PRP Records

Probable Primes Top 10000

(224926 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 (> 30000) Who ? When ?
5012^805745-459763242554Enzo Doria05/2015
5022^805353+782687242436Enzo Doria11/2016
5032^804277-417933242112Enzo Doria01/2014
5042^803468-269039241868Enzo Doria10/2013
5052^803172+80851241779Enzo Doria07/2016
5063^506233-2241535Robert Price11/2013
5072^802025-25999241434Enzo Doria10/2013
508(3^505823+3^252912+1)/7241339Serge Batalov03/2014
5092^801303+1872923241217Enzo Doria05/2016
5102^800579-1862947240999Enzo Doria12/2015
5113^504206+2240568Luke W. Richards03/2018
5122^798973-26283240515Enzo Doria10/2013
5132^798671-69487240424Enzo Doria12/2015
5142^797220+79831239988Enzo Doria06/2016
5152^796910-26001239894Enzo Doria10/2013
5162^796598+653119239800Enzo Doria12/2016
5172^796432-1859729239750Enzo Doria11/2015
5182^796002-1852211239621Enzo Doria08/2015
5192^795709+75767239533Enzo Doria04/2016
5202^795708+81721239532Enzo Doria08/2016
5212^795468-2786249239460Enzo Doria10/2015
5222^795442+80779239452Enzo Doria07/2016
5232^795075-1852057239342Enzo Doria08/2015
5242^794043+1875023239031Enzo Doria06/2016
5252^793347-69577238822Enzo Doria01/2016
5262^792988-344429238714Enzo Doria08/2015
5272^792700-2786369238627Enzo Doria11/2015
5282^792663-1844797238616Enzo Doria06/2015
5292^792605-291943238598Enzo Doria07/2015
530(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
5312^789373+1869377237625Enzo Doria05/2016
532((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
5332^788942+1866409237496Enzo Doria02/2016
5342^788844-114329237466Enzo Doria01/2015
5352^788705-1859713237424Enzo Doria11/2015
5362^786180+1871971236664Enzo Doria05/2016
53711^227092-90236492Enzo Doria11/2012
5382^785260+1866361236387Enzo Doria02/2016
5392^785220+1880611236375Enzo Doria10/2016
54019^184650-2236122Robert Price10/2014
54110^236059+216513236060Patrick De Geest04/2016
54210^236059-20909236059Robert Price09/2015
5432^782634-113981235597Enzo Doria11/2014
5442^782423+1879733235533Enzo Doria09/2016
5452^781682-2789543235310Enzo Doria12/2015
5462^780408-113453234927Enzo Doria08/2014
5472^780368-1864829234915Enzo Doria01/2016
5482^779593-1836559234681Enzo Doria05/2015
549(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
550(5^335429+1)/6234455Paul Bourdelais08/2010
5512^778395-113617234321Enzo Doria08/2014
5522^776245-2792353233674Enzo Doria02/2016
5532^776060-114029233618Enzo Doria11/2014
5542^775987-2789557233596Enzo Doria12/2015
5552^775672+1866721233501Enzo Doria03/2016
556(11^223999+1)/12233270Paul Bourdelais02/2010
5572^774118+1885789233033Enzo Doria04/2017
55821^176191-20^176191232964Jean-Louis Charton01/2015
5592^773679-113425232901Enzo Doria08/2014
56010^232599+192489232600Patrick De Geest12/2013
56110^232599-3232599Markus Tervooren10/2010
5622^772552-458879232562Enzo Doria04/2015
5632^772214+1874899232460Enzo Doria06/2016
5642^771994-1862771232394Enzo Doria12/2015
5652^771889+1876037232362Enzo Doria07/2016
5662^771660+1866511232293Enzo Doria02/2016
5675^332150-18188232163Enzo Doria06/2014
5683^485977-2^485977231870Mike Oakes09/2009
5692^770082-114161231818Enzo Doria01/2015
570(20^177967+1)/21231540Paul Bourdelais05/2013
5712^767622-9221231078Lelio R Paula01/2016
5722^767344+1880311230994Enzo Doria09/2016
573(3^483611-1)/2230741Paul Bourdelais02/2010
574(10^230706+179)/9230706Serge Batalov12/2014
5752^766309+1875257230682Enzo Doria06/2016
5762^765635+1879883230480Enzo Doria09/2016
5772^764348-113697230092Enzo Doria09/2014
5782^764131+78863230027Enzo Doria05/2016
5792^763701+60197229897Enzo Doria03/2016
5802^762841-25905229639Enzo Doria10/2013
5812^761117-113569229120Enzo Doria08/2014
5822^757985-2790013228177Enzo Doria12/2015
5832^757038-1862081227892Enzo Doria12/2015
5842^756839+95849227832Makoto Morimoto10/2013
585(2^756839+6989)/756091227826Makoto Morimoto09/2016
5862^756773-112723227812Enzo Doria07/2014
587524309#+616367227431Makoto Morimoto02/2016
5882^755097-114193227307Enzo Doria12/2014
5892^754473-2791513227120Enzo Doria01/2016
5902^751426-764321226202Enzo Doria12/2013
591(18^180181-1)/17226176Andy Steward04/2007
5922^750740-3225996Paul Bourdelais03/2012
5932^750725+60227225991Enzo Doria02/2016
5942^750525-113743225931Enzo Doria09/2014
595(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
5962^749444-1861889225606Enzo Doria12/2015
597tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
5982^749096+1876861225501Enzo Doria07/2016
5992^748657+79607225369Enzo Doria06/2016
6002^746653-291583224765Enzo Doria07/2015
6012^746461-114043224708Enzo Doria11/2014
6022^745098-350471224297Enzo Doria06/2015
603(154*10^224061-1)/9224063Serge Batalov12/2014
6042^744211-1845787224030Enzo Doria07/2015
605234178^9+9^234178223463Anatoly F. Selevich07/2011
6062^741651-461197223260Enzo Doria07/2015
6072^741362-1845251223173Enzo Doria07/2015
6082^740455-1863877222900Enzo Doria12/2015
6092^739636-2792219222653Enzo Doria02/2016
61011^213654-180222498Enzo Doria01/2013
6112^738957-1859743222449Enzo Doria11/2015
612(10^221654+179)/9221654Serge Batalov12/2014
6132^736281+79817221643Enzo Doria06/2016
61410^221631+247617221632Patrick De Geest10/2013
61510^221631-9221631Alexander Gramolin02/2011
6162^735970-1839821221550Enzo Doria06/2015
6172^735367+60293221368Enzo Doria03/2016
618(29^151153+1)/30221045Paul Bourdelais09/2017
6192^733264-2784089220735Enzo Doria10/2015
6202^733114-24555220690Enzo Doria09/2013
6212^731891-636259220322Enzo Doria12/2013
6222^731124-25539220091Enzo Doria09/2013
6232^730972-462029220045Enzo Doria07/2015
6242^730833+1868627220003Enzo Doria04/2016
6252^730645-2787133219947Enzo Doria11/2015
6262^730547-25581219917Enzo Doria09/2013
6272^730460+82291219891Enzo Doria09/2016
628L(1051849)219824Renaud Lifchitz03/2009
62911^210961-240219694Enzo Doria01/2013
6302^729611-113437219635Enzo Doria08/2014
631F(1049897)219416Henri Lifchitz10/2008
6322^728604+1879321219332Enzo Doria10/2016
63333^144412+2219292Robert Price04/2015
6342^727998-1862711219150Enzo Doria12/2015
6352^727729-114073219069Enzo Doria12/2014
6362^727496-1851809218999Enzo Doria08/2015
6372^726591+2793143218726Enzo Doria02/2016
6382^725534-2791931218408Enzo Doria02/2016
6392^722184+1877821217400Enzo Doria08/2016
640(109*10^217360-1)/9217362Serge Batalov12/2014
641281*499979#/46410-2702372216849Robert Smith08/2016
642281*499979#/46410+2400766216849Robert Smith08/2016
643tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
6442^718756-114107216368Enzo Doria12/2014
6452^717305+80327215931Enzo Doria07/2016
6462^717069-59773215860Enzo Doria10/2015
64730^146021-29^146021215691Jean-Louis Charton09/2018
648277^88301-276^88301215674Jean-Louis Charton06/2012
649227^91413-40215372Enzo Doria04/2015
6502^714717+782897215152Enzo Doria11/2016
651tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
6522^713241+1879157214707Enzo Doria08/2016
65311^206081-10^206081214612Jean-Louis Charton10/2011
6542^712801-69553214575Enzo Doria01/2016
6552^712603-25357214515Enzo Doria09/2013
6562^711721-1846723214250Enzo Doria07/2015
6572^710730-396765213952Enzo Doria09/2013
6582^708468-114329213271Enzo Doria02/2015
659(163*10^212779-1)/9212781Serge Batalov12/2014
6602^706838-69041212780Enzo Doria11/2015
6612^704577-113871212099Enzo Doria10/2014
6622^704110-2792441211959Enzo Doria02/2016
6632^703943-1862947211908Enzo Doria12/2015
664(10^211610-91)/9211610Serge Batalov12/2014
665227^89797+2211565Lelio R Paula08/2012
6662^702194-3211382Paul Bourdelais03/2012
6672^702064+1874911211343Enzo Doria07/2016
6682^701968-113873211314Enzo Doria10/2014
6692^701713-113779211237Enzo Doria09/2014
6702^701449-25201211158Enzo Doria09/2013
6712^701403-2786977211144Enzo Doria11/2015
6722^701189-25423211079Enzo Doria09/2013
6732^701162-459161211071Enzo Doria05/2015
674(24^152783-1)/23210872Paul Bourdelais04/2018
6752^700400+9385210842Lelio R Paula01/2014
6762^700131+1874693210761Enzo Doria06/2016
67711^202357-1140210734Enzo Doria12/2012
6782^698929-2788423210399Enzo Doria11/2015
679(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
6802^698316+1878601210215Enzo Doria08/2016
6812^697036+1878751209829Enzo Doria08/2016
682(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
6832^696254-115151209594Enzo Doria06/2015
684(35^135623+1)/36209410Paul Bourdelais07/2018
6852^694633+1887257209106Enzo Doria05/2017
6862^693959+180923208903Enzo Doria07/2016
6872^693462-1847561208753Enzo Doria07/2015
6882^690890-59981207979Enzo Doria11/2015
689(38^131591+1)/39207884Paul Bourdelais07/2018
6902^690163+1877063207760Enzo Doria07/2016
6912^689286-29381207496Enzo Doria08/2015
6922^689122-114521207447Enzo Doria04/2015
6932^688373+6077207221Enzo Doria02/2016
6942^688201+1875527207170Enzo Doria07/2016
695(42^127609+1)/43207140Paul Bourdelais07/2018
6962^687619+81563206994Enzo Doria08/2016
6972^686572-1845299206679Enzo Doria07/2015
698(21^156217-1)/20206552Paul Bourdelais04/2010
699(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
7002^685578+3206380Paul Bourdelais04/2012
7012^684836-49349206157Enzo Doria10/2015
702(73^110603-1)/72206088Paul Bourdelais06/2018
7032^684163-2790967205954Enzo Doria12/2015
704326^81943-325^81943205941Jean-Louis Charton07/2012
705(2^684127-1)/23765203727205933Jens K. Andersen04/2009
7064^341233-3^341233205443Jean-Louis Charton01/2006
7072^681545+467205166Lelio R Paula11/2013
7082^681306+81049205094Enzo Doria07/2016
7092^680697+1877057204911Enzo Doria07/2016
7102^680415+71783204826Enzo Doria04/2016
7112^679860-459995204659Enzo Doria06/2015
7122^679593+1879547204578Enzo Doria09/2016
7132^678651+1875023204295Enzo Doria07/2016
7142^678561+678561204268Henri Lifchitz05/2006
7152^678101-114043204129Enzo Doria11/2014
7162^678028+1875631204107Enzo Doria06/2016
7172^676992-59783203795Enzo Doria10/2015
7182^676972+1866871203789Enzo Doria03/2016
7192^676761-9203726Robert Price01/2017
7202^676563-2792407203666Enzo Doria02/2016
7212^676306-114713203589Enzo Doria04/2015
722(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
7232^674627-25161203083Enzo Doria09/2013
7242^674603-69337203076Enzo Doria12/2015
7252^674459+74213203033Enzo Doria04/2016
7262^674116-458879202930Enzo Doria04/2015
7272^674076-114755202918Enzo Doria04/2015
7285^289937-4^289937202658Jean-Louis Charton03/2013
7292^672556-1835519202460Enzo Doria04/2015
7302^671446-351401202126Enzo Doria07/2015
7312^671373+77747202104Enzo Doria05/2016
7322^670726-114845201909Enzo Doria05/2015
7332^670539-25045201853Enzo Doria09/2013
73443284^43519-43519^43284201769Norbert Schneider08/2018
7352^670213+282317201755Enzo Doria09/2016
7362^669854-113501201647Enzo Doria08/2014
7372^669718+81619201606Enzo Doria08/2016
738(145*10^201504-1)/9201506Serge Batalov12/2014
7392^668938-1839821201371Enzo Doria06/2015
7402^668492+1879303201237Enzo Doria08/2016
7416^258413-5^258413201085Jean-Louis Charton03/2013
7422^667894+1875589201057Enzo Doria06/2016
7432^667569-1836559200959Enzo Doria05/2015
744(172*10^200746-1)/9200748Serge Batalov12/2014
7452^666430+782569200616Enzo Doria10/2016
746(86^103471+1)/87200163Paul Bourdelais05/2018
748103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
747103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
749numbpart(32235776596)200002Serge Batalov04/2017
750(10^200001+149)/3200001Serge Batalov12/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 18 2018 22:22 (Time in France)

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