PRP Records

Probable Primes Top 10000

(252932 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 (> 50000) Who ? When ?
5012^826733+1882907248872Enzo Doria12/2016
5022^825682+1876549248556Enzo Doria07/2016
5032^824991-114121248348Enzo Doria12/2014
5042^824642-362727248242Enzo Doria12/2013
5052^824565-114265248219Enzo Doria01/2015
506(73*10^248145-1)/9248146Robert Price01/2015
507(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
508(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
5092^822296+76501247536Enzo Doria05/2016
5102^821590-114167247324Enzo Doria12/2014
5112^821512-2790659247300Enzo Doria12/2015
5122^820077+382847246868Enzo Doria11/2016
5132^820001+81269246845Enzo Doria07/2016
5142^819463-59197246683Enzo Doria10/2015
5152^819296+80581246633Enzo Doria07/2016
5162^817160-350369245990Enzo Doria06/2015
51788093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
5182^815111-113857245373Enzo Doria10/2014
5192^814914-4001245314Yves Minet05/2017
520846^83761-845^83761245200Jean-Louis Charton12/2012
5212^814356-2790449245146Enzo Doria12/2015
5222^814276-459029245122Enzo Doria04/2015
5232^814023+180923245046Enzo Doria07/2016
524(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
5252^811842-113675244389Enzo Doria09/2014
5262^811132-2787929244176Enzo Doria11/2015
5272^809746-2790971243758Enzo Doria01/2016
5282^808767-3295243464Yves Minet12/2016
5292^808621-113809243420Enzo Doria09/2014
5302^807724+1879621243150Enzo Doria09/2016
5312^805843-113611242583Enzo Doria08/2014
5322^805745-459763242554Enzo Doria05/2015
5332^805353+782687242436Enzo Doria11/2016
5342^804277-417933242112Enzo Doria01/2014
5352^803468-269039241868Enzo Doria10/2013
5362^803172+80851241779Enzo Doria07/2016
5373^506233-2241535Robert Price11/2013
5382^802025-25999241434Enzo Doria10/2013
539(3^505823+3^252912+1)/7241339Serge Batalov03/2014
5402^801303+1872923241217Enzo Doria05/2016
5412^800579-1862947240999Enzo Doria12/2015
5423^504206+2240568Luke W. Richards03/2018
5432^798973-26283240515Enzo Doria10/2013
5442^798671-69487240424Enzo Doria12/2015
5452^797220+79831239988Enzo Doria06/2016
5462^796910-26001239894Enzo Doria10/2013
5472^796598+653119239800Enzo Doria12/2016
5482^796432-1859729239750Enzo Doria11/2015
5492^796002-1852211239621Enzo Doria08/2015
5502^795709+75767239533Enzo Doria04/2016
5512^795708+81721239532Enzo Doria08/2016
5522^795468-2786249239460Enzo Doria10/2015
5532^795442+80779239452Enzo Doria07/2016
5542^795075-1852057239342Enzo Doria08/2015
555(86^123677+1)/87239252Paul Bourdelais01/2019
5562^794043+1875023239031Enzo Doria06/2016
5572^793347-69577238822Enzo Doria01/2016
5582^792988-344429238714Enzo Doria08/2015
5592^792700-2786369238627Enzo Doria11/2015
5602^792663-1844797238616Enzo Doria06/2015
5612^792605-291943238598Enzo Doria07/2015
562(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
5632^789373+1869377237625Enzo Doria05/2016
564((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
5652^788942+1866409237496Enzo Doria02/2016
5662^788844-114329237466Enzo Doria01/2015
5672^788705-1859713237424Enzo Doria11/2015
5682^786180+1871971236664Enzo Doria05/2016
56911^227092-90236492Enzo Doria11/2012
5702^785260+1866361236387Enzo Doria02/2016
5712^785220+1880611236375Enzo Doria10/2016
57219^184650-2236122Robert Price10/2014
57310^236059+216513236060Patrick De Geest04/2016
57410^236059-20909236059Robert Price09/2015
575(87^121487-1)/86235625Paul Bourdelais12/2018
5762^782634-113981235597Enzo Doria11/2014
5772^782423+1879733235533Enzo Doria09/2016
5782^781682-2789543235310Enzo Doria12/2015
5792^780408-113453234927Enzo Doria08/2014
5802^780368-1864829234915Enzo Doria01/2016
5812^779593-1836559234681Enzo Doria05/2015
582(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
583(5^335429+1)/6234455Paul Bourdelais08/2010
5842^778395-113617234321Enzo Doria08/2014
5852^776245-2792353233674Enzo Doria02/2016
5862^776060-114029233618Enzo Doria11/2014
5872^775987-2789557233596Enzo Doria12/2015
5882^775672+1866721233501Enzo Doria03/2016
589(11^223999+1)/12233270Paul Bourdelais02/2010
5902^774118+1885789233033Enzo Doria04/2017
59121^176191-20^176191232964Jean-Louis Charton01/2015
5922^773679-113425232901Enzo Doria08/2014
59310^232599+192489232600Patrick De Geest12/2013
59410^232599-3232599Markus Tervooren10/2010
5952^772552-458879232562Enzo Doria04/2015
5962^772214+1874899232460Enzo Doria06/2016
5972^771994-1862771232394Enzo Doria12/2015
5982^771889+1876037232362Enzo Doria07/2016
5992^771660+1866511232293Enzo Doria02/2016
6005^332150-18188232163Enzo Doria06/2014
6013^485977-2^485977231870Mike Oakes09/2009
6022^770082-114161231818Enzo Doria01/2015
603(20^177967+1)/21231540Paul Bourdelais05/2013
6042^767622-9221231078Lelio R Paula01/2016
6052^767344+1880311230994Enzo Doria09/2016
606(3^483611-1)/2230741Paul Bourdelais02/2010
607(10^230706+179)/9230706Serge Batalov12/2014
6082^766309+1875257230682Enzo Doria06/2016
6092^765635+1879883230480Enzo Doria09/2016
6102^764348-113697230092Enzo Doria09/2014
6112^764131+78863230027Enzo Doria05/2016
6122^763701+60197229897Enzo Doria03/2016
6132^762841-25905229639Enzo Doria10/2013
6142^761117-113569229120Enzo Doria08/2014
615(98^114859+1)/99228709Paul Bourdelais12/2018
616(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
6172^757985-2790013228177Enzo Doria12/2015
6182^757038-1862081227892Enzo Doria12/2015
6192^756839+95849227832Makoto Morimoto10/2013
620(2^756839+6989)/756091227826Makoto Morimoto09/2016
6212^756773-112723227812Enzo Doria07/2014
622524309#+616367227431Makoto Morimoto02/2016
6232^755097-114193227307Enzo Doria12/2014
6242^754473-2791513227120Enzo Doria01/2016
6252^751426-764321226202Enzo Doria12/2013
626(18^180181-1)/17226176Andy Steward04/2007
6272^750740-3225996Paul Bourdelais03/2012
6282^750725+60227225991Enzo Doria02/2016
6292^750525-113743225931Enzo Doria09/2014
630(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
6312^749444-1861889225606Enzo Doria12/2015
632tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
6332^749096+1876861225501Enzo Doria07/2016
6342^748657+79607225369Enzo Doria06/2016
6352^746653-291583224765Enzo Doria07/2015
6362^746461-114043224708Enzo Doria11/2014
6372^745098-350471224297Enzo Doria06/2015
638(154*10^224061-1)/9224063Serge Batalov12/2014
6392^744211-1845787224030Enzo Doria07/2015
6402^743592-134579223844Hans Havermann10/2018
641234178^9+9^234178223463Anatoly F. Selevich07/2011
6422^741651-461197223260Enzo Doria07/2015
6432^741362-1845251223173Enzo Doria07/2015
6442^740455-1863877222900Enzo Doria12/2015
6452^739636-2792219222653Enzo Doria02/2016
64611^213654-180222498Enzo Doria01/2013
6472^738957-1859743222449Enzo Doria11/2015
648(54^128189+1)/55222073Paul Bourdelais11/2018
649(10^221654+179)/9221654Serge Batalov12/2014
6502^736281+79817221643Enzo Doria06/2016
65110^221631+247617221632Patrick De Geest10/2013
65210^221631-9221631Alexander Gramolin02/2011
6532^735970-1839821221550Enzo Doria06/2015
6542^735367+60293221368Enzo Doria03/2016
655(29^151153+1)/30221045Paul Bourdelais09/2017
6562^733264-2784089220735Enzo Doria10/2015
6572^733114-24555220690Enzo Doria09/2013
6582^731891-636259220322Enzo Doria12/2013
6592^731124-25539220091Enzo Doria09/2013
6602^730972-462029220045Enzo Doria07/2015
6612^730833+1868627220003Enzo Doria04/2016
6622^730645-2787133219947Enzo Doria11/2015
6632^730547-25581219917Enzo Doria09/2013
6642^730460+82291219891Enzo Doria09/2016
665(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
666L(1051849)219824Renaud Lifchitz03/2009
66711^210961-240219694Enzo Doria01/2013
6682^729611-113437219635Enzo Doria08/2014
669F(1049897)219416Henri Lifchitz10/2008
6702^728604+1879321219332Enzo Doria10/2016
67133^144412+2219292Robert Price04/2015
6722^728277-183313219234Hans Havermann10/2018
6732^727998-1862711219150Enzo Doria12/2015
6742^727729-114073219069Enzo Doria12/2014
6752^727496-1851809218999Enzo Doria08/2015
6762^726591+2793143218726Enzo Doria02/2016
6772^725534-2791931218408Enzo Doria02/2016
6782^722184+1877821217400Enzo Doria08/2016
679(109*10^217360-1)/9217362Serge Batalov12/2014
680281*499979#/46410-2702372216849Robert Smith08/2016
681281*499979#/46410+2400766216849Robert Smith08/2016
682tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
6832^718756-114107216368Enzo Doria12/2014
6842^717305+80327215931Enzo Doria07/2016
6852^717069-59773215860Enzo Doria10/2015
68630^146021-29^146021215691Jean-Louis Charton09/2018
687277^88301-276^88301215674Jean-Louis Charton06/2012
688227^91413-40215372Enzo Doria04/2015
6892^714717+782897215152Enzo Doria11/2016
690tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
6912^713241+1879157214707Enzo Doria08/2016
69211^206081-10^206081214612Jean-Louis Charton10/2011
6932^712801-69553214575Enzo Doria01/2016
6942^712603-25357214515Enzo Doria09/2013
6952^711721-1846723214250Enzo Doria07/2015
6962^710730-396765213952Enzo Doria09/2013
6972^708468-114329213271Enzo Doria02/2015
698(163*10^212779-1)/9212781Serge Batalov12/2014
6992^706838-69041212780Enzo Doria11/2015
7002^704577-113871212099Enzo Doria10/2014
7012^704110-2792441211959Enzo Doria02/2016
7022^703943-1862947211908Enzo Doria12/2015
703(60^119083+1)/61211746Paul Bourdelais10/2018
704(10^211610-91)/9211610Serge Batalov12/2014
705227^89797+2211565Lelio R Paula08/2012
7062^702194-3211382Paul Bourdelais03/2012
7072^702064+1874911211343Enzo Doria07/2016
7082^701968-113873211314Enzo Doria10/2014
7092^701713-113779211237Enzo Doria09/2014
7102^701449-25201211158Enzo Doria09/2013
7112^701403-2786977211144Enzo Doria11/2015
7122^701189-25423211079Enzo Doria09/2013
7132^701162-459161211071Enzo Doria05/2015
714(24^152783-1)/23210872Paul Bourdelais04/2018
7152^700400+9385210842Lelio R Paula01/2014
7162^700131+1874693210761Enzo Doria06/2016
71711^202357-1140210734Enzo Doria12/2012
7182^698929-2788423210399Enzo Doria11/2015
719(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
7202^698316+1878601210215Enzo Doria08/2016
7212^697036+1878751209829Enzo Doria08/2016
722(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
7232^696254-115151209594Enzo Doria06/2015
724(35^135623+1)/36209410Paul Bourdelais07/2018
7252^694633+1887257209106Enzo Doria05/2017
7262^693959+180923208903Enzo Doria07/2016
7272^693462-1847561208753Enzo Doria07/2015
7282^690890-59981207979Enzo Doria11/2015
729(38^131591+1)/39207884Paul Bourdelais07/2018
7302^690163+1877063207760Enzo Doria07/2016
7312^689286-29381207496Enzo Doria08/2015
7322^689122-114521207447Enzo Doria04/2015
7332^688373+6077207221Enzo Doria02/2016
7342^688201+1875527207170Enzo Doria07/2016
735(42^127609+1)/43207140Paul Bourdelais07/2018
7362^687619+81563206994Enzo Doria08/2016
7372^686572-1845299206679Enzo Doria07/2015
738(21^156217-1)/20206552Paul Bourdelais04/2010
739(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
7402^685578+3206380Paul Bourdelais04/2012
7412^684836-49349206157Enzo Doria10/2015
742(73^110603-1)/72206088Paul Bourdelais06/2018
7432^684163-2790967205954Enzo Doria12/2015
744326^81943-325^81943205941Jean-Louis Charton07/2012
745(2^684127-1)/23765203727205933Jens K. Andersen04/2009
7464^341233-3^341233205443Jean-Louis Charton01/2006
7472^681545+467205166Lelio R Paula11/2013
7482^681306+81049205094Enzo Doria07/2016
7492^680697+1877057204911Enzo Doria07/2016
7502^680415+71783204826Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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