PRP Records

Probable Primes Top 10000

(280932 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 ?
5251(2^335562+1258)/2101014Stefano Morozzi09/2020
5252(19*10^100997+737)/9100998Robert Price07/2018
525347599!2+1024100991Robert Price02/2015
52542^335468-18629100986Enzo Doria05/2013
52552^335454-20961100982Enzo Doria06/2013
5256(2^335454+3258)/2100982Stefano Morozzi02/2021
525710^100978+61100979Lelio R Paula09/2016
525810^100978-156437100978Patrick De Geest11/2016
5259(2^335422+3114)/2100972Stefano Morozzi09/2020
5260(15*2^335417+1)/481100970Lelio R Paula12/2013
52612^335403-1859167100967Enzo Doria03/2016
526223599^18976+18976^23599100962Hans Havermann10/2018
52636*10^100958+43100959Robert Price07/2020
52649*2^335364-5100956Lelio R Paula08/2014
52652^335349+72287100951Enzo Doria04/2016
52662^335329+16095100945Lelio R Paula09/2016
5267232823#+233663100937Makoto Morimoto10/2017
5268(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
52692^335237-20893100917Enzo Doria06/2013
52702^335222-19337100912Enzo Doria05/2013
52712^335222-109985100912Enzo Doria04/2014
52722^335182-17237100900Enzo Doria05/2013
5273(2^335107+1634)/2100877Stefano Morozzi09/2020
52752^335043-16737100858Enzo Doria05/2013
5274(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
52762^335038-20633100857Enzo Doria06/2013
52772^335031+1873373100855Enzo Doria06/2016
527823489^19650+19650^23489100847Hans Havermann10/2018
52793^211354-8816100842Enzo Doria05/2014
52802^334984-112757100841Enzo Doria06/2014
5281(746*10^100827+1)/9100829Robert Price03/2020
528229451^2648+2648^29451100809Hans Havermann09/2018
528325583^8716+8716^25583100806Hans Havermann08/2018
52852^334857+48527100803Lelio R Paula08/2011
528412^93406+29100803Lelio R Paula10/2016
528628780^3179+3179^28780100796Hans Havermann09/2018
5287(5*2^334825+1)/47100792Lelio R Paula12/2013
52882^334809-13100788Lelio R Paula04/2011
5289(82*10^100780-1)/9100781Robert Price12/2014
529031395^1622+1622^31395100780Hans Havermann09/2018
5291(2^334779+47)/5100778Lelio R Paula12/2013
52922^334751+2049100771Lelio R Paula09/2016
529313^90443-98100749Lelio R Paula10/2016
5294(2^334674+3190)/2100747Stefano Morozzi09/2020
5295(2^334651+1050)/2100740Stefano Morozzi09/2020
5296(7*10^100737+71)/3100738Robert Price05/2018
5297(24737*2^334628+1)/3100737Lelio R Paula07/2014
529815^85639-28100720Lelio R Paula10/2016
529927068^5259+5259^27068100718Hans Havermann08/2018
53002^334562+577294575100711Lelio R Paula09/2016
53014*3^211077-5100710Lelio R Paula08/2014
53022^334524+145100702Lelio R Paula07/2009
5303(2^334451+714)/2100680Stefano Morozzi09/2020
530427648^4375+4375^27648100666Hans Havermann09/2018
5305(1017*2^334391-1)/3535100662Lelio R Paula05/2015
5306(2^334309+3122)/2100637Stefano Morozzi09/2020
53072^334294-113111100633Enzo Doria07/2014
530825581^8582+8582^25581100626Hans Havermann08/2018
53096^129308-17723100622Enzo Doria03/2013
53106^129305+95100619Lelio R Paula10/2016
53112^334244-1167100618Lelio R Paula09/2016
5312(2^334233+3066)/2100614Stefano Morozzi09/2020
5313(76*10^100611+77)/9100612Robert Price10/2019
53147*10^100606-93100607Robert Price08/2020
5315(26*10^100566+49)/3100567Robert Price08/2019
5316(21*2^334050+1)/935100558Lelio R Paula12/2013
531724885^10984+10984^24885100555Hans Havermann07/2018
5318(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
5319(35*10^100542+1)/9100543Serge Batalov11/2010
532023578^18367+18367^23578100538Hans Havermann07/2018
532113^90251+24100535Lelio R Paula10/2016
53222^333963+789100533Lelio R Paula08/2011
53232^333919-1840087100520Enzo Doria06/2015
5324(2^333916+1698)/2100519Stefano Morozzi09/2020
53252^333911+72623100518Enzo Doria04/2016
532624605^12168+12168^24605100517Hans Havermann08/2018
532766*10^100502+7100504Robert Price07/2020
532818^80064-67100503Lelio R Paula10/2016
53295^143742-48100472Lelio R Paula10/2016
533024095^14784+14784^24095100472Hans Havermann08/2018
53312^333757-112123100471Enzo Doria06/2014
53327*10^100457-57100458Robert Price06/2020
533327358^4693+4693^27358100444Hans Havermann07/2018
53348*10^100439-51100440Robert Price08/2019
53352^333603-108861100425Enzo Doria03/2014
53369*7^118818-2100414Lelio R Paula11/2014
53372^333546-17097100408Enzo Doria05/2013
533817^81597+72100401Lelio R Paula10/2016
5339p(20559)#/2+8100384Robert Price01/2017
534011^96390-24100380Lelio R Paula10/2016
5341(2^333385+2730)/2100359Stefano Morozzi09/2020
53434832563059*2^333333+30029100353Donovan Johnson01/2008
534223565^18136+18136^23565100353Hans Havermann07/2018
53442^333354+763100350Lelio R Paula08/2011
5345(25*10^100343-67)/3100344Robert Price06/2019
53462^333289-109483100330Enzo Doria04/2014
53472^333240-2790209100316Enzo Doria03/2016
534823601^17798+17798^23601100314Hans Havermann05/2018
5350(2^333227-2^166614+1)/510031111/2006
53492^333225+719100311Lelio R Paula08/2011
53512^333221-2785333100310Enzo Doria10/2015
535276^53332-75100308Norbert Schneider02/2015
53536^128892-17573100298Enzo Doria03/2013
5354(47*10^100283-119)/9100284Robert Price05/2019
53552^333105-113215100275Enzo Doria07/2014
5356(31*2^333102+1)/2375100272Lelio R Paula11/2013
53574*10^100257-83100258Robert Price10/2018
535817^81476-74100253Lelio R Paula10/2016
535923392^19207+19207^23392100199Hans Havermann06/2018
5360(2^332830+750)/2100192Stefano Morozzi09/2020
5361(206*10^100189-17)/9100191Robert Price01/2020
536217^81417-16100180Theodore Burton11/2005
5363(2^332773+590)/2100175Stefano Morozzi09/2020
53642^332739-113215100165Enzo Doria07/2014
53652^332730-1865621100162Enzo Doria03/2016
536691^51127-2100160Lelio R Paula09/2013
536715^85159-32100155Lelio R Paula10/2016
53686^128661+97100118Lelio R Paula10/2016
536919^78285+40100108Lelio R Paula07/2016
53706^128640+5100102Lelio R Paula11/2014
537122779^22970-22970^22779100093Norbert Schneider08/2020
5372(2^332468+3130)/2100083Stefano Morozzi09/2020
5373(14*10^100075+61)/3100076Robert Price12/2018
5374(2^332435+3098)/2100073Stefano Morozzi09/2020
537528562^3189+3189^28562100072Hans Havermann05/2018
53766^128565-127100044Lelio R Paula08/2016
5377(2^332317+2106)/2100038Stefano Morozzi09/2020
53782^332309-133100035Lelio R Paula02/2011
53792^332307+731100035Lelio R Paula07/2011
53802^332301+12927100033Lelio R Paula04/2013
538123406^18781+18781^23406100031Hans Havermann04/2018
53822^332277-4573100026Yves Minet03/2019
538312^92684-13100023Lelio R Paula07/2016
538478557*2^332193+55669100005Jorge Menendez04/2019
538578557*2^332192+72689100005Jorge Menendez04/2019
538610^100003+45799100004Stefano Morozzi04/2019
538710^100003+155461100004Stefano Morozzi04/2019
538810^100003+211389100004Stefano Morozzi04/2019
538910^100003+381027100004Stefano Morozzi04/2019
539010^100003+540703100004Stefano Morozzi04/2019
539110^100003+823977100004Stefano Morozzi04/2019
540310^100002+236023100003Stefano Morozzi05/2018
540410^100002+433741100003Stefano Morozzi05/2018
53922^332202+104659100003Stefano Morozzi04/2019
53932^332202+857539100003Stefano Morozzi04/2019
53942^332202+181773100003Stefano Morozzi04/2019
53952^332202+687543100003Stefano Morozzi04/2019
53962^332202+941595100003Stefano Morozzi04/2019
53972^332202+445813100003Stefano Morozzi04/2019
53982^332202+1599727100003Stefano Morozzi04/2019
53992^332202+1389567100003Stefano Morozzi04/2019
54002^332202+1206315100003Stefano Morozzi04/2019
54012^332202+1958647100003Stefano Morozzi04/2019
540210^100003-562857100003Patrick De Geest07/2019
5405(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
5406(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
540710^100002-249519100002Patrick De Geest07/2018
540810^100001+314199100002Patrick De Geest07/2018
549810^100000+1751769100001Robert Price08/2012
549910^100000+2155489100001Robert Price10/2012
550010^100000+2483527100001Robert Price12/2012
544510^100000+3938473100001Robert Price05/2015
544610^100000+3979761100001Robert Price05/2015
544710^100000+4293973100001Robert Price09/2015
545110^100000+4858267100001Robert Price12/2015
545210^100000+5113299100001Robert Price02/2016
545310^100000+5169411100001Robert Price02/2016
545410^100000+5354043100001Robert Price05/2016
545510^100000+5717979100001Robert Price05/2016
545610^100000+6080631100001Robert Price07/2016
545710^100000+6308469100001Robert Price07/2016
545810^100000+6512023100001Robert Price08/2016
545910^100000+6596557100001Robert Price08/2016
546010^100000+7115409100001Robert Price10/2016
546110^100000+7235803100001Robert Price10/2016
548510^100000+7867333100001Robert Price12/2016
548610^100000+8743093100001Robert Price02/2017
548710^100000+8955391100001Robert Price03/2017
548810^100000+9180019100001Robert Price03/2017
548910^100000+9225987100001Robert Price04/2017
549010^100000+9265587100001Robert Price04/2017
549110^100000+9287049100001Robert Price04/2017
549210^100000+9425053100001Robert Price05/2017
549310^100000+9450769100001Robert Price05/2017
549410^100000+9528747100001Robert Smith05/2017
549510^100000+9548071100001Robert Price06/2017
549610^100000+10064287100001Robert Price08/2017
549710^100000+10229569100001Robert Price10/2017
540910^100000+11187931100001Robert Price03/2018
541010^100000+11264721100001Robert Price04/2018
541110^100000+11477661100001Robert Price05/2018
541210^100000+11644653100001Robert Price07/2018
541310^100001-431439100001Patrick De Geest07/2018
541410^100000+11769399100001Robert Price08/2018
541510^100000+11848159100001Robert Price08/2018
541610^100000+11863467100001Robert Price08/2018
544810^100000+11992051100001Robert Price09/2018
54492^332196-1-2*29696100001Matt Stath11/2018
545010^100000+12363957100001Robert Price11/2018
54172^332196+1+2*17152100001Matt Stath12/2018
541810^100000+12778033100001Robert Price02/2019
541910^100000+13581679100001Robert Price05/2019
542010^100000+13613199100001Robert Price05/2019
542110^100000+13752327100001Robert Price05/2019
542210^100000+14139243100001Robert Price06/2019
542310^100000+14151057100001Robert Price06/2019
542410^100000+14218923100001Robert Price06/2019
542510^100000+15136771100001Robert Price09/2019
542610^100000+15219873100001Robert Price10/2019
542710^100000+15274039100001Robert Price10/2019
542810^100000+15394069100001Robert Price10/2019
542910^100000+15547119100001Robert Price10/2019
543010^100000+15932923100001Robert Price11/2019
543110^100000+16345467100001Robert Price12/2019
543210^100000+16672143100001Robert Price01/2020
543310^100000+16731939100001Robert Price02/2020
543410^100000+16907049100001Robert Price03/2020
543510^100000+17652523100001Robert Price05/2020
543610^100000+18047167100001Robert Price05/2020
543710^100000+18471819100001Robert Price06/2020
543810^100000+18494793100001Robert Price07/2020
543910^100000+18762609100001Robert Price07/2020
544010^100000+19204141100001Robert Price08/2020
544110^100000+19349793100001Robert Price08/2020
544210^100000+19495699100001Robert Price09/2020
544310^100000+19668927100001Robert Price09/2020
544410^100000+19704313100001Robert Price09/2020
546210^100000+19956229100001Robert Price09/2020
546310^100000+3*(10^37093-1)/9*10^31454+1100001Makoto Morimoto09/2020
546410^100000+4*(10^36149-1)/9*10^31926+1100001Makoto Morimoto09/2020
546510^100000+6*(10^41029-1)/9*10^29486+1100001Makoto Morimoto09/2020
546610^100000+7*(10^55505-1)/9*10^22248+1100001Makoto Morimoto09/2020
546710^100000+20234607100001Robert Price10/2020
546810^100000+20752303100001Robert Price11/2020
546910^100000+20774041100001Robert Price11/2020
547010^100000+20854741100001Robert Price11/2020
547110^100000+20908917100001Robert Price11/2020
547210^100000+20994793100001Robert Price11/2020
547310^100000+21354249100001Robert Price12/2020
547410^100000+21455559100001Robert Price12/2020
547510^100000+21538873100001Robert Price12/2020
547610^100000+21830901100001Robert Price01/2021
547710^100000+21842629100001Robert Price01/2021
547810^100000+21930861100001Robert Price01/2021
547910^100000+22092943100001Robert Price03/2021
548010^100000+22278417100001Robert Price03/2021
548110^100000+22388581100001Robert Price03/2021
548210^100000+22390933100001Robert Price03/2021
548310^100000+22436169100001Robert Price03/2021
548410^100000+22714557100001Robert Price04/2021


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!