 1804, 2256, 6614, 13496, 15494, 16696, 22386, 54486, 88066, 95330, 207084, 283034, 561816, 804534, 811230, 1491852, 2139912, 2167800, 2915954, 3015762, 3511774, 5775996, 18233956, 20267500 | |
| 9 | 3 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 2297 | 66 | 1, 2, 3, 6, 7, 11, 14, 17, 33, 42, 43, 63, 65, 67, 81, 134, 162, 206, 211, 366, 663, 782, 1305, 1411, 1494, 2297, 2826, 3230, 3354, 3417, 3690, 4842, 5802, 6937, 7967, 9431, 13903, 22603, 24422, 39186, 43963, 47003, 49902, 67943, 114854, 127003, 145247, 147073, 149143, 304607, 384990, 412034, 435743, 461081, 834810, 1051026, 1807574, 2543551, 3497442, 5642513, 9778263, 11158963, 11366286, 11500843, 12406887, 13334487 |
| 11 | 2023-01-08 | 9,000,000 | 1387 | 37 | 1, 3, 5, 7, 19, 21, 43, 81, 125, 127, 209, 211, 3225, 4543, 10179, 15329, 18759, 28277, 93279, 105741, 268009, 412447, 525589, 644677, 886071, 960901, 1343347, 2230369, 2476839, 2691961, 2897409, 3771821, 8103463, 9381365, 10797109, 10803449, 15502315 | |
| 13 | Low | 2023-10-11 | 9,000,000 | 920 | 28 | 2, 8, 10, 20, 28, 82, 188, 308, 316, 1000, 28280, 38008, 43856, 88018, 109258, 114296, 521306, 562456, 684560, 1038896, 1499876, 1861732, 4998362, 5523860, 6481780, 8989858, 15294536, 16828072 |
| 15 | 315 | 2024-09-02 | 9,000,000 | 2873 | 65 | 1, 2, 4, 9, 10, 12, 27, 37, 38, 44, 48, 78, 112, 168, 229, 297, 339, 517, 522, 654, 900, 1518, 2808, 2875, 3128, 3888, 4410, 6804, 7050, 7392, 19219, 21445, 21550, 24105, 24995, 34224, 34260, 43388, 48444, 61758, 184290, 294894, 300488, 403929, 483098, 635989, 701902, 734400, 1229600, 1244377, 1276177, 1368428, 1418605, 1597510, 1667744, 2393365, 2785940, 2988834, 3162659, 4246384, 4800315, 7300254, 7619838, 9312889, 9830108 |
| 17 | Low | 2021-04-01 | 9,000,000 | 672 | 20 | 3, 15, 27, 51, 147, 243, 267, 347, 471, 747, 2163, 3087, 5355, 6539, 7311, 99231, 824451, 1388355, 1990299, 8636199 |
| 19 | Low | 2021-04-01 | 9,000,000 | 828 | 21 | 6, 10, 46, 366, 1246, 2038, 4386, 4438, 6838, 7498, 7998, 9450, 11890, 17034, 23290, 73338, 149146, 323638, 853546, 2206266, 6833086 |
| 21 | 3 | 2021-04-01 | 9,000,000 | 2374 | 48 | 1, 4, 5, 7, 9, 12, 16, 17, 41, 124, 128, 129, 187, 209, 276, 313, 397, 899, 1532, 1613, 1969, 2245, 2733, 4585, 4644, 6712, 6981, 13344, 17524, 27124, 29769, 47337, 55828, 91008, 94801, 164901, 179457, 191337, 200568, 220992, 686632, 856865, 1022168, 1240067, 1421741, 1830919, 3065701, 6048861 |
| 23 | Low | 2021-04-01 | 9,000,000 | 826 | 19 | 1, 9, 13, 29, 41, 49, 69, 73, 341, 381, 389, 649, 1961, 3929, 977541, 1399841, 1448461, 2425641, 4300741 |
| 25 | 2022-09-21 | 9,000,000 | 2198 | 46 | 2, 4, 6, 10, 20, 22, 52, 64, 78, 184, 232, 268, 340, 448, 554, 664, 740, 748, 1280, 1328, 1640, 3314, 3904, 3938, 5152, 9522, 57488, 66872, 148060, 154254, 216092, 302194, 367294, 627710, 966414, 1211488, 1258562, 1298186, 2141884, 2583690, 2927222, 3733144, 4481024, 8456828, 8788628, 13719266 | |
| 27 | 3 | 2024-05-23 | 10,000,000 | 2142 | 49 | 2, 4, 7, 16, 19, 20, 22, 26, 40, 44, 46, 47, 50, 56, 59, 64, 92, 175, 215, 275, 407, 455, 1076, 1090, 3080, 3322, 6419, 7639, 19360, 30500, 38770, 44164, 50696, 114760, 117784, 153847, 160874, 178739, 379880, 405514, 672007, 974752, 1164664, 1476347, 2218064, 5213635, 7046834, 7963247, 12184319 |
| 29 | 2021-04-01 | 9,000,000 | 2120 | 45 | 1, 3, 5, 11, 27, 43, 57, 75, 77, 93, 103, 143, 185, 231, 245, 391, 1053, 1175, 2027, 3627, 4727, 5443, 7927, 8533, 9067, 14185, 25723, 88117, 96947, 144937, 219317, 252227, 261031, 339123, 343601, 627167, 742191, 800191, 1152765, 1416873, 1574753, 3964697, 4532463, 7374577, 7899985 | |
| 31 | Low | 2021-04-01 | 9,000,000 | 839 | 14 | 8, 60, 68, 140, 216, 416, 1808, 1944, 9096, 76596, 93168, 4673544, 5560820, 8348000 |
| 33 | 3 | 2021-04-01 | 9,000,000 | 1960 | 41 | 1, 6, 13, 18, 21, 22, 25, 28, 66, 93, 118, 289, 412, 453, 525, 726, 828, 1420, 1630, 3076, 3118, 4452, 4941, 5236, 6346, 9133, 13401, 14214, 18766, 37249, 42685, 47805, 61372, 74178, 600270, 922782, 1130884, 2345001, 3176269, 3570132, 3649810 |
| 35 | 2021-04-01 | 9,000,000 | 2115 | 43 | 1, 3, 7, 9, 13, 15, 31, 45, 47, 49, 55, 147, 245, 327, 355, 663, 1423, 1443, 2493, 3627, 4737, 6541, 9667, 22645, 27321, 61963, 68281, 144397, 151741, 187859, 191509, 273251, 494607, 696935, 768063, 831411, 1040005, 1357881, 1765449, 2099769, 2241049, 3570777, 3587843 | |
| 37 | 2022-11-08 | 9,000,000 | 2532 | 57 | 2, 4, 8, 10, 12, 16, 22, 26, 68, 82, 84, 106, 110, 166, 236, 254, 286, 290, 712, 1240, 1706, 1804, 1904, 2240, 2632, 3104, 5870, 8750, 11514, 11972, 14434, 16322, 18044, 19050, 23014, 32424, 59354, 62350, 120196, 157128, 167326, 211056, 218550, 230716, 233968, 239902, 256954, 331144, 548012, 551830, 939364, 2128328, 4046360, 10599476, 11855148, 14166940, 15474010 | |
| 39 | 3 | 2021-04-01 | 9,000,000 | 3219 | 88 | 1, 2, 3, 5, 7, 10, 11, 13, 14, 18, 21, 22, 31, 42, 67, 70, 71, 73, 251, 370, 375, 389, 407, 518, 818, 865, 1057, 1602, 2211, 3049, 4802, 4865, 5317, 7583, 8061, 9853, 10217, 12103, 13721, 14927, 15441, 15931, 16709, 18907, 20221, 21882, 25654, 28437, 30325, 31485, 33593, 37393, 46362, 62429, 66971, 77242, 82191, 94449, 105063, 107778, 113490, 113549, 138009, 204681, 378861, 421590, 510595, 512997, 529642, 534973, 555902, 587850, 634441, 778233, 1612681, 1824871, 2188855, 2705367, 2978894, 3240990, 3961129, 4657951, 5119458, 6164630, 6648997, 6684941, 7946769, 8413422 |
| 41 | Low | 2022-06-20 | 9,000,000 | 893 | 18 | 1, 11, 19, 215, 289, 379, 1991, 7607, 8411, 12493, 13235, 13823, 274897, 364861, 462023, 1530313, 5651731, 11676439 |
| 43 | 2021-04-01 | 9,000,000 | 1641 | 37 | 2, 6, 12, 18, 26, 32, 94, 98, 104, 144, 158, 252, 778, 1076, 2974, 3022, 3528, 4344, 5322, 10416, 10422, 29862, 33526, 163354, 167618, 175542, 217584, 762212, 835934, 894766, 1087992, 1235298, 1795628, 1799016, 2795582, 2994958, 3063674 | |
| 45 | 315 | 2021-04-01 | 9,000,000 | 2581 | 57 | 2, 9, 12, 14, 23, 24, 29, 60, 189, 200, 333, 372, 443, 464, 801, 1374, 6146, 6284, 6359, 6923, 12293, 16679, 18660, 19301, 29240, 32018, 38457, 48612, 56754, 67394, 76416, 79160, 91403, 97116, 110303, 129731, 159318, 202304, 243321, 426653, 458712, 574506, 949353, 1086062, 1111703, 1134357, 1365167, 1427666, 1779971, 2014557, 2347187, 2507894, 2711732, 3677787, 5308037, 7513661, 7661004 |
| 47 | Low | 2021-04-01 | 9,000,000 | 197 | 3 | 583, 1483, 6115 |
| 49 | 2022-09-11 | 9,000,000 | 1209 | 26 | 2, 6, 10, 30, 42, 54, 66, 118, 390, 594, 1202, 2334, 6242, 7446, 11858, 48666, 68050, 72210, 88090, 113022, 406814, 501238, 1103430, 1646042, 3837090, 9187790 | |
| 51 | 3 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 3076 | 63 | 1, 3, 7, 9, 13, 17, 25, 43, 53, 83, 89, 92, 119, 175, 187, 257, 263, 267, 321, 333, 695, 825, 1485, 1917, 2660, 2967, 3447, 3659, 4121, 5225, 7377, 8543, 9584, 10707, 18032, 18465, 20733, 20807, 26703, 45541, 59217, 68956, 73571, 103664, 140504, 142327, 156443, 195353, 282719, 301244, 367413, 415055, 437036, 490673, 1358372, 1859193, 2578652, 2881227, 3308171, 3490971, 4923905, 6753404, 6945567 |
| 63 | 3 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 3116 | 71 | 1, 4, 5, 9, 10, 14, 17, 18, 21, 25, 37, 38, 44, 60, 65, 94, 133, 153, 228, 280, 314, 326, 334, 340, 410, 429, 626, 693, 741, 768, 1150, 1290, 1441, 2424, 2478, 3024, 3293, 4956, 5221, 6416, 8480, 20746, 24633, 30053, 34074, 88366, 121917, 125218, 130221, 131325, 141497, 151269, 222861, 263413, 270094, 425028, 448833, 521925, 775857, 892164, 898308, 1070449, 1356980, 1530888, 1625970, 1686050, 1784498, 2807130, 2898957, 7743186, 8741225 |
| 93 | 3 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 3116 | 67 | 2, 4, 6, 10, 12, 30, 42, 44, 52, 70, 76, 108, 122, 164, 170, 226, 298, 398, 686, 1020, 1110, 1478, 1646, 2032, 2066, 2800, 2816, 8568, 9678, 11108, 16930, 20917, 24210, 24994, 38288, 61904, 63016, 67722, 89310, 122056, 135908, 155174, 191748, 197778, 272034, 273044, 360132, 399218, 586453, 642909, 977284, 1087202, 1112805, 1299926, 1408246, 1493877, 1511692, 1561686, 1673893, 1965880, 2263894, 3544744, 4232892, 5323466, 6750726, 7241494, 8898285 |
| 119 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 1429 | 26 | 1, 3, 7, 13, 21, 23, 45, 63, 553, 1115, 2471, 2773, 7363, 25767, 26265, 32445, 41291, 55583, 113637, 376951, 787017, 858427, 915371, 1242207, 1759247, 3161195 | |
| 121 | 2021-04-08 | 10,000,000 | 1004 | 25 | 8, 12, 44, 84, 96, 228, 264, 320, 732, 788, 1808, 7928, 12264, 37784, 59196, 91112, 112208, 168716, 251184, 264632, 272052, 513020, 636564, 674360, 9584444 | |
| 127 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 1773 | 33 | 2, 12, 18, 24, 54, 72, 114, 180, 214, 504, 558, 964, 1098, 1420, 2764, 4322, 5582, 10538, 14634, 23970, 61054, 67618, 88958, 96744, 297350, 357840, 376162, 723530, 916980, 925012, 1472718, 1817862, 5391378 | |
| 129 | 3 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 2357 | 39 | 3, 5, 21, 27, 59, 75, 111, 287, 414, 786, 966, 1071, 2433, 2817, 3165, 4958, 5895, 12450, 39399, 50019, 57386, 72599, 75866, 82026, 112497, 268271, 284975, 478538, 564990, 630843, 739023, 851306, 872765, 1774709, 1956915, 2255199, 3218214, 3328805, 5453363 |
| 165 | 315 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 5158 | 109 | 1, 2, 3, 5, 7, 9, 12, 17, 25, 33, 39, 43, 51, 65, 71, 72, 84, 100, 104, 168, 198, 264, 282, 293, 352, 379, 611, 676, 719, 729, 745, 1013, 1407, 1417, 1532, 1887, 1902, 1993, 2137, 2294, 2381, 2509, 3259, 4224, 4713, 5719, 6613, 7515, 8575, 8935, 11598, 12500, 13347, 14504, 16732, 20865, 21396, 21525, 22843, 27975, 33197, 44442, 45387, 49095, 57633, 64108, 67326, 87580, 94484, 120400, 126928, 139459, 143437, 147953, 180740, 187588, 230803, 237948, 247446, 335275, 335871, 345749, 422468, 509812, 746994, 758432, 781224, 826425, 838479, 928724, 1010133, 1100755, 1117217, 1177856, 1207393, 1244739, 1408117, 1510977, 1533368, 1703392, 1705093, 2090645, 2319575, 2732983, 2870868, 3960664, 4375458, 4379097, 5416628 |
| 167 | Low | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 259 | 6 | 7, 103, 151, 247, 10183, 55447 |
| 177 | 3 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 3473 | 77 | 2, 4, 6, 12, 16, 20, 23, 32, 38, 48, 54, 60, 100, 116, 118, 119, 140, 150, 163, 170, 190, 244, 271, 294, 299, 320, 334, 414, 439, 442, 468, 724, 794, 842, 864, 1032, 1750, 2050, 3980, 4010, 4756, 5096, 5963, 5966, 6836, 14160, 16748, 16844, 19814, 25398, 37702, 41148, 62159, 65806, 143626, 151308, 210340, 269320, 324326, 332846, 333364, 358114, 365164, 385438, 419600, 434336, 463598, 490500, 501106, 657458, 751028, 798443, 1121720, 2816050, 3411847, 3717746, 4162494 |
| 207 | 3 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 3570 | 69 | 2, 3, 4, 6, 7, 10, 14, 15, 16, 34, 42, 44, 46, 62, 66, 106, 127, 130, 171, 202, 231, 232, 238, 248, 256, 296, 314, 412, 604, 956, 1023, 1287, 1454, 1564, 1766, 2036, 5215, 5911, 6092, 9190, 9916, 10410, 13456, 14336, 14444, 15490, 30835, 32558, 34770, 41218, 46666, 56590, 58720, 62966, 63595, 70250, 128850, 141556, 186754, 288591, 317203, 555422, 755470, 1249252, 1471290, 1913067, 2649810, 2903535, 3095391 |
| 255 | 315 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 2629 | 67 | 2, 5, 32, 36, 38, 41, 57, 69, 71, 72, 116, 137, 156, 197, 237, 336, 353, 489, 545, 678, 1040, 1137, 1217, 1451, 1577, 1589, 1836, 3077, 4640, 4850, 5145, 7139, 7766, 8051, 9662, 11159, 13433, 13763, 15998, 16862, 19002, 25412, 35558, 47916, 48509, 86900, 88046, 116228, 161486, 253233, 265808, 373580, 411408, 463229, 668348, 883046, 884769, 942620, 1122897, 1155630, 1275596, 1675403, 1765113, 2488562, 2668448, 3395661, 3824348 |
| 259 | Low | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 431 | 8 | 38, 70, 3230, 62918, 82878, 1282582, 3094582, 4395550 |
| 261 | 3 | 2024-07-25 PrimeGrid Proth Prime Search (MR1) |
5,200,000 | 4016 | 96 | 1, 3, 4, 5, 7, 9, 11, 27, 29, 37, 57, 59, 67, 71, 73, 101, 117, 155, 157, 160, 193, 195, 208, 273, 303, 328, 357, 433, 443, 444, 479, 587, 1095, 1101, 1149, 1291, 1319, 1580, 2065, 2137, 2225, 2796, 3025, 3195, 4396, 6309, 6396, 6933, 6955, 8271, 8691, 10688, 11709, 11711, 12993, 15120, 16509, 18105, 20115, 21685, 22213, 24411, 27227, 41868, 42201, 56939, 57371, 61444, 62445, 96360, 100677, 107639, 119447, 152951, 165575, 231025, 258179, 260997, 271361, 345171, 492999, 715965, 768815, 806980, 895203, 933869, 1331356, 1586347, 1751160, 1848217, 1995105, 2152805, 2671677, 2879941, 3066009, 4106385 |
| 289 | Low | 2024-04-30 | 5,000,000 | 990 | 21 | 10, 22, 34, 42, 150, 1758, 6706, 11634, 18502, 52614, 102150, 194830, 207546, 252858, 333406, 638902, 989182, 1117182, 1317378, 1522650, 4911870 |
| 297 | 3 | 2024-04-30 | 5,000,000 | 1682 | 36 | 3, 6, 14, 15, 20, 27, 38, 123, 276, 327, 380, 411, 546, 819, 1155, 1274, 1800, 1875, 3135, 3411, 7514, 9446, 12615, 23400, 23564, 99344, 108258, 148988, 153818, 157623, 306596, 622800, 2660048, 3087543, 3765140, 4432947 |
Proth primes
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