PRP Records

Probable Primes Top 10000

(168024 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 20000) Who ? When ?
1(2^13372531+1)/34025533Ryan Propper09/2013
2(2^13347311+1)/34017941Ryan Propper09/2013
32^9092392+402912737083Engracio Esmenda / Five or Bust02/2011
4(2^5240707-1)/753928109031577600Tony Prest / Never Odd Or Even07/2016
52^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
62^4583176+21311379674Ben Maloney / Five or Bust09/2009
7(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
8(13^1199467+1)/141336138Paul Bourdelais12/2015
9(2^4187251-1)/722343423715191260475Tony Prest / Never Odd Or Even05/2016
10(14^1091401+1)/151250885Paul Bourdelais03/2014
11(16^1025393+1)/171234695Paul Bourdelais08/2014
12(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
13(106*23^800873-7)/111090573Curtis Bright05/2015
14(7^1264699-1)/61068794Paul Bourdelais01/2014
15(2^3464473-1)/6048745082991771042896Anand Nair10/2014
1610^999999+5934991000000Peter Kaiser02/2013
172^2976221+2041857895932Makoto Morimoto09/2014
18(12^769543-1)/11830476Paul Bourdelais12/2014
19(64*10^779465-1)/81779465Serge Batalov09/2014
20(64*10^762811-1)/9762812Serge Batalov09/2014
21(10^718580+269)/9718580Serge Batalov12/2014
22(2^2327417-1)/23915387348002001700606Anand Nair08/2014
23(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
24(10^685224+89)/9685224Serge Batalov12/2014
252^2249255+28433677094Ben Maloney / Five or Bust01/2009
26(10^675470+269)/9675470Serge Batalov12/2014
27(9^703393+1)/10671207Paul Bourdelais08/2015
28(15^551927+1)/16649116Paul Bourdelais07/2013
29(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
30Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
31(51*21^479149-1243)/4633542Curtis Bright11/2015
32Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
33(20^472709-1)/19615008Paul Bourdelais01/2015
34PIPrime(613373)613373Adrian Bondrescu05/2016
35(19^476929+1)/20609874Paul Bourdelais03/2015
36F(2904353)606974Henri Lifchitz07/2014
37(18^481147+1)/19603970Paul Bourdelais07/2011
38(15^505117-1)/14594063Paul Bourdelais01/2015
39(152^270217-1)/(152-1)589570Michael Stocker06/2015
40(3^1205459+1)/4575150Paul Bourdelais08/2015
41(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
428^615997-7^615997556301Jean-Louis Charton07/2009
43Tau(773^34960)555339Nik Lygeros / Olivier Rozier09/2015
44((((((((((1361^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840)^3+1623568555154Serge Batalov08/2013
45(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
46(18^414269-1)/17520020Paul Bourdelais12/2014
47(20^393257+1)/21511638Paul Bourdelais12/2014
48(14^441697-1)/13506241Paul Bourdelais12/2014
493^1059503-2^1059503505512Mike Oakes04/2012
50(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
51(64*10^499210+53)/9499211Serge Batalov03/2015
52Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
53(2^1572882+5)/3473485Serge Batalov08/2015
54(6^608099-1)/5473193Paul Bourdelais05/2010
552^1518191+75353457022Ben Maloney / Five or Bust01/2009
56(21^328129-1)/20433858Paul Bourdelais06/2014
57(17^348259+1)/18428514Paul Bourdelais05/2014
58(10^427912+89)/9427912Serge Batalov12/2014
59(10^424861-7)/3424861Leonid Durman01/2012
60138^196873-137^196873421285Jean-Louis Charton12/2009
612^1398269+131595420921Makoto Morimoto10/2013
62(3^877843-1)/2418838Paul Bourdelais07/2010
63(89*10^411590+1)/9411591Serge Batalov09/2014
64F(1968721)411439Henri Lifchitz11/2009
65(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
66Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
67(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
6815^328574+328574^15386434Serge Batalov05/2014
69(10^380976-7)/3380976Leonid Durman01/2012
702^1257787+1447761378632Makoto Morimoto10/2013
71F(1803059)376817Henri Lifchitz06/2009
723^761457-2363308Ryan Propper07/2015
73(64*10^360173-1)/243360173Serge Batalov09/2014
742^1191375+8543358640Phil Moore06/2008
75(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
76(10^352237-1)/90380699499072573352221Robert Price07/2016
77(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
78(7*10^348724-61)/9348724Erik Branger09/2016
79(127^165601-1)/126348390Alexander Zhirkov09/2015
80(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
812^1145882+80779344945Enzo Doria09/2016
82F(1636007)341905Henri Lifchitz03/2009
83(11^327001+1)/12340536Paul Bourdelais09/2013
84(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
85Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
86(3^700897+1)/4334413Paul Bourdelais04/2010
872^1104408-114539332460Enzo Doria03/2015
88(10^330906+71)/9330906Serge Batalov07/2015
892^1095679+1878713329833Enzo Doria09/2016
902^1094740-1851539329550Enzo Doria08/2015
912^1091469-379369328565Enzo Doria03/2014
922^1072118-7321953322740Enzo Doria02/2015
932^1069293-1147195321890Enzo Doria05/2015
942^1065897-1147195320867Enzo Doria05/2015
952^1061095-1061095319422Henri Lifchitz10/2013
962^1052186-458165316740Enzo Doria03/2015
972^1046613-114685315062Enzo Doria04/2015
982^1045625-459373314765Enzo Doria06/2015
99(7*10^314564-61)/9314564Erik Branger09/2016
100(7^371669-1)/6314096Paul Bourdelais02/2010
1012^1041153-114391313419Enzo Doria02/2015
1022^1038871+1866983312732Enzo Doria04/2016
1032^1036867+1865843312129Enzo Doria02/2016
1042^1036020-114539311874Enzo Doria02/2015
1052^1030352+1870021310167Enzo Doria06/2016
106(11^293831-1)/10305993Paul Bourdelais03/2010
1072^1015321-1015321305643Henri Lifchitz08/2013
1082^1014224-2791229305312Enzo Doria01/2016
1092^1010751-107709304267Enzo Doria03/2014
110(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
1112^1009577+1869587303913Enzo Doria06/2016
1128^336419-7^336419303817Jean-Louis Charton01/2008
1132^1008301+1869377303529Enzo Doria06/2016
114(2^1007838+5)/3303389Serge Batalov08/2015
1152^1004929+1877567302514Enzo Doria08/2016
1162^1003494+1874899302082Enzo Doria06/2016
1172^1003046+60529301947Enzo Doria04/2016
1182^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
1192^999646+1874029300924Enzo Doria06/2016
12010^300476+3300477Ed Trice10/2012
12110^300476-530913300476Patrick De Geest03/2016
1222^998053+1879667300444Enzo Doria09/2016
123314738^9+9^314738300337Anatoly F. Selevich02/2011
1247^355039-6^355039300043Jean-Louis Charton05/2011
1252^996182-114431299881Enzo Doria02/2015
1262^995214-2788361299590Enzo Doria12/2015
1272^994791-114319299462Enzo Doria01/2015
1282^994490-1863791299372Enzo Doria01/2016
1292^992711-2788807298836Enzo Doria12/2015
1302^992525-114199298780Enzo Doria12/2014
131(2^986191+1)/3296873Vincent Diepeveen06/2008
1322^985217-114553296580Enzo Doria03/2015
1332^984131-1828009296253Enzo Doria01/2015
1342^983620+60451296100Phil Moore03/2008
1352^982721-2683295829Yves Minet02/2016
1362^981298-2788421295401Enzo Doria12/2015
1372^981163-2790967295360Enzo Doria12/2015
1382^979594+1865839294888Enzo Doria02/2016
1392^974441+1878407293336Enzo Doria08/2016
1402^974180+1876831293258Enzo Doria07/2016
1412^972744-114419292826Enzo Doria03/2015
142CopelandErdos(292447)292447Mark Rodenkirch12/2015
1432^970911+1873373292274Enzo Doria07/2016
1442^970141-100363292042Enzo Doria02/2014
1452^969945+1874717291983Enzo Doria06/2016
1462^962194+60139289650Enzo Doria02/2016
1472^959307-1861507288781Enzo Doria11/2015
1482^957192-1864049288144Enzo Doria01/2016
1492^956446+1875199287919Enzo Doria06/2016
150(17^233689+1)/18287542Paul Bourdelais09/2013
1512^954001+1875257287183Enzo Doria07/2016
1522^952268+1878601286662Enzo Doria09/2016
1532^950801+81557286220Enzo Doria08/2016
154(11*2^948635-13)/15285568Renaud Lifchitz11/2011
1552^948374-114137285490Enzo Doria01/2015
1562^947739+1872923285298Enzo Doria06/2016
1572^942533+82067283731Enzo Doria09/2016
1582^940950+1874989283255Enzo Doria06/2016
1592^940426-2786141283097Enzo Doria11/2015
1602^939881-114115282933Enzo Doria12/2014
16110^282493-9^282493282493Jean-Louis Charton03/2007
1623^591827-2^591827282374Mike Oakes08/2009
163Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
1642^936716-1835519281980Enzo Doria04/2015
1652^936588+79411281942Enzo Doria06/2016
1662^936047+1877423281779Enzo Doria08/2016
1672^935713+1869377281678Enzo Doria05/2016
1682^933082+1877059280886Enzo Doria08/2016
169(5*10^280710+1)/3280711Serge Batalov10/2014
170(10^279978+11)/3279978Serge Batalov07/2015
1712^929524-1864829279815Enzo Doria01/2016
1722^929152+60181279703Enzo Doria02/2016
1732^928621-2787883279543Enzo Doria11/2015
1742^925330-1301278553Yves Minet06/2015
175(21^210599+1)/22278457Paul Bourdelais08/2013
1762^923261-69175277930Enzo Doria11/2015
177757^96487-756^96487277796Jean-Louis Charton12/2012
178((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
179(5^396413-1)/4277081Paul Bourdelais06/2010
1802^920318+2792299277044Enzo Doria02/2016
1812^918596-2786939276525Enzo Doria11/2015
1822^916639+60563275936Enzo Doria04/2016
1832^916385-2786383275860Enzo Doria11/2015
1842^915928+82081275722Enzo Doria09/2016
1852^915576-114137275616Enzo Doria01/2015
1862^914828+1876741275391Enzo Doria07/2016
1872^914757-2203275370Yves Minet12/2015
1882^911900+1871245274510Enzo Doria05/2016
1892^909988-1862249273934Enzo Doria12/2015
1902^909297+1879157273726Enzo Doria08/2016
1912^909257-1864423273714Enzo Doria01/2016
1922^908579-1861747273510Enzo Doria12/2015
1932^907635-2791597273226Enzo Doria01/2016
1942^906594-113201272912Enzo Doria08/2014
1952^904773+1872167272364Enzo Doria06/2016
1962^904149-1862473272176Enzo Doria12/2015
197(7*10^271757-61)/9271757Erik Branger03/2012
1982^902497+1880117271679Enzo Doria09/2016
1992^901858+77689271487Enzo Doria06/2016
2002^901372+1875301271341Enzo Doria06/2016
2012^899121-115033270663Enzo Doria07/2015
2022^898762-251511270555Enzo Doria12/2013
2032^898589+47270503Lelio R Paula03/2016
204187322*10^270343-187321270349Danilo Nitsche09/2013
20548358*10^270343-48357270348Danilo Nitsche09/2013
206(10^270343-1)/9270343Maksym Voznyy07/2007
2072^897849-115273270280Enzo Doria07/2015
2082^896616-114179269909Enzo Doria12/2014
2092^894673-39343269324Enzo Doria08/2015
210F(1285607)268676Henri Lifchitz11/2008
2112^892112+187663268553Enzo Doria08/2016
212(10^268207+1)/11268206Paul Bourdelais02/2010
2132^890957-69583268205Enzo Doria12/2015
2142^890122-351401267954Enzo Doria07/2015
215(19^209359-1)/18267718Paul Bourdelais08/2010
2162^886324+77791266811Enzo Doria06/2016
21711^255426+255426^11265999Serge Batalov05/2014
2182^883462-343421265949Enzo Doria07/2015
2192^883442+1875019265943Enzo Doria06/2016
2202^883333-291583265910Enzo Doria07/2015
2212^879530-2788031264765Enzo Doria12/2015
2222^878118+2793079264340Enzo Doria02/2016
2232^875748-461129263627Enzo Doria07/2015
2242^875181-2789923263456Enzo Doria12/2015
2252^875101-350083263432Enzo Doria08/2015
2262^874616+1872211263286Enzo Doria05/2016
2272^874073+2792957263123Enzo Doria02/2016
2282^873628+1878751262989Enzo Doria08/2016
2292^873288-269262886Yves Minet01/2015
2302^871146-3173262242Yves Minet07/2016
2312^869601-163261776Yves Minet01/2015
2322^869035-114181261606Enzo Doria12/2014
2332^865715+80303260607Enzo Doria07/2016
2342^864899-113871260361Enzo Doria10/2014
235(7*10^260198-61)/9260198Erik Branger11/2011
2362^864298-2788421260180Enzo Doria12/2015
2372^864039-2791357260102Enzo Doria01/2016
2382^863621-113833259976Enzo Doria10/2014
2392^862837+75767259740Enzo Doria05/2016
2402^862088+1874941259515Enzo Doria06/2016
2412^861516-1854029259343Enzo Doria09/2015
2422^860975-1853977259180Enzo Doria09/2015
2432^860625-1858843259074Enzo Doria10/2015
2442^860110+77689258919Enzo Doria05/2016
2452^859433+494711258716Makoto Morimoto10/2013
2462^859240+1875271258658Enzo Doria06/2016
247Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
248(11*2^857159-13)/15258031Renaud Lifchitz08/2011
2492^857016-633113257988Enzo Doria12/2013
2502^855732-113969257602Enzo Doria10/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2016 23:13 (Time in France)

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