PRP Records

Probable Primes Top 10000

(211563 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 ?
5012^800579-1862947240999Enzo Doria12/2015
5023^504206+2240568Luke W. Richards03/2018
5032^798973-26283240515Enzo Doria10/2013
5042^798671-69487240424Enzo Doria12/2015
5052^797220+79831239988Enzo Doria06/2016
5062^796910-26001239894Enzo Doria10/2013
5072^796598+653119239800Enzo Doria12/2016
5082^796432-1859729239750Enzo Doria11/2015
5092^796002-1852211239621Enzo Doria08/2015
5102^795709+75767239533Enzo Doria04/2016
5112^795708+81721239532Enzo Doria08/2016
5122^795468-2786249239460Enzo Doria10/2015
5132^795442+80779239452Enzo Doria07/2016
5142^795075-1852057239342Enzo Doria08/2015
5152^794043+1875023239031Enzo Doria06/2016
5162^793347-69577238822Enzo Doria01/2016
5172^792988-344429238714Enzo Doria08/2015
5182^792700-2786369238627Enzo Doria11/2015
5192^792663-1844797238616Enzo Doria06/2015
5202^792605-291943238598Enzo Doria07/2015
521(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
5222^789373+1869377237625Enzo Doria05/2016
523((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
5242^788942+1866409237496Enzo Doria02/2016
5252^788844-114329237466Enzo Doria01/2015
5262^788705-1859713237424Enzo Doria11/2015
5272^786180+1871971236664Enzo Doria05/2016
52811^227092-90236492Enzo Doria11/2012
5292^785260+1866361236387Enzo Doria02/2016
5302^785220+1880611236375Enzo Doria10/2016
53119^184650-2236122Robert Price10/2014
53210^236059+216513236060Patrick De Geest04/2016
53310^236059-20909236059Robert Price09/2015
5342^782634-113981235597Enzo Doria11/2014
5352^782423+1879733235533Enzo Doria09/2016
5362^781682-2789543235310Enzo Doria12/2015
5372^780408-113453234927Enzo Doria08/2014
5382^780368-1864829234915Enzo Doria01/2016
5392^779593-1836559234681Enzo Doria05/2015
540(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
541(5^335429+1)/6234455Paul Bourdelais08/2010
5422^778395-113617234321Enzo Doria08/2014
5432^776245-2792353233674Enzo Doria02/2016
5442^776060-114029233618Enzo Doria11/2014
5452^775987-2789557233596Enzo Doria12/2015
5462^775672+1866721233501Enzo Doria03/2016
547(11^223999+1)/12233270Paul Bourdelais02/2010
5482^774118+1885789233033Enzo Doria04/2017
54921^176191-20^176191232964Jean-Louis Charton01/2015
5502^773679-113425232901Enzo Doria08/2014
55110^232599+192489232600Patrick De Geest12/2013
55210^232599-3232599Markus Tervooren10/2010
5532^772552-458879232562Enzo Doria04/2015
5542^772214+1874899232460Enzo Doria06/2016
5552^771994-1862771232394Enzo Doria12/2015
5562^771889+1876037232362Enzo Doria07/2016
5572^771660+1866511232293Enzo Doria02/2016
5585^332150-18188232163Enzo Doria06/2014
5593^485977-2^485977231870Mike Oakes09/2009
5602^770082-114161231818Enzo Doria01/2015
561(20^177967+1)/21231540Paul Bourdelais05/2013
5622^767622-9221231078Lelio R Paula01/2016
5632^767344+1880311230994Enzo Doria09/2016
564(3^483611-1)/2230741Paul Bourdelais02/2010
565(10^230706+179)/9230706Serge Batalov12/2014
5662^766309+1875257230682Enzo Doria06/2016
5672^765635+1879883230480Enzo Doria09/2016
5682^764348-113697230092Enzo Doria09/2014
5692^764131+78863230027Enzo Doria05/2016
5702^763701+60197229897Enzo Doria03/2016
5712^762841-25905229639Enzo Doria10/2013
5722^761117-113569229120Enzo Doria08/2014
5732^757985-2790013228177Enzo Doria12/2015
5742^757038-1862081227892Enzo Doria12/2015
5752^756839+95849227832Makoto Morimoto10/2013
576(2^756839+6989)/756091227826Makoto Morimoto09/2016
5772^756773-112723227812Enzo Doria07/2014
578524309#+616367227431Makoto Morimoto02/2016
5792^755097-114193227307Enzo Doria12/2014
5802^754473-2791513227120Enzo Doria01/2016
5812^751426-764321226202Enzo Doria12/2013
582(18^180181-1)/17226176Andy Steward04/2007
5832^750740-3225996Paul Bourdelais03/2012
5842^750725+60227225991Enzo Doria02/2016
5852^750525-113743225931Enzo Doria09/2014
586(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
5872^749444-1861889225606Enzo Doria12/2015
588tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
5892^749096+1876861225501Enzo Doria07/2016
5902^748657+79607225369Enzo Doria06/2016
5912^746653-291583224765Enzo Doria07/2015
5922^746461-114043224708Enzo Doria11/2014
5932^745098-350471224297Enzo Doria06/2015
594(154*10^224061-1)/9224063Serge Batalov12/2014
5952^744211-1845787224030Enzo Doria07/2015
596234178^9+9^234178223463Anatoly F. Selevich07/2011
5972^741651-461197223260Enzo Doria07/2015
5982^741362-1845251223173Enzo Doria07/2015
5992^740455-1863877222900Enzo Doria12/2015
6002^739636-2792219222653Enzo Doria02/2016
60111^213654-180222498Enzo Doria01/2013
6022^738957-1859743222449Enzo Doria11/2015
603(10^221654+179)/9221654Serge Batalov12/2014
6042^736281+79817221643Enzo Doria06/2016
60510^221631+247617221632Patrick De Geest10/2013
60610^221631-9221631Alexander Gramolin02/2011
6072^735970-1839821221550Enzo Doria06/2015
6082^735367+60293221368Enzo Doria03/2016
609(29^151153+1)/30221045Paul Bourdelais09/2017
6102^733264-2784089220735Enzo Doria10/2015
6112^733114-24555220690Enzo Doria09/2013
6122^731891-636259220322Enzo Doria12/2013
6132^731124-25539220091Enzo Doria09/2013
6142^730972-462029220045Enzo Doria07/2015
6152^730833+1868627220003Enzo Doria04/2016
6162^730645-2787133219947Enzo Doria11/2015
6172^730547-25581219917Enzo Doria09/2013
6182^730460+82291219891Enzo Doria09/2016
619L(1051849)219824Renaud Lifchitz03/2009
62011^210961-240219694Enzo Doria01/2013
6212^729611-113437219635Enzo Doria08/2014
622F(1049897)219416Henri Lifchitz10/2008
6232^728604+1879321219332Enzo Doria10/2016
62433^144412+2219292Robert Price04/2015
6252^727998-1862711219150Enzo Doria12/2015
6262^727729-114073219069Enzo Doria12/2014
6272^727496-1851809218999Enzo Doria08/2015
6282^726591+2793143218726Enzo Doria02/2016
6292^725534-2791931218408Enzo Doria02/2016
6302^722184+1877821217400Enzo Doria08/2016
631(109*10^217360-1)/9217362Serge Batalov12/2014
632281*499979#/46410-2702372216849Robert Smith08/2016
633281*499979#/46410+2400766216849Robert Smith08/2016
634tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
6352^718756-114107216368Enzo Doria12/2014
6362^717305+80327215931Enzo Doria07/2016
6372^717069-59773215860Enzo Doria10/2015
638277^88301-276^88301215674Jean-Louis Charton06/2012
639227^91413-40215372Enzo Doria04/2015
6402^714717+782897215152Enzo Doria11/2016
641tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
6422^713241+1879157214707Enzo Doria08/2016
64311^206081-10^206081214612Jean-Louis Charton10/2011
6442^712801-69553214575Enzo Doria01/2016
6452^712603-25357214515Enzo Doria09/2013
6462^711721-1846723214250Enzo Doria07/2015
6472^710730-396765213952Enzo Doria09/2013
6482^708468-114329213271Enzo Doria02/2015
649(163*10^212779-1)/9212781Serge Batalov12/2014
6502^706838-69041212780Enzo Doria11/2015
6512^704577-113871212099Enzo Doria10/2014
6522^704110-2792441211959Enzo Doria02/2016
6532^703943-1862947211908Enzo Doria12/2015
654(10^211610-91)/9211610Serge Batalov12/2014
655227^89797+2211565Lelio R Paula08/2012
6562^702194-3211382Paul Bourdelais03/2012
6572^702064+1874911211343Enzo Doria07/2016
6582^701968-113873211314Enzo Doria10/2014
6592^701713-113779211237Enzo Doria09/2014
6602^701449-25201211158Enzo Doria09/2013
6612^701403-2786977211144Enzo Doria11/2015
6622^701189-25423211079Enzo Doria09/2013
6632^701162-459161211071Enzo Doria05/2015
664(24^152783-1)/23210872Paul Bourdelais04/2018
6652^700400+9385210842Lelio R Paula01/2014
6662^700131+1874693210761Enzo Doria06/2016
66711^202357-1140210734Enzo Doria12/2012
6682^698929-2788423210399Enzo Doria11/2015
669(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
6702^698316+1878601210215Enzo Doria08/2016
6712^697036+1878751209829Enzo Doria08/2016
672(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
6732^696254-115151209594Enzo Doria06/2015
6742^694633+1887257209106Enzo Doria05/2017
6752^693959+180923208903Enzo Doria07/2016
6762^693462-1847561208753Enzo Doria07/2015
6772^690890-59981207979Enzo Doria11/2015
6782^690163+1877063207760Enzo Doria07/2016
6792^689286-29381207496Enzo Doria08/2015
6802^689122-114521207447Enzo Doria04/2015
6812^688373+6077207221Enzo Doria02/2016
6822^688201+1875527207170Enzo Doria07/2016
6832^687619+81563206994Enzo Doria08/2016
6842^686572-1845299206679Enzo Doria07/2015
685(21^156217-1)/20206552Paul Bourdelais04/2010
6862^685578+3206380Paul Bourdelais04/2012
6872^684836-49349206157Enzo Doria10/2015
688(73^110603-1)/72206088Paul Bourdelais06/2018
6892^684163-2790967205954Enzo Doria12/2015
690326^81943-325^81943205941Jean-Louis Charton07/2012
691(2^684127-1)/23765203727205933Jens K. Andersen04/2009
6924^341233-3^341233205443Jean-Louis Charton01/2006
6932^681545+467205166Lelio R Paula11/2013
6942^681306+81049205094Enzo Doria07/2016
6952^680697+1877057204911Enzo Doria07/2016
6962^680415+71783204826Enzo Doria04/2016
6972^679860-459995204659Enzo Doria06/2015
6982^679593+1879547204578Enzo Doria09/2016
6992^678651+1875023204295Enzo Doria07/2016
7002^678561+678561204268Henri Lifchitz05/2006
7012^678101-114043204129Enzo Doria11/2014
7022^678028+1875631204107Enzo Doria06/2016
7032^676992-59783203795Enzo Doria10/2015
7042^676972+1866871203789Enzo Doria03/2016
7052^676761-9203726Robert Price01/2017
7062^676563-2792407203666Enzo Doria02/2016
7072^676306-114713203589Enzo Doria04/2015
708(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
7092^674627-25161203083Enzo Doria09/2013
7102^674603-69337203076Enzo Doria12/2015
7112^674459+74213203033Enzo Doria04/2016
7122^674116-458879202930Enzo Doria04/2015
7132^674076-114755202918Enzo Doria04/2015
7145^289937-4^289937202658Jean-Louis Charton03/2013
7152^672556-1835519202460Enzo Doria04/2015
7162^671446-351401202126Enzo Doria07/2015
7172^671373+77747202104Enzo Doria05/2016
7182^670726-114845201909Enzo Doria05/2015
7192^670539-25045201853Enzo Doria09/2013
7202^670213+282317201755Enzo Doria09/2016
7212^669854-113501201647Enzo Doria08/2014
7222^669718+81619201606Enzo Doria08/2016
723(145*10^201504-1)/9201506Serge Batalov12/2014
7242^668938-1839821201371Enzo Doria06/2015
7252^668492+1879303201237Enzo Doria08/2016
7266^258413-5^258413201085Jean-Louis Charton03/2013
7272^667894+1875589201057Enzo Doria06/2016
7282^667569-1836559200959Enzo Doria05/2015
729(172*10^200746-1)/9200748Serge Batalov12/2014
7302^666430+782569200616Enzo Doria10/2016
731(86^103471+1)/87200163Paul Bourdelais05/2018
732103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
733103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
734numbpart(32235776596)200002Serge Batalov04/2017
735(10^200001+149)/3200001Serge Batalov12/2014
7362^662103-29287199313Enzo Doria08/2015
737(2*10^199283+457)/9199283Robert Price01/2018
738(10^199248-19)/9199248Robert Price01/2018
7392^660482-2891198825Yves Minet05/2016
7402^659583+1879223198555Enzo Doria08/2016
741(53*10^198529+1)/9198530Serge Batalov07/2010
7422^658828-29819198327Enzo Doria08/2015
7432^658776-2791229198312Enzo Doria01/2016
744(4*10^198268+137)/3198269Robert Price03/2018
7452^658544-1854029198242Enzo Doria09/2015
746(157^90239-1)/156198154Alexander Zhirkov06/2016
747(4*10^197778+173)/3197779Robert Price02/2018
7482^656462+1874419197615Enzo Doria06/2016
749(89^101363+1)/90197595Paul Bourdelais11/2017
7502^655893-344563197444Enzo Doria07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

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