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 TTn 2003-06-05 19:48

[SIZE=6]Updated list at [url]http://www.15k.org/homecandidate.htm[/url][/SIZE]

We will leave this list here for the forum search function.

[size=18][color=green]15k*2^n -1 is frequently prime n, for values 15k: [/color][/size]
Payam#k [b]w=weight/nash weight[/b] (reserved or tested)prover code

15k = 2889081195, w = 4.16/7261(reserved by Lars D.)
15k = 3428677395, w = 4.06/7102
15k = 1650292215, w = 4.04/7057(reserved b Luigi)
15k = 4142541975, w = 4.03/7066(reserved by Thomas R.)
15k = 3611911875, w = 4.03/7048(reserved by Kosmaj)
15k = 1748348745, w = 4.00/7006(reserved by James)
15k = 413468055, w = 3.99/6982(155000)L9
15k = 1019370495, w = 3.98/6959(reserved by wpolly)
15k = 1880720985, w = 3.97/6974(250000)
15k = 387376275, w = 3.97/6970(250000)
15k = 1014793065, w = 3.97/6967(reserved by James)
15k = 115029915, w = 3.97/6966 (reserved by Kosmaj)
15k = 290499495, w = 3.97/6961
15k = 1581823815, w = 3.97/6954(L83 has a prime for n=846116)
15k = 464857965, w = 3.95/6936
15k = 244716615, w = 3.94/6887(L9 has a prime for this 15k at n=136894)
15k = 4075360575, w = 3.93/6864(reserved by CedricVonck)
15k = 245630385, w = 3.91/6864(reserved by Larry)
15k = 775784295, w = 3.91/6832(L26 has a prime for this 15k at n=137131)
15k = 666625245, w = 3.90/6829(Reserved by Mark)
15k = 97102005, w = 3.90/6829(145000)L9
15k = 2809771965, w =3.88/6804(reserved by Thomas R. )
15k = 736320585, w = 3.88/6793(reserved by Cruelty)
15k = 869688105, w = 3.87/6779(reserved by Amphoria)
15k = 504017085, w = 3.87/6784(250000)
15k = 959657985, w = 3.85/59 66(155000)
15k = 404643525, w = 3.84/6716
15k = 949473525, w = 3.82 64 67(reserved by Antiroach)
15k = 509070705, w = 3.82/6701(L8 has a prime for this 15k at n=174286)
15k = 190053435, w = 3.82/6694(reserved by James)
15k = 1803385155, w : 3.81/6667(reserved by James)
15k = 2175868695, w : 3.81/6674
15k = 54896985, w = 3.80/6669(reserved by James)
15k = 187466565, w = 3.79/6659(reserved by gribozavr)
15k = 954218265, w = 3.78/6616
15k = 825273735, w = 3.78/6616
15k = 8311875, w = 3.77/6584(215000 already tested by g73)
15k = 868409685, w = 3.76/6608(reserved by Thomas W.)
15k = 515106735, w = 3.76/6583
15k = 794977755, w = 3.75/6576
15k = 10474035, w = 3.74/6554(reserved by James)
15k = 518066835, w = 3.74/6553(250000)
15k = 810151485, w = 3.73/6520(250000)
15k = 954977595, w = 3.69 50 61(reserved by Lars D.)
15k = 904522905, w = 3.68/6440(290000)
15k = 978847155, w = 3.68/6471(L58 has a prime at n=211221)
15k = 968186505, w = 3.68/6459
15k = 1973886915, w = 3.68/6438
15k = 860541825, w = 3.67/6429
15k = 14549535, w = 3.66/6416(reserved by levitate)
15k = 99311355, w = 3.66/6424(reserved by James)
15k = 985389405, w = 3.66/6424(L104 has a prime at n=348347)
15k = 995887035, w = 3.63/6362(L58 has a prime at n=217131)
15k = 891103785, w = 3.63/6365(L27 has a prime at n=228056)
15k = 973197225, w = 3.62/6347(250k)
15k = 2305225065, w = 3.61/6336(200k)
15k = 854917635, w = 3.61/6331(263K Reserved by Mark)
15k = 853836555, w = 3.60/6317(Reserved by Mark)
15k = 801095295, w = 3.60/6330(Reserved by Mark)
15k = 957761805, w = 3.59/6293(Reserved by Mark)
15k = 391533285, w = 3.47/6081(Reserved by Mark)
15k = 786775275, w = 3.45/6060(Reserved by Mark)
15k = 706427865, w = 3.44/6010(Reserved by Mark)
15k = 316299555, w = 3.42/6018(Reserved by Mark)
15k = 627830775, w = 3.40/5936(250000)
15k = 621472995, w = 3.40/5975
15k = 597590565, w = 3.40/5961(L40 has a prime at n=206106)
15k = 373065, w = 3.37/5933(Reserved by James)
15k = 957860475 w = 3.36/5898(Reserved by James)
15k = 997867365, w = 3.55/6235
15k = 998895645, w = 3.50/6134(L40 has a prime at n=218527)
15k = 994508625, w = 3.47/6083(L40 has a prime at n=200033)
15k = 995233965, w = 3.44/6030(L40 has a prime at n=218448)
15k = 999096285, w = 3.40/5970(L40 has a prime at n=215410)
15k = 890505, w = 3.35/5858(reserved by Lars D.)
15k = 1105845, w = 3.28/5772(reserved by James)
15k = 906015, w = 3.26/5705(reserved by James)
15k = 405405, w =3.23/5686(reserved by Harsh A.)
15k = 868409685

Here are some untested 2805k, I recommend first testing all 15k up to n=5000, to make sure you find at least 50 primes, otherwise you may try another one. I've noted those k's which have primes on the top-5000 list
as of Oct 1, 2005.

np = Number of primes for the range n=0-10k.

15k : 13236795, w : 3.71(reserved by CedricVonck)
15k : 18487755, w : 3.64, np : 55
15k : 39547695, w : 3.69, np : 74
15k : 39418665, w : 3.64, np : 74
15k : 51003315, w : 3.71, np : 66
15k : 55951335, w : 3.65, np : 73 (reserved by grobie)
15k : 60714225, w : 3.62, np : 68
15k : 78290355, w : 3.60, np : 77
15k : 84854055, w : 3.62, np : 59
15k : 93532725, w : 3.64, np : 63 (g96 has a prime at 24k)
15k : 118547715, w : 3.67, np : 54
15k : 136151895, w : 3.62, np : 69
15k : 146261115, w : 3.66, np : 60
15k : 153784125, w : 3.67(reserved by lalera)
15k : 165054615, w : 3.60, np : 82 (250k)
15k : 166900305, w : 3.68, np : 60
15k : 168196215, w : 3.64, np : 75
15k : 187466565, w : 3.79, np : 56
15k : 190383765, w : 3.61, np : 73
15k : 205917855, w : 3.65, np : 64
15k : 208391865, w : 3.61, np : 67
15k : 210001935, w : 3.63, np : 55
15k : 228986175, w : 3.63, np : 75
15k : 240924255, w : 3.64, np : 71
15k : 244133175, w : 3.67, np : 76
15k : 244716615, w : 3.94 (L92 has a prime at n=216352)
15k : 252884775, w : 3.70, np : 64
15k : 271044345, w : 3.79(reserved by masser)
15k : 286578435, w : 3.63, np : 59
15k : 326325285, w : 3.66, np : 68
15k : 334639305, w : 3.63, np : 60 (g100 has a prime at n=91802)
15k : 355424355, w : 3.82 (reserved by the 15k team)
15k : 428062635, w : 3.67, np : 54
15k : 428573145, w : 3.66, np : 59
15k : 445419975, w : 3.65, np : 80 (reserved by Kosmaj)
15k : 451035585, w : 3.81, np : 66
15k : 475977645, w : 3.88, np : 62 (g78 has a prime at n=44640)
15k : 483124785, w : 3.64, np : 59
15k : 487281795, w : 3.60, np : 56
15k : 490271925, w : 3.71, np : 55
15k : 506036025, w : 3.75, np : 61
15k : 511090635, w : 3.61, np : 58
15k : 563701215, w : 3.60, np : 61
15k : 576312495, w : 3.62, np : 65
15k : 576839835, w : 3.74, np : 71
15k : 603885645, w : 3.68, np: 65
15k : 623442105, w : 3.66 (L40 has a prime at n=278654)
15k : 637220265, w : 3.62, np: 56
15k : 640872375, w : 3.70 (reserved by lalera)
15k : 646269195, w : 3.72(L20 has a prime at n=136630)
15k : 669545085, w : 3.60, np: 69
15k : 698632935, w : 3.67, np: 71
15k : 700383255, w : 3.63, np: 49
15k : 720708285, w : 3.60 , np: 58
15k : 721774185, w : 3.84 (L26 has a prime at n=176398)
15k : 736354575, w : 3.63, np: 63
15k : 743922465, w : 3.76, np: 62
15k : 744797625, w : 3.74, np: 62,
15k : 745818645, w : 3.70, np: 59
15k : 765414375, w : 3.80, np: 68
15k : 795085665, w : 3.60, np: 60
15k : 828010755, w : 3.64, np: 47
15k : 857996205, w : 3.67, np: 76
15k : 905215575, w : 3.62, np: 52
15k : 931863075, w : 3.69, np: 67
15k : 944984865, w : 3.63, np: 63
15k : 965337945, w : 3.60, np: 63
15k : 968911515, w : 3.70, np: 66
15k : 974392485, w : 3.67, np: 65
15k : 984008025, w : 3.63, np: 65
2145k
15k : 511893525, w : 3.62, np: 57
15k : 515179665, w : 3.64, np: 69
15k : 516080565, w : 3.60, np: 63
15k : 524857905, w : 3.68, np: 52
15k : 525359835, w : 3.63, np: 57
15k : 528229845, w : 3.60, np: 64
15k : 528980595, w : 3.61, np: 65
15k : 531803415, w : 3.65, np: 62
15k : 533026065, w : 3.66, np: 59
15k : 538169775, w : 3.66, np: 62
15k : 541546005, w : 3.63, np: 58
15k : 545544285, w : 3.60, np: 83 (reserved by Larry)
15k : 552193785, w : 3.61, np: 67
15k : 553956975, w : 3.65, np: 54
15k : 563948385, w : 3.66, np: 59 (g96 has a prime at n=24335)
15k : 565908915, w : 3.65, np: 52
15k : 565964685, w : 3.61, np: 71
15k : 576659655, w : 3.63, np: 53
15k : 577551975, w : 3.60, np: 73
15k : 584222925, w : 3.65, np: 69
15k : 586239225, w : 3.62, np: 59
15k : 586839825, w : 3.69, np: 56
15k : 587650635, w : 3.68, np: 74
15k : 576771195, w : 3.60, np: 66
15k : 595213905, w : 3.65, np: 69
15k : 613806765, w : 3.60 (prime at n=222487)
15k : 616385055, w : 3.60 (prime at n=264520)
15k : 617178705, w : 3.64 (prime at n=292998)
15k : 623442105, w : 3.66 (prime at n=278654)
15k : 625394055, w : 3.62 (prime at n=237601)
15k : 626157675, w : 3.61 (prime at n=294055)
15k : 636951315, w : 3.68 (prime at n=296737)
15k : 641494425, w : 3.69 (prime at n=280755)
15k : 648452805, w : 3.63 (prime at n=212227)
15k : 649023375, w : 3.66 (prime at n=295010)
15k : 688366965, w : 3.66 (prime at n=228788)
15k : 691490085, w : 3.66 (Lprime at n=281288)
15k : 725196615, w : 3.68 (prime at n=276377)
15k : 778049415, w : 3.62 (prime at n=276160)
15k : 770464695, w : 3.63 (prime at n=291529)
15k : 775393905, w : 3.62 (prime at n=296576)
15k : 757980795, w : 3.63 (prime at n=280165)
15k : 763094475, w : 3.66 (prime at n=426143)
15k : 742837095, w : 3.67
15k : 692305185, w : 3.65 (prime at n=282552)
15k : 698632935, w : 3.67, np: 71
15k : 16291275, w : 3.61(reserved by wpolly)
(top bound of 15k = 4294967295):banana:

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To reserve it, just post it, including your name or screen name in the
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