Compiled by Wilfrid Keller
The following list of primes k.2n - 1 is
an extension and a current update of Table 6 in Hans Riesel's book
Prime Numbers and Computer Methods for Factorization
[Riesel94]. A listing like:
k
n1,
n2, . . ., nh [Lim]
indicates that the list of primes for
n = n1, n2, . . .,
nh is complete for all
n < Lim. In a listing like:
k
n1,
n2, . . ., nh [Lim]
nh+1, nh+2,
. . .
further primes are added without knowledge of a higher limit
possibly reached through systematic search. So the partial list
of primes for n = nh+1,
nh+2, . . . may or may not be complete
up to the highest prime known.
For each individual k < 300, partial intervals of n that have been searched for primes are listed on the page of searched intervals along with the names of the respective contributors. Note that someone supplying the valuable information that a certain interval is void of primes is also considered a contributor to the project. In case of duplication, only the first submission for a given interval is recorded here.
The larger of the primes are included in Chris Caldwell's list of the largest known primes. If you are interested in the primes by their overall ranking rather than by values of k, or to know who first discovered them, you should search the database for primes of the form k.2n - 1.
The minimum limit currently attained for all k in the list is Lim = 100000. Previously, the overall limit of Lim = 32000 had been established by May 1st, 2000. Several errors in the list have been detected and corrected since then.
On David Broadhurst's kind initiative, efforts have been made to harmonize our list with a similar one of the recent parallel project 15k Search. In addition, David Broadhurst has carefully checked the existing table for completeness up to Lim = 100000, which entailed the material extension to numerous individual intervals. Up to Lim = 32000, no omission was found. These computations were performed in July and August of 2004 (completed August 31), and are warmly acknowledged.
1 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917 [15541000] 20996011 G6, 24036583 G7, 25964951 G8, 30402457, 32582657 G9
3 1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, 827, 1274, 3276, 4204, 5134, 7559, 12676, 14898, 18123, 18819, 25690, 26459, 41628, 51387, 71783, 80330, 85687, 88171, 97063, 123630, 155930, 164987, 234760, 414840, 584995, 702038, 727699, 992700, 1201046, 1232255, 2312734, 3136255 [3270000]
5 2, 4, 8, 10, 12, 14, 18, 32, 48, 54, 72, 148, 184, 248, 270, 274, 420, 1340, 1438, 1522, 1638, 1754, 1884, 2014, 2170, 2548, 2622, 2652, 2704, 13510, 21738, 25624, 41934, 51478, 52540, 53230, 172300, 245728, 350028 [470000] 1194164 L478
7 1, 5, 9, 17, 21, 29, 45, 177, 18381, 22529, 24557, 26109, 34857, 41957, 67421, 70209, 169085, 173489, 177977, 363929, 372897 [2055000]
9 1, 3, 7, 13, 15, 21, 43, 63, 99, 109, 159, 211, 309, 343, 415, 469, 781, 871, 939, 1551, 3115, 3349, 5589, 5815, 5893, 7939, 8007, 11547, 12495, 22555, 23647, 35647, 83415, 103059, 184999 [200000] 275859, 384243, 484975, 503893, 828709 L38, 1010277 L80
11 2, 26, 50, 54, 126, 134, 246, 354, 362, 950, 1310, 2498, 6926, 11826, 31734, 67850, 74726, 96150, 374114, 696438, 743322, 1044086, 1104606 [1200000] 1261478 L163
13 3, 7, 23, 287, 291, 795, 2203, 5711, 7927, 9443, 10095, 19071, 29611, 34651, 51875, 55343, 77511, 166303, 233207 [1000000]
15 1, 2, 4, 5, 10, 14, 17, 31, 41, 73, 80, 82, 116, 125, 145, 157, 172, 202, 224, 266, 289, 293, 463, 1004, 1246, 2066, 2431, 2705, 4622, 5270, 7613, 21727, 21962, 40742, 41054, 60622, 83263, 83669, 91457, 103940, 104177, 108124, 115327, 161453, 172714, 454681 [502000] 568780, 656264, 712294, 902474 L52, 1084010, 1344313 L139
17 2, 4, 6, 16, 20, 36, 54, 60, 96, 124, 150, 252, 356, 460, 612, 654, 664, 698, 702, 972, 1188, 1312, 3062, 4214, 4288, 5280, 9100, 20262, 21676, 24828, 46144, 62148, 79974, 117784 [205000] 211464, 310744, 310754, 429318, 601158 g267, 605394 L141
19 1, 3, 5, 21, 41, 49, 89, 133, 141, 165, 189, 293, 305, 395, 651, 665, 771, 801, 923, 953, 3689, 5315, 6989, 15641, 48819, 78389, 134053, 167843, 181395, 311091, 353661 [517700] 645555, 916763 L177
21 1, 2, 3, 7, 10, 13, 18, 27, 37, 51, 74, 157, 271, 458, 530, 891, 1723, 1793, 1849, 1986, 2191, 2869, 4993, 7777, 11730, 15313, 29171, 35899, 36227, 71570, 199219, 233914, 297499, 332523, 348547, 538657, 986130, 999599 [1000000]
23 4, 6, 12, 46, 72, 244, 264, 544, 888, 1146, 14826, 24978, 103386 [226600] 323668, 458362, 496422
25 3, 9, 11, 17, 23, 35, 39, 75, 105, 107, 155, 161, 215, 225, 335, 635, 651, 687, 1479, 1515, 1953, 2435, 2963, 3671, 5979, 7551, 8091, 9791, 15015, 20897, 26279, 43371, 130407 [400000] 587585, 716769 L137, 942563 L183
27 1, 2, 4, 5, 8, 10, 14, 28, 37, 38, 70, 121, 122, 160, 170, 253, 329, 362, 454, 485, 500, 574, 892, 962, 1213, 1580, 2642, 2708, 4505, 8152, 11858, 13300, 15041, 16118, 16778, 19069, 22769, 29020, 30298, 30377, 35942, 42817, 42869, 62024, 74629, 90449, 91042, 117901, 128594, 143330, 152530, 157898, 175852 [276100] 340682, 444622 L1, 627794 L107, 729314 L125, 777992 L151
29 4, 16, 76, 148, 184, 11008, 147316, 644044, 1478344 [1600000]
31 1, 5, 7, 11, 13, 23, 33, 35, 37, 47, 115, 205, 235, 271, 409, 739, 837, 887, 2189, 3465, 4653, 5073, 8011, 8061, 21957, 24589, 25657, 44653, 50321, 57647, 62083, 78179, 80021, 81655, 111667, 150265, 177089, 196433, 274115, 306751, 311389, 315523 [500000] 666285, 773227 L330
33 2, 3, 6, 8, 10, 22, 35, 42, 43, 46, 56, 91, 102, 106, 142, 190, 208, 266, 330, 360, 382, 462, 503, 815, 1038, 1651, 1855, 1858, 1992, 2232, 4462, 4726, 5475, 6702, 9710, 10931, 11503, 20552, 22291, 26575, 35931, 39271, 51326, 57695, 63115, 67182, 109848, 128635, 136971, 173110, 174182 [250000] 373446 L38, 585400, 598248, 674050 L138, 773030 L488
35 2, 6, 10, 20, 44, 114, 146, 156, 174, 260, 306, 380, 654, 686, 702, 814, 906, 1196, 1316, 3062, 4116, 9382, 23562, 25742, 32564, 72444, 97550, 112390, 118510, 246732, 252910 [420000] 634402, 805222 L142, 839082 L325
37 1, 2553, 4893, 7897, 14353, 32125, 51477, 78973 [210000] 341365 L38
39 3, 24, 105, 153, 188, 605, 795, 813, 839, 2135, 2619, 4053, 8333, 15519, 16025, 16505, 30684, 40700, 43683, 52233, 142205, 222345, 225333, 292839, 322613 [500000] 747219, 781220 L138
41 2, 10, 14, 18, 50, 114, 122, 294, 362, 554, 582, 638, 758, 3334, 6630, 42450, 64218, 89282, 149238 [500000] 511718 L290
43 7, 31, 67, 251, 767, 1171, 1643, 25423, 38863, 50867, 60391, 100303 [210000] 286171, 399767 L38
45 1, 2, 3, 4, 5, 6, 8, 9, 14, 15, 16, 22, 28, 29, 36, 37, 54, 59, 85, 93, 117, 119, 161, 189, 193, 256, 308, 322, 327, 411, 466, 577, 591, 902, 928, 946, 1162, 1428, 1708, 1724, 2063, 2922, 2951, 3111, 3402, 4024, 4485, 5859, 6124, 8981, 10628, 19283, 23522, 26591, 28914, 33954, 34743, 76367, 103546, 103912, 104452, 125132, 139883, 174102, 249065, 306394, 368553 [500000] 528245 L167, 645542, 818648 L282
47 4, 14, 70, 78, 1374, 1824, 2158, 2654, 4494, 9598, 10068, 11524, 15128, 55408, 87324 [210000] 450470 L38
49 1, 5, 7, 9, 13, 15, 29, 33, 39, 55, 81, 95, 205, 279, 581, 807, 813, 2551, 2565, 3183, 6661, 11989, 16911, 22605, 30799, 39969, 41167, 43421, 54559, 212745, 290631, 332231 [417500] 460989, 542945, 691469 L217
51 1, 9, 10, 19, 22, 57, 69, 97, 141, 169, 171, 195, 238, 735, 885, 1287, 1365, 2026, 2211, 2361, 2889, 3159, 3709, 5031, 19066, 33622, 43162, 188517, 194875 [210000] 217971, 286965, 331546, 468417 L38, 657705 L148, 832630, 845494 L80
53 2, 6, 8, 42, 50, 62, 362, 488, 642, 846, 2870, 3042, 5096, 10556, 12642, 17850, 21710, 25230, 30392, 43122, 206970 [520000] 582078 L251
55 1, 3, 5, 7, 15, 33, 41, 57, 69, 75, 77, 131, 133, 153, 247, 305, 351, 409, 471, 1251, 1259, 2253, 2411, 2425, 2699, 3221, 4099, 4173, 4291, 4905, 5349, 6723, 7143, 7505, 10539, 10557, 12099, 17373, 23721, 27895, 33801, 35519, 45927, 63589, 73287, 96933, 106659, 218043, 253047, 397941 [520000] 651015 L325
57 1, 2, 4, 5, 8, 10, 20, 22, 25, 26, 32, 44, 62, 77, 158, 317, 500, 713, 1657, 1790, 2761, 2794, 3704, 4174, 6772, 14348, 16132, 16160, 16766, 21097, 29125, 40094, 44824, 49006, 67585, 74650, 94798, 162538, 173585, 239854 [400000] 450430 L171, 565994 L261, 707245 L384, 839446 L80
59 12, 16, 72, 160, 256, 916, 1216, 1840, 3280, 8140, 10816, 15776, 40256, 72116, 134240, 145532, 358276 [1000000]
61 3, 5, 9, 13, 17, 19, 25, 39, 63, 67, 75, 119, 147, 225, 419, 715, 895, 1025, 1103, 1179, 1345, 1829, 3855, 4159, 4493, 6039, 7799, 9073, 10543, 12883, 23807, 23957, 36163, 44047, 51975, 65573, 79393, 79949, 81987, 86349, 384287 [400000] 499175 L290, 762417 L548, 971585 L80
63 2, 3, 8, 11, 14, 16, 28, 32, 39, 66, 68, 91, 98, 116, 126, 164, 191, 298, 323, 443, 714, 758, 759, 1059, 1168, 1511, 1792, 2116, 3148, 3836, 4084, 4622, 6164, 9268, 10062, 14623, 15799, 23634, 44198, 53971, 55244, 81519, 99411 [100000] 112554, 114906, 123774, 132203, 155998, 218694 g267, 323432, 340463 L145, 610704 L442
65 4, 6, 12, 22, 28, 52, 78, 94, 124, 162, 174, 192, 204, 304, 376, 808, 930, 972, 1714, 1776, 2176, 2568, 4392, 4728, 5548, 8046, 12474, 26856, 27156, 45240, 52026 [100000] 134598, 179658, 185946 g267, 578512 L132, 647130 L148
67 5, 9, 21, 45, 65, 77, 273, 677, 1049, 1721, 17105, 18645, 27761, 61661, 79773 [400000] 403461 L83, 527037, 722805 L268
69 1, 4, 5, 7, 9, 11, 13, 17, 19, 23, 29, 37, 49, 61, 79, 99, 121, 133, 141, 164, 173, 181, 185, 193, 233, 299, 313, 351, 377, 540, 569, 909, 1057, 1081, 1189, 1679, 2043, 2641, 3471, 3533, 3943, 5607, 9681, 12879, 14513, 15300, 21573, 30895, 32163, 39983, 47167, 47657, 49325, 51881, 64801, 65385, 65723, 66017, 69020, 74111, 76803, 79956, 83761, 84437, 100916, 110617, 165841 [186000] 195515 L68, 234305, 234916, 236989, 239019, 352196, 362787, 464843 L38, 580596, 613781, 820237, 831617, 867653 L138, 978209 L260
71 2, 14, 410, 1390, 3770, 5434, 202642, 735802 [736000]
73 7, 11, 19, 71, 79, 131, 1167, 1191, 6771, 12627, 17947, 20079, 26347, 40327, 41231, 69379, 109587, 193559, 212451, 499391, 783831 [1000000]
75 1, 3, 5, 6, 18, 19, 20, 22, 28, 29, 39, 43, 49, 75, 85, 92, 111, 126, 136, 159, 162, 237, 349, 381, 767, 969, 1247, 1893, 1951, 2363, 2657, 3065, 3090, 3836, 4110, 4342, 5671, 6807, 21945, 24658, 30082, 31811, 54510, 70828, 79292, 80938, 84432, 92235, 113429, 170933, 182433, 196071, 199819, 231580, 306789, 424392, 434323 [500000] 631091 L257, 814857 L80, 995721 L257
77 2, 4, 14, 26, 58, 60, 64, 100, 122, 212, 566, 638, 1214, 2080, 4852, 5356, 5720, 7044, 8320, 8556, 10684, 14584, 39016, 47972, 72008, 217956, 223512, 387680, 441528, 607920, 855770 [1340000] 1467554 L145
79 1, 3, 7, 15, 43, 57, 61, 75, 145, 217, 247, 2803, 3403, 4375, 5113, 9883, 14565, 17397, 65977, 82081, 92517, 214453, 248055, 369535 [740000]
81 3, 5, 11, 17, 21, 27, 81, 101, 107, 327, 383, 387, 941, 1665, 3515, 4007, 4727, 7137, 16257, 16833, 21243, 24239, 35435, 59925, 91673 [100000] 153455 anon, 165341, 183167, 190349 L55, 240743, 253385, 308325 L142, 741917 L268
83 2, 4, 8, 10, 14, 18, 22, 24, 26, 28, 36, 42, 58, 64, 78, 158, 198, 206, 424, 550, 676, 904, 1276, 1374, 1536, 1642, 2124, 2796, 5266, 5318, 8828, 11638, 22968, 35836, 53348, 55808 79826, 105282, 112418, 129804, 144456, 216954 [400000] 624398, 654488 L323, 791926 L425, 851092 L80
85 5, 11, 71, 113, 115, 355, 473, 563, 883, 1235, 5735, 9809, 11311, 14491, 25495, 125675, 128459, 147115, 656039, 683573, 1034069 [1080000]
87 1, 2, 8, 9, 10, 12, 22, 29, 32, 50, 57, 69, 81, 122, 138, 200, 296, 514, 656, 682, 778, 881, 1422, 1494, 1857, 3060, 3489, 4106, 5129, 5378, 8096, 8546, 10138, 10941, 13749, 21758, 23554, 24582, 27526, 28581, 29306, 29588, 36101, 36681, 41378, 45689, 55769, 56049, 65676, 77361, 96426, 110189, 128630, 142738, 154352, 155794, 188689, 353734, 360829, 382268, 796341, 942790 [1000000]
89 4, 8, 12, 24, 48, 52, 64, 84, 96, 1272, 2028, 3224, 4952, 6892, 7372, 16476, 56968, 68632, 185868, 208824, 369628 [740000]
91 1, 3, 9, 13, 15, 17, 19, 23, 47, 57, 67, 73, 77, 81, 83, 191, 301, 321, 435, 867, 869, 917, 6009, 6051, 8077, 9003, 10355, 10719, 11217, 20197, 22011, 36379, 45373, 53441, 77013, 86329, 89853, 90341, 104783, 169779, 187407, 245989 [300000] 313849 L163, 535819, 563469 L145, 633169 L425, 711335 L323, 787173 L323
93 3, 4, 7, 10, 15, 18, 19, 24, 27, 39, 60, 84, 111, 171, 192, 222, 639, 954, 2400, 2587, 4012, 4359, 5250, 6012, 6183, 7344, 10603, 12403, 13215, 29154, 78192, 81294, 103744, 107991, 174412, 176479, 203728, 205158 [210000] 251199 L128, 362268 L147, 580482 L147, 903187 L282
95 2, 6, 26, 32, 66, 128, 170, 288, 320, 470, 1278, 1296, 1316, 1536, 1608, 13230, 15438, 31268, 42198, 46688, 71636, 140840, 259076, 271590 [700000]
97 1, 9, 45, 177, 585, 1409, 2617, 3465, 6981, 843205 [930000]
99 1, 4, 5, 7, 8, 11, 19, 25, 28, 35, 65, 79, 212, 271, 361, 461, 1237, 1297, 1577, 1747, 1901, 1943, 2741, 3203, 3425, 5069, 6368, 8372, 9761, 12260, 13472, 24032, 26227, 34028, 34492, 54244, 55660, 56056, 60965, 67283, 74576, 118711, 170867, 175921 [210000] 269809, 275113, 305803, 358891, 390373, 435301, 586088 L167, 1106989 L486
101 10, 18, 54, 70, 1330, 1638, 3894, 4114, 9990, 94194 [100000] 900358 L183
103 3, 7, 11, 19, 63, 75, 95, 127, 155, 163, 171, 283, 563, 1739, 2243, 3971, 4375, 5227, 8307, 9943, 18383, 19835, 25879, 26927, 36895 [100000] 304771 L33, 422939 L186, 602483 L488, 686251 L488
105 2, 3, 5, 6, 8, 9, 25, 32, 65, 113, 119, 155, 177, 299, 335, 426, 462, 617, 896, 1377, 1847, 2495, 2810, 3743, 3884, 3897, 5235, 6418, 6550, 8066, 8757, 9518, 11610, 16542, 17485, 17984, 18530, 18885, 25017, 26642, 30366, 40470, 45770, 56903, 57819, 66077, 69958, 75569, 92357 [100000] 108867, 145422 anon, 201556, 262670, 280022, 472430, 484658 L38, 530360 L325, 801978, 814850 L384
107 10, 12, 18, 24, 28, 40, 90, 132, 214, 238, 322, 532, 858, 940, 2044, 5316, 6232, 7074, 8316, 15868, 45838, 46828, 48384, 50862, 57000, 69972 [100000] 153552 anon, 162502 L38, 267916 g23, 306334 L171, 471382 L145, 494896 L138
109 9, 149, 177, 419, 617, 1799, 3227, 6017, 12957, 141227 [350000] 646403 L426
111 2, 3, 6, 7, 21, 22, 23, 26, 29, 31, 58, 59, 67, 78, 83, 146, 159, 162, 165, 183, 262, 511, 718, 815, 1181, 1255, 1422, 1506, 1541, 1734, 2213, 3623, 4223, 4551, 5741, 5878, 6599, 11349, 12102, 17811, 19798, 20559, 26887, 32499, 40626, 43151, 49194, 52859, 98462, 101962, 126754, 133062, 147346, 217034, 279227, 345867, 362466, 378595, 448102, 520923, 602565, 656935 [700000] 791502, 959671 L282
113 8, 14, 74, 80, 274, 334, 590, 608, 614, 650, 1016, 1814, 1904, 4400, 5474, 144866, 174898, 343214, 422866, 464386 [500000]
115 1, 3, 11, 13, 19, 21, 31, 49, 59, 69, 73, 115, 129, 397, 597, 623, 769, 1131, 4581, 6229 13477, 20995, 24541, 31089, 48535, 57375, 87151, 98543 [210000] 267443 L141, 357829 L138
117 1, 2, 4, 6, 12, 16, 18, 20, 22, 24, 37, 40, 48, 49, 57, 62, 154, 172, 184, 236, 265, 374, 409, 445, 478, 664, 718, 928, 1186, 1369, 1804, 2006, 2140, 2618, 4456, 4846, 12604, 17680, 18318, 18812, 20320, 20660, 21494, 24977, 27749, 30734, 31720, 41742, 51928, 54216, 60386, 61882, 64408, 72078 [100000] 111698, 129820, 135318 anon, 151594, 225165, 373045 L38, 511361 L171, 560848 L145, 697458, 834916 L261, 877874 L488
119 12, 16, 52, 160, 192, 216, 376, 436 [200000] 266136, 401552 L38
121 1, 3, 21, 27, 37, 43, 91, 117, 141, 163, 373, 421, 1581, 2035, 10701, 18931, 21307, 51195, 64579, 156541, 302097, 334257, 368059, 383061, 410131, 494317, 541621, 990219, 1039965, 1526097, 1589157, 1695499, 1954243, 2033941 [2800000]
123 2, 3, 11, 15, 23, 24, 27, 35, 71, 84, 108, 122, 123, 138, 236, 242, 290, 392, 500, 611, 747, 771, 1106, 1490, 3560, 5111, 6066, 8660, 8927, 19451, 19730, 28316, 30471, 49515, 93762, 117083, 168435, 206663, 249242, 255402, 261530, 355727, 389052, 516456, 518540, 521031 [700000]
125 2, 4, 44, 182, 496, 904, 1196, 3034, 4004, 5474, 18122, 21952, 24874, 27614, 31166, 35386, 44234, 51104, 96346 [100000] 100966, 109454, 123634 anon, 388934, 418034 L142, 659314 L138, 918494 L384
127 25, 113, 39545, 170393 [200000] 220417 TG, 1398889 L486
129 1, 3, 4, 5, 8, 9, 12, 16, 28, 51, 56, 59, 72, 73, 88, 93, 105, 148, 165, 292, 368, 445, 635, 771, 773, 940, 1173, 1965, 2661, 3092, 5001, 5091, 8741, 9773, 13960, 15328, 19408, 19911, 21228, 34876, 37341, 38564, 39055, 39152, 45395, 68825, 72360, 78365 [100000] 126303, 130240, 150808 anon, 214985, 254975, 292573, 310619, 314188, 331384, 356373, 398288 L38, 536615 L145, 603488 L260, 690893 L425
131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974, 1878, 3718, 4050, 5466, 6478, 35662, 40046, 56346, 98626 [100000] 131026, 138658 anon, 603738 L426
133 3, 11, 15, 19, 31, 59, 75, 103, 163, 235, 375, 615, 767, 1223, 1411, 26655, 47351, 75027, 83323 [100000] 121571 anon, 238163 g23, 312359 L141, 359915 L138, 471455 L145
135 1, 9, 10, 13, 16, 21, 24, 34, 54, 153, 177, 184, 226, 238, 286, 334, 586, 618, 870, 3151, 3397, 4987, 5160, 14737, 15309, 15319, 16870, 29430, 39298, 40117, 56443, 58449, 77845 [100000] 105870, 127405 anon, 170613, 183373 L40, 235315, 245754, 259951 L142, 437544 L199, 474178 L140, 525544 L171, 876997 L260
137 2, 18, 38, 62, 2180, 2900, 3132, 3462, 3578, 5724, 5810, 18468, 30044, 36122, 37610, 43782, 310790, 1849238 [2000000]
139 1, 5, 7, 9, 15, 19, 21, 35, 37, 39, 41, 49, 69, 111, 115, 141, 159, 181, 201, 217, 487, 567, 677, 765, 811, 841, 917, 1279, 1407, 1505, 1521, 1587, 2047, 2469, 2649, 3019, 7427, 10257, 33685, 34479, 35177, 43641, 49211, 65031, 84907, 90231, 95021 [100000] 124375 anon, 176425 L40, 224947, 382441 L157, 451367 L442
141 1, 2, 7, 10, 11, 13, 38, 46, 61, 170, 299, 445, 815, 983, 4237, 6146, 7255, 7459, 7585, 8411, 8647, 14855, 20338, 21671, 29293, 89318, 92498, 98686 [100000] 121142 anon, 250271 L163, 619742 L426
143 2, 4, 6, 8, 12, 18, 26, 32, 34, 36, 42, 60, 78, 82, 84, 88, 154, 174, 208, 256, 366, 448, 478, 746, 1178, 1290, 2284, 3606, 35706, 36920, 45882, 47308, 70932, 96278 [100000] 111886, 144736 anon, 303284 L171, 374626 L168
145 5, 13, 15, 31, 77, 151, 181, 245, 445, 447, 883, 1037, 3557, 43733 [100000] 290861 L141, 464887 L145, 530181 L163
147 1, 2, 4, 5, 12, 25, 33, 40, 44, 53, 60, 74, 92, 133, 177, 397, 453, 669, 977, 2226, 2612, 3230, 3314, 5001, 5333, 5376, 7384, 7924, 10265, 18349, 19554, 21854, 30426, 33533, 49280, 70530, 92445 [100000] 105789 anon, 177017, 198692 L40, 464300 L163
149 4, 16, 48, 60, 240, 256, 304, 2644, 3720, 25132, 39472 [100000] 212460 L70, 592968 L171
151 5, 221, 641, 2783, 6423, 9053, 23271, 29159, 88409, 113655, 241271, 263895 [500000]
153 3, 4, 6, 7, 10, 11, 12, 19, 20, 22, 23, 39, 66, 106, 120, 124, 151, 312, 411, 447, 474, 507, 574, 671, 787, 826, 979, 1690, 1954, 2047, 3003, 4323, 4426, 5903, 6267, 6846, 14550, 17470, 21520, 31711, 36724, 45291, 45654, 51778, 55420, 63439, 68451, 78423, 109696, 125128, 130710, 169836, 192900, 195028, 383083, 545716 [700000]
155 2, 8, 14, 16, 44, 46, 82, 172, 196, 254, 556, 806, 2828, 4462, 5558, 8086, 8216, 9862, 12026, 12842, 26054, 57044, 85364, 105098, 127262, 296822, 310312, 310622, 353384, 374288, 496604 [500000]
157 1, 5, 33, 97, 121, 125, 305, 445, 473, 513, 1581, 3077, 3517, 6345, 8797, 15265, 16641, 32185, 32581, 43905, 77025, 84377, 202345, 230777, 234401, 473073 [500000]
159 1, 4, 5, 11, 24, 25, 41, 67, 185, 215, 235, 277, 445, 465, 647, 844, 1420, 1505, 2385, 6451, 7475, 9549, 10800, 11585, 16079, 47795, 51839, 89285, 106481, 186331, 201429, 293235, 338477, 442189, 482581, 611020 [700000] 736144 L323
161 2, 6, 18, 22, 34, 54, 98, 122, 146, 222, 306, 422, 654, 682, 862, 1010, 1346, 1582, 7890, 9714, 12498, 21742, 27810, 34798, 74382, 97746, 205370, 249710, 371426, 394974, 447330 [500000] 447330 L63
163 3, 31, 63, 303, 4731, 31651, 45171, 96111, 105219, 341611 [500000]
165 2, 3, 5, 6, 8, 11, 12, 15, 18, 23, 27, 36, 39, 44, 45, 56, 59, 63, 81, 84, 150, 188, 264, 275, 282, 299, 321, 338, 390, 552, 657, 722, 930, 1139, 1388, 1491, 1625, 2196, 2519, 2541, 2736, 2766, 3630, 4202, 4875, 5643, 6150, 10134, 20328, 20805, 22902, 25770, 30918, 30978, 33389, 40901, 54311, 62145, 67224, 83811, 89465, 93846 [100000] 109719, 148758 anon, 167457, 173396 L18, 221667, 236051, 246426 L32, 325922 L56, 396642, 487961 L32
167 4, 6, 8, 10, 16, 32, 38, 42, 52, 456, 576, 668, 1082, 1512, 1614, 1922, 2072, 2672, 3210, 3616, 3682, 7754, 7906, 10536, 12282, 12338, 25162, 25460, 49672, 66318, 132738, 133188 [200000] 225232 L138, 275680, 314000, 315872 L171
169 1, 5, 11, 17, 67, 137, 157, 203, 209, 227, 263, 917, 1039, 2581, 3659, 3691, 4337, 8249, 8927, 9749, 20807, 33439, 158003, 192323 [210000] 458099 L145
171 2, 3, 5, 10, 25, 29, 39, 73, 103, 109, 123, 198, 378, 434, 825, 925, 1265, 1802, 2134, 2199, 2629, 3154, 3490, 4093, 4814, 5490, 7029, 9074, 9298, 10249, 10505, 12185, 16382, 19030, 26237, 28890, 40123, 61483, 129309, 133527, 182745, 259262, 269539, 290403, 576733, 590818, 684003 [700000]
173 2, 4, 6, 16, 32, 50, 76, 80, 96, 104, 162, 212, 230, 260, 480, 612, 1044, 1440, 1910, 2488, 3140, 3628, 5284, 6332, 7494, 9762, 27100, 29632, 37732, 44036, 47284, 65970, 116870, 145956, 360004, 409470, 483932, 632000, 828808 [1000000]
175 1, 3, 9, 21, 23, 41, 47, 57, 69, 83, 193, 249, 291, 421, 433, 997, 1269, 1619, 1893, 2457, 3527, 9579, 14699, 15677, 16479, 21293, 30729, 33609, 47437 143691 [210000] 244073, 244393 L138, 282719, 309593 L171, 387513 L145
177 1, 12, 13, 24, 25, 34, 36, 48, 61, 66, 196, 264, 376, 672, 732, 877, 1032, 1104, 1177, 1242, 2664, 7756, 35034, 37728, 57796, 96978, 98353, 277458, 282546, 418816, 582454, 653686, 663601, 665874, 668682, 769026 [1275000]
179 8, 68, 108, 20780, 25488, 25656, 38684, 57096, 159108 [210000] 236856, 490800 L138
181 3, 5, 7, 9, 11, 17, 23, 31, 35, 43, 47, 83, 85, 99, 101, 195, 267, 281, 363, 391, 519, 623, 653, 673, 701, 1091, 1147, 1565, 3273, 3661, 3923, 4127, 4783, 5267, 5345, 5747, 6151, 6299, 7569, 9033, 11843, 14139, 14175, 15779, 21557, 32295, 49823, 60979, 65195, 132367, 133895 [150000] 186827 L15, 268299 L138, 293551 L171, 308759, 327407 L138, 334579 L144, 400849, 458303 L145, 491487 L171, 553989 L138, 563997 L145, 655067, 823853 L138
183 4, 11, 22, 31, 52, 56, 59, 67, 88, 104, 251, 572, 724, 1379, 2696, 3616, 3928, 8518, 9239, 9419, 10547, 20396, 42136, 43936, 69422, 313127, 330275, 358568, 411974 [700000]
185 2, 6, 10, 18, 26, 40, 46, 78, 230, 542, 1286, 1550, 1728, 2138, 2226, 2686, 3742, 5002, 12730, 42936, 64290, 86602, 86686, 109346, 113966, 133346 [210000] 229850 L141, 238230 L169, 294662 L138, 391322, 459352 L145
187 1, 17, 21, 53, 253, 2173, 3313, 5197, 5333, 6929, 28017, 40429, 47877, 80617 [100000] 110513, 139673, 141201 anon, 263093, 379649, 483153 L138
189 3, 4, 5, 8, 11, 12, 24, 33, 44, 48, 56, 76, 93, 108, 172, 216, 304, 363, 401, 420, 500, 545, 581, 756, 875, 1552, 1931, 2740, 2787, 2825, 3443, 5235, 8444, 10523, 12755, 14585, 21161, 24404, 25880, 31316, 31965, 32040, 34233, 34323, 36443, 54436, 69403, 175901, 213856, 235068, 237968, 239891, 246356, 255372, 323900, 480835, 487601, 496835 [770000]
191 226, 3594, 59770, 240802 [500000]
193 3, 15, 27, 63, 87, 135, 543, 1383, 1455, 7767, 18543, 22143, 40967, 198719, 405483, 439107, 880287 [885000]
195 1, 3, 4, 6, 8, 9, 10, 14, 23, 26, 28, 35, 44, 46, 50, 55, 60, 63, 65, 78, 99, 100, 106, 111, 163, 178, 180, 364, 569, 825, 838, 958, 1292, 1425, 1531, 2020, 2259, 2434, 2492, 2520, 3310, 3624, 4195, 4206, 5103, 5139, 5478, 7198, 7335, 8123, 9903, 12239, 12826, 12830, 16954, 22535, 28943, 29238, 31470, 40958, 46815, 52983, 69094, 76259, 84016, 92376 [100000] 100974, 113681, 132478, 185009 g292, 196785, 197051, 205668, 225594 L4, 243999 L5, 272695 L138, 311215 L5, 561444 L138
197 2, 16, 20, 22, 40, 82, 112, 178, 230, 302, 304, 328, 374, 442, 472, 500, 580, 694, 1264, 1634, 1784, 3080, 5722, 7174, 8908, 18502, 18746, 39094, 99338, 170066, 202534 [267000] 325610, 510940, 569222 L167, 635042, 825188 L282
199 1, 5, 7, 15, 19, 23, 25, 27, 43, 65, 99, 125, 141, 165, 201, 211, 331, 369, 389, 445, 461, 463, 467, 513, 583, 835, 1071, 1085, 1107, 1187, 1197, 1491, 1513, 2505, 3859, 3941, 5989, 9693, 13125, 17009, 19459, 33147, 46433, 51091, 72813 [100000] 105169, 118531, 153127 anon, 263051 L147, 301193, 332985 L157, 531357, 541753, 548533, 560987, 581119 L426
201 1, 3, 9, 10, 14, 17, 21, 37, 57, 66, 70, 87, 94, 99, 123, 141, 147, 183, 207, 246, 269, 291, 313, 341, 361, 363, 615, 743, 1318, 1515, 1798, 2413, 2797, 3254, 3826, 7574, 11770, 15029, 21313, 21543, 21637, 30289, 31078, 37511, 70919, 80238, 81215, 81459, 85995 [100000] 121215, 147429, 164255 anon, 193141 L40, 254039 g219, 285534, 302666, 356889, 374891, 376594, 382059, 432315, 434118, 484583 L167, 520586, 540810, 775453, 799611, 840735 L282
203 2, 22, 82, 142, 190, 232, 314, 1682, 2302, 5598, 6632, 6720, 11080, 22094, 31310, 53088, 105890, 115350, 235480, 248862 [260000] 313474 L163, 455190 L145, 480918 L163
205 1, 9, 39, 45, 49, 67, 75, 99, 129, 159, 177, 445, 721, 771, 829, 849, 865, 1971, 3045, 8397, 9019, 10749, 21037, 30529, 38349, 46257, 53577, 64695, 77451, 128019 [250000] 420297 L148, 462261 L171
207 2, 9, 12, 17, 20, 21, 50, 53, 132, 168, 341, 360, 381, 501, 1065, 1169, 1545, 2109, 2520, 2661, 3149, 4077, 11252, 21588, 21692, 39509, 52685, 67196, 87708 [100000] 232436 L40, 372312, 417818, 481385 L186, 507833, 643478 L330
209 4, 8, 16, 28, 40, 52, 80, 148, 328, 8464, 11704, 52372, 60172 [100000] 675232, 692692 L421
211 1, 13, 23, 37, 43, 67, 83, 151, 661, 811, 3937, 5027, 5365, 9307, 11971, 60295, 89071, 89303 [100000] 262877 L145, 680135 L426
213 4, 10, 19, 30, 36, 47, 80, 82, 92, 100, 103, 114, 126, 140, 144, 152, 170, 210, 264, 514, 726, 967, 1662, 2423, 3116, 3974, 4396, 5735, 6680, 6707, 9947, 23814, 24330, 43074, 43775, 77922, 98179, 120362, 171154 [250000] 303670 L145, 709727, 760942 L261
215 2, 6, 14, 16, 38, 60, 64, 124, 198, 200, 210, 296, 890, 1486, 1646, 1848, 1906, 2540, 6908, 10430, 10848, 13636, 17858, 18386, 18916, 20802, 23936, 30620, 32858, 34860, 34990, 36978, 54394, 55298, 58822, 88508, 109130, 224036 [250000] 331784 L163
217 1, 9, 21, 133, 233, 1393, 1453, 1769, 2041, 3985, 17501, 80341, 148089, 205525 [260000] 327829 L145, 377581, 398605 L163
219 7, 81, 381, 412, 657, 853, 1317, 3261, 3768, 6081, 14017, 19993, 25863, 31801, 40113, 48877, 558313 [700000]
221 2, 6, 42, 354, 402, 914, 1562, 10382, 34986, 81042 [100000] 104846 anon, 730986 L426
223 3, 19, 91, 211, 699, 819, 1323, 4635, 38019 [100000] 307755 L138
225 1, 23, 25, 53, 65, 139, 149, 481, 613, 1343, 1601, 2125, 4385, 9005, 9169, 57013, 99821, 113893, 162653, 206293, 491135 [700000]
227 2, 4, 8, 12, 14, 26, 32, 80, 124, 230, 284, 562, 866, 1830, 2630, 3122, 3428, 6278, 9900, 19888, 20092, 22706, 29088, 31412, 44402, 47914, 53120 [100000] 102330, 135164 anon, 299306 L171, 345918 L138
229 1, 3, 7, 19, 25, 27, 71, 97, 231, 235, 291, 295, 313, 347, 491, 511, 531, 571, 803, 1499, 1523, 1607, 1743, 2161, 2231, 3113, 5511, 5863, 6039, 8055, 8443, 9707, 12155, 12195, 21049, 24271, 34403, 34879, 56491, 58839 [100000] 162583 L1, 207863 L21, 220147 L79, 586795 L145
231 1, 3, 6, 7, 21, 29, 46, 49, 54, 57, 73, 90, 118, 169, 207, 267, 287, 333, 354, 366, 370, 463, 493, 497, 507, 655, 729, 735, 757, 1054, 1377, 1770, 2098, 2886, 3225, 3611, 3625, 3657, 4849, 5706, 5749, 5771, 7110, 8395, 12150, 15658, 16182, 16693, 17363, 20279, 27619, 35953, 39733, 53949, 75349, 80638, 82887, 92154 [150000] 162154 L15, 169955 L29, 205017, 224297 L63, 248359 L102, 345183, 369583, 465391, 498961, 535713, 668218 L87, 749301, 959375 L138
233 4, 10, 12, 22, 24, 34, 48, 60, 100, 562, 574, 640, 838, 852, 2002, 4198, 4932, 5860, 10492, 13834, 17398, 25944, 133030 [150000] 179992 L69
235 3, 9, 15, 75, 143, 425, 693, 803, 903, 953, 1079, 1613, 1667, 2937, 7157, 7899, 136767 [150000] 178739, 191973 L75, 231927 g384, 312345 L141, 315773 L171
237 2, 5, 9, 13, 17, 18, 25, 26, 30, 38, 69, 88, 89, 94, 133, 198, 205, 289, 360, 402, 438, 445, 498, 637, 914, 934, 973, 1265, 2965, 3813, 6096, 11560, 13977, 19816, 33673, 43128, 47869, 50370, 70649, 72809, 82453, 84904, 89210, 102618, 109334, 181610 [260000] 421862 L138, 729654, 832053 L261
239 4, 92, 25780, 104956, 140116 [230000] 356300 L138
241 11, 17, 19, 39, 69, 321, 653, 1109, 3819, 5729, 9659, 9911, 13217, 16707, 22307, 65107, 75419, 97587, 99667 [260000] 336197 L163, 407709 L171, 497679 L145
243 2, 6, 8, 11, 12, 18, 24, 27, 36, 38, 44, 56, 58, 62, 116, 134, 162, 242, 274, 348, 358, 478, 512, 548, 658, 824, 1242, 1287, 1531, 2846, 3343, 4818, 4856, 5051, 6024, 7431, 7434, 9432, 9667, 13059, 13482, 18111, 19004, 33571, 40174, 41467, 53206, 57978, 61438, 85392, 86468, 116103, 148191 [150000] 152454 L29, 187966 L55, 206302 L21, 387836 p48, 510491, 518736, 539016, 616662 L442, 670891, 744442 p48
245 4, 6, 28, 76, 96 ,124, 294, 396, 726, 868, 928, 1400, 3056, 6594, 12588, 15708, 88576, 144288 [150000] 238468 L118, 606706, 619938 L426
247 133, 277, 805, 2341, 68845 [230000] 952069 L138
249 8, 9, 12, 41, 57, 156, 201, 249, 612, 956, 1617, 2064, 2091, 2547, 4512, 5696, 9608, 11444, 20556, 33896, 77079, 89004, 251036 [260000]
251 6, 110, 1302, 4598, 74030 [213000] 359790 L15
253 71, 1007, 27623 [213000] 1722623 L145
255 1, 2, 3, 4, 6, 11, 12, 24, 40, 41, 61, 75, 86, 95, 158, 207, 223, 242, 276, 338, 390, 488, 673, 804, 1084, 1332, 1467, 1588, 2894, 3650, 4367, 6001, 6372, 10162, 10235, 10660, 12988, 17470, 18323, 18673, 24137, 24335, 24797, 28573, 35636, 36275, 44015, 49167, 55106, 58106, 58202, 58476, 90852, 118030, 120342, 138101, 154397, 206716, 230830, 259537, 281366, 405467, 450144, 450762, 481837, 577903, 592080, 601910, 635715 [796000]
257 4, 6, 10, 16, 24, 60, 66, 82, 184, 256, 324, 424, 632, 756, 814, 872, 1114, 1702, 3282, 3420, 3862, 3864, 4162, 4510, 7030, 8410, 47974, 59236, 61084, 78034, 133980, 194312, 286832 [320000] 541402 L145
259 5, 7, 9, 27, 33, 37, 59, 179, 289, 389, 917, 1885, 2987, 3683, 4807, 8709, 10153, 11067, 11665, 18909, 22085, 32489, 36233 [135000] 143133 anon, 202609 L23, 278567 L145, 316403 L171, 347159 L145, 423467 L163, 425257 L138, 427623 L163
261 1, 3, 6, 9, 21, 34, 43, 49, 114, 115, 178, 322, 411, 438, 454, 589, 598, 754, 801, 1173, 1546, 1699, 2155, 2994, 4038, 5439, 6442, 10699, 12274, 13314, 13911, 19309, 28675, 29658, 31173, 33606, 65763, 90861, 116706, 185823 [260000] 618918 L145, 660709 L384, 802123, 827599 L261, 850383 L478
263 2, 6, 26, 114, 134, 180, 542, 882, 936, 2382, 3702, 5082, 6722, 15590, 19910, 26964, 29148, 48062, 54870, 69642, 73788, 79922, 95460 [135000] 215712 L23
265 11, 17, 19, 21, 37, 49, 59, 145, 163, 289, 587, 737, 1029, 1061, 1873, 2265, 3271, 3943, 5429, 6067, 6133, 6277, 10101, 10967, 11497, 18799, 27551, 34883, 37459, 44897, 74743, 113473 [135000] 323083 L138
267 4, 5, 8, 14, 16, 17, 20, 26, 28, 34, 40, 44, 53, 58, 74, 80, 86, 94, 128, 130, 140, 149, 178, 365, 448, 878, 920, 1217, 2417, 3400, 3725, 3934, 4454, 5276, 7360, 9544, 11860, 16270, 32038, 37468, 116537, 117358, 119006, 147838, 198536, 211358, 216137, 238670, 287537 [300000] 415916 L199, 471230 L171, 607688 L261, 662524 L400, 705028 L260
269 8, 24, 272, 2304, 3840, 3848, 58748, 63992, 104768 [120000] 264932 L15, 628904 L426
271 1, 7, 21, 55, 175, 235, 2289, 12419, 19917, 19971, 21979, 54007, 66241, 68757, 98595 [130000] 241211 g320, 274509, 322971 L138, 342349 L171, 470529 L145
273 2, 6, 10, 15, 22, 26, 31, 42, 47, 98, 107, 123, 126, 175, 178, 203, 223, 230, 239, 279, 371, 402, 519, 607, 755, 830, 871, 927, 980, 1527, 1770, 2007, 2218, 2247, 2250, 3982, 4367, 4510, 9716, 13018, 20906, 26340, 40186, 63332, 84599, 119743, 156155, 206118, 238687 [260000] 522287 L171, 742930 L323
275 6, 12, 16, 22, 34, 40, 72, 198, 220, 348, 376, 552, 594, 814, 972, 3168, 3702, 3834, 4642, 5116, 9720, 20434, 53692 [100000] 123678 g252, 147802 L21, 204516 g320, 398928 L163
277 5, 21, 101, 105, 333, 461, 933, 1041, 2157, 3321, 5177, 5513, 5781, 9737, 11505, 16457, 17357, 490805 [885000]
279 1, 4, 12, 29, 35, 56, 77, 93, 209, 221, 412, 441, 460, 899, 1859, 1896, 2504, 5315, 6520, 9324, 9460, 11336, 11760, 12317, 21080, 25029, 27064, 29236, 35396, 42791, 55851, 57752, 61551, 73272, 117820, 123253, 162705, 201152 [260000] 277455, 318317 L138, 455704 L153, 479437 L199, 587881, 616044 L145
281 2, 38, 62, 82, 598, 890, 1810, 2242, 2450, 17786, 51470, 65558, 91870, 93850 [260000] 628898 L426
283 11, 55, 91, 99, 235, 319, 1835, 16731, 25471, 31199, 123975, 149351 [260000]
285 1, 7, 8, 12, 19, 23, 41, 44, 47, 62, 63, 79, 197, 293, 472, 788, 956, 1083, 1232, 1533, 1539, 1673, 2399, 2827, 2993, 3327, 3816, 4072, 4152, 4156, 4392, 4436, 4492, 5079, 5112, 5747, 7193, 7604, 7934, 8640, 9699, 10361, 10870, 12374, 16197, 18120, 29199, 35807, 43443, 43817, 44627, 55047, 61064, 92091, 113660, 120326, 134121, 145143, 149907, 155107, 161183, 163071, 211544, 278758, 353143, 359364, 376840, 392397 [470000] 780300 L425, 881240 L323
287 4, 6, 8, 14, 16, 18, 28, 64, 114, 248, 644, 978, 1214, 1928, 1954, 3604, 4234, 6964, 7466, 12316, 14464, 35106, 92986 [260000] 525378 L145
289 1, 3, 13, 21, 25, 33, 73, 93, 115, 127, 397, 1255, 3751, 3801, 4771, 8997, 10063, 11253, 18663, 27525, 28009, 34041, 55693, 60243, 67891, 77391, 90201, 501991, 509401 [520000] 610737, 728205, 1098117 L6
291 2, 5, 9, 11, 17, 21, 29, 30, 33, 50, 59, 62, 137, 161, 281, 290, 533, 842, 1410, 1553, 4794, 5529, 5661, 7013, 7470, 19605, 63477, 72513, 152942, 201494, 220562, 236117 [260000] 291705 L171, 313433 L148, 372342 L138, 386430 L199, 389225, 531347 L171, 565917 L261, 810347 L421, 832410 L261
293 2, 26, 34, 66, 124, 560, 600, 1344, 1714, 1904, 5200, 7602, 10344, 63484, 196258, 213346, 243698 [260000] 421330 L140, 517242 L145
295 5, 23, 35, 53, 59, 65, 113, 149, 205, 275, 365, 503, 1019, 2105, 2473, 2999, 4813, 8873, 10985, 16495, 32065, 47689, 52727, 63413 [130000] 177695 g63, 374035, 389903 L171
297 1, 2, 4, 8, 9, 10, 14, 18, 24, 25, 30, 42, 48, 49, 56, 90, 97, 182, 336, 348, 434, 546, 769, 1148, 1294, 1394, 1654, 2265, 2966, 3608, 4201, 4878, 5449, 7944, 8889, 9114, 10508, 11224, 15706, 17730, 18564, 21122, 21806, 21882, 24462, 24602, 29384, 35306, 60114, 60282, 61370, 65456, 82782 [130000] 225274, 227030, 227870 L21, 253070 g320, 283484, 378102, 492450, 493726 L195, 583464 L421
299 4, 8, 12, 32, 52, 80, 84, 112, 140, 144, 532, 5388, 6308, 19752, 34456, 35820, 45780, 119852 [130000] 211324 L21, 233188 g320, 295640 L138