Summary of Constant-n Searches (k · 2ⁿ - 1 prime)

Started: 2008-12-03 Last update: 2012-09-16

This page reflects searches with constant n-values, known so far.

Most of the information are from C.Caldwell's Largest Known Primes, so the searched ranges are not known for sure and perhaps not all primes are shown.

Note: All listed primes with Top5000-link are displayed in the data pages (others will inserted later).

n	Contributor	Last Update	#k	max k/ range tested	k · 2ⁿ - 1 is prime for the following k's
3021377 (37th Mers.)	L.Zhou	2008-12-03	0	1-25.0M sieving	-
2976221 (36th Mers.)	L.Zhou	2008-12-14	1	1-20.0M sieved	4348099
1398269 (35th Mers.)	L.Zhou	2008-02-09	1	1-200k 800k-900k 1.5M-1.6M 1.8M-2.0M 2.6M-2.7M	1564347
1257787 (34th Mers.)	L.Zhou	2008-01-23	2	1-100k 2.0M-2.1M 2.4M-2.5M 2.6M-2.7M	26869, 2084259
859433 (33th Mers.)	L.Zhou	2009-04-17	5	1-3800000?	1283911, 1486245, 2013289, 3512185, 3793717
832040 (30th Fib.)	L.Zhou	2008-04-01	1	1-393167	393047
756839 (32th Mers.)	L.Zhou	2008-07-06	5	1-3515500	755061, 1081255, 1334079, 1391281, 3512673
666777	(Svenie25)	2009-06-22	0	?	(Sieving 2 ≤ k ≤ 1G in progress at p = 110T)
666670	PrimeGrid	2009-08-18	1	?	(...) 16385432895
666669	PrimeGrid	2010-07-26	3	?	(...) 39222855075, 60999971445, (...) 5102779049445
666668	PrimeGrid	2009-08-19	4	?	(...) 68717499255, 81519140415, 108871789005, 108940034175
666667	PrimeGrid	2009-10-04	5		(...) 4197278295, 7668057255, 163271945865, 188910734745, (...) 819745524885
666666	PrimeGrid	2010-06-22	18	6.5M? ?-?	192201, 2031801, 2172225, 2403341, 2806367, 3028517, 4658895, 4834137, 5135955, 5194163, 6476615, (...) 29820115785, 32140685925, 43474951665, 45659554125, (...) 188178691305, 40990038691455, 40991571874515
664385 (200k digits)	L.Zhou	2010-11-13	12	1-2930637	398355, 566971, 1197385, 1662657, 1693305, 1749375, 2207995, 3240639, 4827229, 4866867, 5558095, 6571327
524288 (2^2^19)	L.Zhou	2010-03-04	24	1-5.0M?	428079, 685299, 1204313, 1267013, 1862525, 3077949, 3085109, 3278729, 3780035, 3905237, 4444973, 4795019, 4797425, 4988033, 5909037, 6048203, 6203225, 6316275, 6518315, 6731483, 6980865, 6992213, (...) 379482687, 575600367
514229 (29th Fib.)	L.Zhou	2010-03-10	10	1-2.5M?	3681, 14161, 103939, 834961, 926197, 1452459, 2548237, 2554711, 2677177, 3417615
505050	D.Metcalfe	2007-10-24	5	1-1.3M	225507, 247005, 817263, 1208955, 1224255
505000	P.Minovic	2005-01-12	1	1-100k	395
377666	P.Kenny	2007-07-06	23	4.5M?	23505, 221813, 597101, 771267, 981957, 1053875, 1143735, 1242947, 1310075, 1333365, 1597343, 1773251, 2201363, 2436435, 2454305, 2756817, 2776497, 2809527, 3740345, 3839897, 3861095, 3898023, 4477233
376666	P.Kenny	2006-11-29	21	4.5M?	670383, 796971, 1297355, 1313571, 1400835, 1709835, 1762173, 1835255, 2176491, 2265965, 2833857, 2952747, 3068073, 3335025, 3502703, 3968621, 4072643, 4132365, 4393557, 4437105, 4504577
366666	P.Kenny	2006-08-06	15	4.0M?	23015, 397731, 831501, 1066197, 1137873, 1549203, 1618965, 2224281, 2664281, 2765733, 2841003, 2883957, 3255045, 3484053, 3970967
360000	D.Stevens	2009-02-07	2	100k	56627, 73065
346666	P.Kenny	2006-02-21	9	3.0M?	119015, 387197, 856715, 1339011, 1584695, 2010447, 2262647, 2622893, 2785511
336666	P.Kenny	2005-11-17	9	1-2.1M?	429321, 867867, 1182663, 1413975, 1566575, 1668585, 1815081, 2042415, 2111393
333666	P.Kenny	2005-09-06	12	1-3.0M?	238695, 411227, 449195, 588341, 760665, 1172771, 1528373, 2114415, 2215241, 2619953, 2642723, 2996523
333333	Twin Prime Search D.Heuer, D.Broadhurst		3276	?	49371, 63727, 926679, 1295581, 1315347, 1454329, 2504451, 2894469, 3276805, 3278589, 3280321, 11867229, (...) 39044367561, (...) 99890074371, (...) 137137137300427, (...) 137137147110115, (...) 1371371371371653539, (...) 1371371371372049709
332666	P.Kenny	2004-06-18	4	1-1.0M?	129297, 316865, 645215, 666587
300666	P.Kenny	2005-07-18	13	1-3.0M?	371405, 1029915, 1194675, 1471523, 1545737, 1555283, 1729431, 1785713, 1851903, 2415735, 2604623, 2663681, 2839695
299666	P.Kenny	2005-06-09	26	1-3.5M?	56097, 336285, 346797, 390221, 550571, 899697, 902735, 1130721, 1299521, 1381677, 1557897, 1788261, 1788975, 1913405, 1999613, 2368265, 2446451, 2555165, 2704145, 2728817, 2897445, 2934603, 3142983, 3249135, 3313923, 3503141
296666	P.Kenny	2005-04-12	10	1-1.7M?	116567, 135177, 166181, 188241, 723273, 729455, 1146621, 1366935, 1461647, 1708083
295666	P.Kenny	2004-07-20	4	1-1.0M?	170847, 523811, 792261, 988197
266671	P.Kenny	2003-10-02	4	1-300k?	7821, 94593, 226693, 281223
266667	P.Kenny	2003-12-06	3	1-600k?	249513, 375811, 568683
266666	P.Kenny	2003-09-18	3	1-500k?	108477, 237171, 497061
260199	P.Kenny	2006-01-12	15	1-3.0M?	62815, 1149901, 1201219, 1230829, 1333929, 1549573, 1556529, 1746535, 1782763, 2434663, 2547543, 2704153, 2705185, 2739721, 2865355
255529	P.Kenny	2003-08-01	9	1-1.0M?	14847, 309241, 310971, 595405, 656701, 772585, 800827, 811939, 909375
255259	P.Kenny	2003-08-12	4	1-1.0M?	24859, 61831, 265411, 982959
246666	P.Kenny	2004-11-15	4	1-1.5M?	28415, 196563, 745065, 1499747
242424	B.Xiao	2004-03-15	24	?	(...) 262802445, 329039025, 437119347, 660522495, 797479167, 1034137977, 1175957085, 1252805967, 1290660597, 1386369507, 2321382807, 2330771235, 2394391575, 2671257087, 2883779955, 3131681367, 3139813035, 3186758235, 3429571005, 3777587235, 3998199285, 3999831327, 4131747417, 4232710317
236666	P.Kenny	2005-01-06	13	500k?-2.5M?	603557, 745791, 873705, 914271, 929841, 1020317, 1318563, 1431027, 1750085, 2095583, 2272991, 2342397, 2432757
201024	T.Ritschel	2005-07-29	69	10.0M?	8729, (...)
100000	D.Stevens	2009-03-19	17	1.0M	62967, 192797, 230753, 237123, 237915, 323169, 420147, 422427, 537243, 548249, 581159, 594387, 640293, 654827, 835955, 914187, 944007
86243 (28th Mers.)	L.Zhou	2009-05-30	1606	100M	(available on request)
44497 (27th Mers.)	L.Zhou	2009-05-30	3162	100M	(available on request)
23209 (26th Mers.)	L.Zhou	2009-05-30	6303	100M	(available on request)
21701 (25th Mers.)	L.Zhou	2009-05-30	6703	100M	(available on request)
19937 (24th Mers.)	L.Zhou	2009-05-30	7131	100M	(available on request)
11213 (23th Mers.)	L.Zhou	2009-05-30	12830	100M	(available on request)
9941 (22th Mers.)	L.Zhou	2009-05-30	14468	100M	(available on request)
9689 (21th Mers.)	L.Zhou	2009-05-30	14925	100M	(available on request)
4423 (20th Mers.)	L.Zhou	2009-05-30	32240	100M	(available on request)
4253 (19th Mers.)	L.Zhou	2009-05-30	33786	100M	(available on request)
3217 (18th Mers.)	L.Zhou	2009-05-30	44439	100M	(available on request)
2281 (17th Mers.)	L.Zhou	2009-05-30	62253	100M	(available on request)
2203 (16th Mers.)	L.Zhou	2009-05-30	64658	100M	(available on request)
1279 (15th Mers.)	L.Zhou	2009-05-30	110508	100M	(available on request)
607 (14th Mers.)	L.Zhou	2009-05-30	228744	100M	(available on request)
521 (13th Mers.)	L.Zhou	2009-05-30	264083	100M	(available on request)
127 (12th Mers.)	L.Zhou	2009-05-30	948453	100M	(available on request)
107 (11th Mers.)	L.Zhou	2009-05-30	1090723	100M	(available on request)
89 (10th Mers.)	L.Zhou	2009-05-30	1265601	100M	(available on request)
61 (9th Mers.)	L.Zhou	2009-05-30	1676264	100M	(available on request)

Summary of Constant-n Searches (k · 2n - 1 prime)

Summary of Constant-n Searches (k · 2ⁿ - 1 prime)