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Proth primes of the form k•2n+1, k < 300

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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 40 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 2024-04-15
PrimeGrid 321 Prime Search (MR22)
21,484,280 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 2021-04-01 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 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 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 2023-08-19 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 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 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 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 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 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 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 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 3116 66 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, 6750726, 7241494, 8898285
119 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 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 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 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 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 1773 32 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
129 3 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 2357 38 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
165 315 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 5158 108 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
177 3 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 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 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 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 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 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 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 431 8 38, 70, 3230, 62918, 82878, 1282582, 3094582, 4395550
261 3 2024-05-13
PrimeGrid Proth Prime Search (MR1)
5,000,000 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