PRP Records

Probable Primes Top 10000

(252402 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 (> 50000) Who ? When ?
5012^814276-459029245122Enzo Doria04/2015
5022^814023+180923245046Enzo Doria07/2016
503(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
5042^811842-113675244389Enzo Doria09/2014
5052^811132-2787929244176Enzo Doria11/2015
5062^809746-2790971243758Enzo Doria01/2016
5072^808767-3295243464Yves Minet12/2016
5082^808621-113809243420Enzo Doria09/2014
5092^807724+1879621243150Enzo Doria09/2016
5102^805843-113611242583Enzo Doria08/2014
5112^805745-459763242554Enzo Doria05/2015
5122^805353+782687242436Enzo Doria11/2016
5132^804277-417933242112Enzo Doria01/2014
5142^803468-269039241868Enzo Doria10/2013
5152^803172+80851241779Enzo Doria07/2016
5163^506233-2241535Robert Price11/2013
5172^802025-25999241434Enzo Doria10/2013
518(3^505823+3^252912+1)/7241339Serge Batalov03/2014
5192^801303+1872923241217Enzo Doria05/2016
5202^800579-1862947240999Enzo Doria12/2015
5213^504206+2240568Luke W. Richards03/2018
5222^798973-26283240515Enzo Doria10/2013
5232^798671-69487240424Enzo Doria12/2015
5242^797220+79831239988Enzo Doria06/2016
5252^796910-26001239894Enzo Doria10/2013
5262^796598+653119239800Enzo Doria12/2016
5272^796432-1859729239750Enzo Doria11/2015
5282^796002-1852211239621Enzo Doria08/2015
5292^795709+75767239533Enzo Doria04/2016
5302^795708+81721239532Enzo Doria08/2016
5312^795468-2786249239460Enzo Doria10/2015
5322^795442+80779239452Enzo Doria07/2016
5332^795075-1852057239342Enzo Doria08/2015
5342^794043+1875023239031Enzo Doria06/2016
5352^793347-69577238822Enzo Doria01/2016
5362^792988-344429238714Enzo Doria08/2015
5372^792700-2786369238627Enzo Doria11/2015
5382^792663-1844797238616Enzo Doria06/2015
5392^792605-291943238598Enzo Doria07/2015
540(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
5412^789373+1869377237625Enzo Doria05/2016
542((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
5432^788942+1866409237496Enzo Doria02/2016
5442^788844-114329237466Enzo Doria01/2015
5452^788705-1859713237424Enzo Doria11/2015
5462^786180+1871971236664Enzo Doria05/2016
54711^227092-90236492Enzo Doria11/2012
5482^785260+1866361236387Enzo Doria02/2016
5492^785220+1880611236375Enzo Doria10/2016
55019^184650-2236122Robert Price10/2014
55110^236059+216513236060Patrick De Geest04/2016
55210^236059-20909236059Robert Price09/2015
5532^782634-113981235597Enzo Doria11/2014
5542^782423+1879733235533Enzo Doria09/2016
5552^781682-2789543235310Enzo Doria12/2015
5562^780408-113453234927Enzo Doria08/2014
5572^780368-1864829234915Enzo Doria01/2016
5582^779593-1836559234681Enzo Doria05/2015
559(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
560(5^335429+1)/6234455Paul Bourdelais08/2010
5612^778395-113617234321Enzo Doria08/2014
5622^776245-2792353233674Enzo Doria02/2016
5632^776060-114029233618Enzo Doria11/2014
5642^775987-2789557233596Enzo Doria12/2015
5652^775672+1866721233501Enzo Doria03/2016
566(11^223999+1)/12233270Paul Bourdelais02/2010
5672^774118+1885789233033Enzo Doria04/2017
56821^176191-20^176191232964Jean-Louis Charton01/2015
5692^773679-113425232901Enzo Doria08/2014
57010^232599+192489232600Patrick De Geest12/2013
57110^232599-3232599Markus Tervooren10/2010
5722^772552-458879232562Enzo Doria04/2015
5732^772214+1874899232460Enzo Doria06/2016
5742^771994-1862771232394Enzo Doria12/2015
5752^771889+1876037232362Enzo Doria07/2016
5762^771660+1866511232293Enzo Doria02/2016
5775^332150-18188232163Enzo Doria06/2014
5783^485977-2^485977231870Mike Oakes09/2009
5792^770082-114161231818Enzo Doria01/2015
580(20^177967+1)/21231540Paul Bourdelais05/2013
5812^767622-9221231078Lelio R Paula01/2016
5822^767344+1880311230994Enzo Doria09/2016
583(3^483611-1)/2230741Paul Bourdelais02/2010
584(10^230706+179)/9230706Serge Batalov12/2014
5852^766309+1875257230682Enzo Doria06/2016
5862^765635+1879883230480Enzo Doria09/2016
5872^764348-113697230092Enzo Doria09/2014
5882^764131+78863230027Enzo Doria05/2016
5892^763701+60197229897Enzo Doria03/2016
5902^762841-25905229639Enzo Doria10/2013
5912^761117-113569229120Enzo Doria08/2014
592(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
5932^757985-2790013228177Enzo Doria12/2015
5942^757038-1862081227892Enzo Doria12/2015
5952^756839+95849227832Makoto Morimoto10/2013
596(2^756839+6989)/756091227826Makoto Morimoto09/2016
5972^756773-112723227812Enzo Doria07/2014
598524309#+616367227431Makoto Morimoto02/2016
5992^755097-114193227307Enzo Doria12/2014
6002^754473-2791513227120Enzo Doria01/2016
6012^751426-764321226202Enzo Doria12/2013
602(18^180181-1)/17226176Andy Steward04/2007
6032^750740-3225996Paul Bourdelais03/2012
6042^750725+60227225991Enzo Doria02/2016
6052^750525-113743225931Enzo Doria09/2014
606(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
6072^749444-1861889225606Enzo Doria12/2015
608tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
6092^749096+1876861225501Enzo Doria07/2016
6102^748657+79607225369Enzo Doria06/2016
6112^746653-291583224765Enzo Doria07/2015
6122^746461-114043224708Enzo Doria11/2014
6132^745098-350471224297Enzo Doria06/2015
614(154*10^224061-1)/9224063Serge Batalov12/2014
6152^744211-1845787224030Enzo Doria07/2015
6162^743592-134579223844Hans Havermann10/2018
617234178^9+9^234178223463Anatoly F. Selevich07/2011
6182^741651-461197223260Enzo Doria07/2015
6192^741362-1845251223173Enzo Doria07/2015
6202^740455-1863877222900Enzo Doria12/2015
6212^739636-2792219222653Enzo Doria02/2016
62211^213654-180222498Enzo Doria01/2013
6232^738957-1859743222449Enzo Doria11/2015
624(54^128189+1)/55222073Paul Bourdelais11/2018
625(10^221654+179)/9221654Serge Batalov12/2014
6262^736281+79817221643Enzo Doria06/2016
62710^221631+247617221632Patrick De Geest10/2013
62810^221631-9221631Alexander Gramolin02/2011
6292^735970-1839821221550Enzo Doria06/2015
6302^735367+60293221368Enzo Doria03/2016
631(29^151153+1)/30221045Paul Bourdelais09/2017
6322^733264-2784089220735Enzo Doria10/2015
6332^733114-24555220690Enzo Doria09/2013
6342^731891-636259220322Enzo Doria12/2013
6352^731124-25539220091Enzo Doria09/2013
6362^730972-462029220045Enzo Doria07/2015
6372^730833+1868627220003Enzo Doria04/2016
6382^730645-2787133219947Enzo Doria11/2015
6392^730547-25581219917Enzo Doria09/2013
6402^730460+82291219891Enzo Doria09/2016
641(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
642L(1051849)219824Renaud Lifchitz03/2009
64311^210961-240219694Enzo Doria01/2013
6442^729611-113437219635Enzo Doria08/2014
645F(1049897)219416Henri Lifchitz10/2008
6462^728604+1879321219332Enzo Doria10/2016
64733^144412+2219292Robert Price04/2015
6482^728277-183313219234Hans Havermann10/2018
6492^727998-1862711219150Enzo Doria12/2015
6502^727729-114073219069Enzo Doria12/2014
6512^727496-1851809218999Enzo Doria08/2015
6522^726591+2793143218726Enzo Doria02/2016
6532^725534-2791931218408Enzo Doria02/2016
6542^722184+1877821217400Enzo Doria08/2016
655(109*10^217360-1)/9217362Serge Batalov12/2014
656281*499979#/46410-2702372216849Robert Smith08/2016
657281*499979#/46410+2400766216849Robert Smith08/2016
658tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
6592^718756-114107216368Enzo Doria12/2014
6602^717305+80327215931Enzo Doria07/2016
6612^717069-59773215860Enzo Doria10/2015
66230^146021-29^146021215691Jean-Louis Charton09/2018
663277^88301-276^88301215674Jean-Louis Charton06/2012
664227^91413-40215372Enzo Doria04/2015
6652^714717+782897215152Enzo Doria11/2016
666tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
6672^713241+1879157214707Enzo Doria08/2016
66811^206081-10^206081214612Jean-Louis Charton10/2011
6692^712801-69553214575Enzo Doria01/2016
6702^712603-25357214515Enzo Doria09/2013
6712^711721-1846723214250Enzo Doria07/2015
6722^710730-396765213952Enzo Doria09/2013
6732^708468-114329213271Enzo Doria02/2015
674(163*10^212779-1)/9212781Serge Batalov12/2014
6752^706838-69041212780Enzo Doria11/2015
6762^704577-113871212099Enzo Doria10/2014
6772^704110-2792441211959Enzo Doria02/2016
6782^703943-1862947211908Enzo Doria12/2015
679(60^119083+1)/61211746Paul Bourdelais10/2018
680(10^211610-91)/9211610Serge Batalov12/2014
681227^89797+2211565Lelio R Paula08/2012
6822^702194-3211382Paul Bourdelais03/2012
6832^702064+1874911211343Enzo Doria07/2016
6842^701968-113873211314Enzo Doria10/2014
6852^701713-113779211237Enzo Doria09/2014
6862^701449-25201211158Enzo Doria09/2013
6872^701403-2786977211144Enzo Doria11/2015
6882^701189-25423211079Enzo Doria09/2013
6892^701162-459161211071Enzo Doria05/2015
690(24^152783-1)/23210872Paul Bourdelais04/2018
6912^700400+9385210842Lelio R Paula01/2014
6922^700131+1874693210761Enzo Doria06/2016
69311^202357-1140210734Enzo Doria12/2012
6942^698929-2788423210399Enzo Doria11/2015
695(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
6962^698316+1878601210215Enzo Doria08/2016
6972^697036+1878751209829Enzo Doria08/2016
698(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
6992^696254-115151209594Enzo Doria06/2015
700(35^135623+1)/36209410Paul Bourdelais07/2018
7012^694633+1887257209106Enzo Doria05/2017
7022^693959+180923208903Enzo Doria07/2016
7032^693462-1847561208753Enzo Doria07/2015
7042^690890-59981207979Enzo Doria11/2015
705(38^131591+1)/39207884Paul Bourdelais07/2018
7062^690163+1877063207760Enzo Doria07/2016
7072^689286-29381207496Enzo Doria08/2015
7082^689122-114521207447Enzo Doria04/2015
7092^688373+6077207221Enzo Doria02/2016
7102^688201+1875527207170Enzo Doria07/2016
711(42^127609+1)/43207140Paul Bourdelais07/2018
7122^687619+81563206994Enzo Doria08/2016
7132^686572-1845299206679Enzo Doria07/2015
714(21^156217-1)/20206552Paul Bourdelais04/2010
715(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
7162^685578+3206380Paul Bourdelais04/2012
7172^684836-49349206157Enzo Doria10/2015
718(73^110603-1)/72206088Paul Bourdelais06/2018
7192^684163-2790967205954Enzo Doria12/2015
720326^81943-325^81943205941Jean-Louis Charton07/2012
721(2^684127-1)/23765203727205933Jens K. Andersen04/2009
7224^341233-3^341233205443Jean-Louis Charton01/2006
7232^681545+467205166Lelio R Paula11/2013
7242^681306+81049205094Enzo Doria07/2016
7252^680697+1877057204911Enzo Doria07/2016
7262^680415+71783204826Enzo Doria04/2016
7272^679860-459995204659Enzo Doria06/2015
7282^679593+1879547204578Enzo Doria09/2016
7292^678651+1875023204295Enzo Doria07/2016
7302^678561+678561204268Henri Lifchitz05/2006
7312^678101-114043204129Enzo Doria11/2014
7322^678028+1875631204107Enzo Doria06/2016
7332^676992-59783203795Enzo Doria10/2015
7342^676972+1866871203789Enzo Doria03/2016
7352^676761-9203726Robert Price01/2017
7362^676563-2792407203666Enzo Doria02/2016
7372^676306-114713203589Enzo Doria04/2015
738(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
7392^674627-25161203083Enzo Doria09/2013
7402^674603-69337203076Enzo Doria12/2015
7412^674459+74213203033Enzo Doria04/2016
7422^674116-458879202930Enzo Doria04/2015
7432^674076-114755202918Enzo Doria04/2015
7445^289937-4^289937202658Jean-Louis Charton03/2013
7452^672556-1835519202460Enzo Doria04/2015
7462^671446-351401202126Enzo Doria07/2015
7472^671373+77747202104Enzo Doria05/2016
7482^670726-114845201909Enzo Doria05/2015
7492^670539-25045201853Enzo Doria09/2013
75043284^43519-43519^43284201769Norbert Schneider08/2018


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!