PRP Records

Probable Primes Top 10000

(290751 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 ?
700110^100978-156437100978Patrick De Geest11/2016
7002(2^335422+3114)/2100972Stefano Morozzi09/2020
7003(35*10^100970-89)/9100971Robert Price02/2022
7004(15*2^335417+1)/481100970Lelio R Paula12/2013
70052^335403-1859167100967Enzo Doria03/2016
700623599^18976+18976^23599100962Hans Havermann10/2018
70076*10^100958+43100959Robert Price07/2020
70089*2^335364-5100956Lelio R Paula08/2014
7009(7998^25867-1)/7997100955Serge Batalov06/2022
70102^335349+72287100951Enzo Doria04/2016
70112^335329+16095100945Lelio R Paula09/2016
7012232823#+233663100937Makoto Morimoto10/2017
7013(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
70142^335237-20893100917Enzo Doria06/2013
70152^335222-19337100912Enzo Doria05/2013
70162^335222-109985100912Enzo Doria04/2014
70172^335182-17237100900Enzo Doria05/2013
7018(2^335107+1634)/2100877Stefano Morozzi09/2020
70192^335043-16737100858Enzo Doria05/2013
7020(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
70212^335038-20633100857Enzo Doria06/2013
70222^335031+1873373100855Enzo Doria06/2016
702323489^19650+19650^23489100847Hans Havermann10/2018
70243^211354-8816100842Enzo Doria05/2014
70252^334984-112757100841Enzo Doria06/2014
7026(746*10^100827+1)/9100829Robert Price03/2020
702729451^2648+2648^29451100809Hans Havermann09/2018
702825583^8716+8716^25583100806Hans Havermann08/2018
70302^334857+48527100803Lelio R Paula08/2011
702912^93406+29100803Lelio R Paula10/2016
703128780^3179+3179^28780100796Hans Havermann09/2018
7032(5*2^334825+1)/47100792Lelio R Paula12/2013
7033(328^40063-1)/327100791Serge Batalov06/2022
70342^334809-13100788Lelio R Paula04/2011
7035(3552^28387-1)/3551100784Serge Batalov06/2022
7036(82*10^100780-1)/9100781Robert Price12/2014
703731395^1622+1622^31395100780Hans Havermann09/2018
7038(2^334779+47)/5100778Lelio R Paula12/2013
70392^334751+2049100771Lelio R Paula09/2016
704013^90443-98100749Lelio R Paula10/2016
7041(2^334674+3190)/2100747Stefano Morozzi09/2020
7042(2^334651+1050)/2100740Stefano Morozzi09/2020
7043(7*10^100737+71)/3100738Robert Price05/2018
7044(24737*2^334628+1)/3100737Lelio R Paula07/2014
704515^85639-28100720Lelio R Paula10/2016
704627068^5259+5259^27068100718Hans Havermann08/2018
70472^334562+577294575100711Lelio R Paula09/2016
70484*3^211077-5100710Lelio R Paula08/2014
70492^334524+145100702Lelio R Paula07/2009
7050(2^334451+714)/2100680Stefano Morozzi09/2020
705127648^4375+4375^27648100666Hans Havermann09/2018
7052(1017*2^334391-1)/3535100662Lelio R Paula05/2015
7053(2^334309+3122)/2100637Stefano Morozzi09/2020
70542^334294-113111100633Enzo Doria07/2014
705525581^8582+8582^25581100626Hans Havermann08/2018
70566^129308-17723100622Enzo Doria03/2013
70576^129305+95100619Lelio R Paula10/2016
70582^334244-1167100618Lelio R Paula09/2016
7059(2^334233+3066)/2100614Stefano Morozzi09/2020
7060(76*10^100611+77)/9100612Robert Price10/2019
70617*10^100606-93100607Robert Price08/2020
7062(26*10^100566+49)/3100567Robert Price08/2019
7063(21*2^334050+1)/935100558Lelio R Paula12/2013
706424885^10984+10984^24885100555Hans Havermann07/2018
7065(1351^32119-1)/1350100551Serge Batalov06/2022
7066(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
7067(35*10^100542+1)/9100543Serge Batalov11/2010
706823578^18367+18367^23578100538Hans Havermann07/2018
706913^90251+24100535Lelio R Paula10/2016
70702^333963+789100533Lelio R Paula08/2011
70712^333919-1840087100520Enzo Doria06/2015
7072(2^333916+1698)/2100519Stefano Morozzi09/2020
70732^333911+72623100518Enzo Doria04/2016
707424605^12168+12168^24605100517Hans Havermann08/2018
707566*10^100502+7100504Robert Price07/2020
707618^80064-67100503Lelio R Paula10/2016
7077(13*10^100487+137)/3100488Robert Price06/2021
70785^143742-48100472Lelio R Paula10/2016
707924095^14784+14784^24095100472Hans Havermann08/2018
70802^333757-112123100471Enzo Doria06/2014
7081(7953^25759-1)/7952100470Serge Batalov06/2022
70827*10^100457-57100458Robert Price06/2020
708327358^4693+4693^27358100444Hans Havermann07/2018
70848*10^100439-51100440Robert Price08/2019
70852^333603-108861100425Enzo Doria03/2014
70869*7^118818-2100414Lelio R Paula11/2014
70872^333546-17097100408Enzo Doria05/2013
708817^81597+72100401Lelio R Paula10/2016
7089(3613^28219-1)/3612100396Serge Batalov06/2022
7090p(20559)#/2+8100384Robert Price01/2017
709111^96390-24100380Lelio R Paula10/2016
7092(2^333385+2730)/2100359Stefano Morozzi09/2020
70934832563059*2^333333+30029100353Donovan Johnson01/2008
709423565^18136+18136^23565100353Hans Havermann07/2018
70952^333354+763100350Lelio R Paula08/2011
7096(25*10^100343-67)/3100344Robert Price06/2019
70972^333289-109483100330Enzo Doria04/2014
70982^333240-2790209100316Enzo Doria03/2016
709923601^17798+17798^23601100314Hans Havermann05/2018
7101(2^333227-2^166614+1)/510031111/2006
71002^333225+719100311Lelio R Paula08/2011
71022^333221-2785333100310Enzo Doria10/2015
710376^53332-75100308Norbert Schneider02/2015
7104(29*10^100302+583)/9100303Robert Price06/2021
71056^128892-17573100298Enzo Doria03/2013
7106(47*10^100283-119)/9100284Robert Price05/2019
71072^333105-113215100275Enzo Doria07/2014
7108(31*2^333102+1)/2375100272Lelio R Paula11/2013
71094*10^100257-83100258Robert Price10/2018
711017^81476-74100253Lelio R Paula10/2016
711123392^19207+19207^23392100199Hans Havermann06/2018
7112(2^332830+750)/2100192Stefano Morozzi09/2020
7113(206*10^100189-17)/9100191Robert Price01/2020
711417^81417-16100180Theodore Burton11/2005
7115(2^332773+590)/2100175Stefano Morozzi09/2020
71162^332739-113215100165Enzo Doria07/2014
71172^332730-1865621100162Enzo Doria03/2016
711891^51127-2100160Lelio R Paula09/2013
711915^85159-32100155Lelio R Paula10/2016
71206^128661+97100118Lelio R Paula10/2016
712119^78285+40100108Lelio R Paula07/2016
71226^128640+5100102Lelio R Paula11/2014
712310^100095-400001100095Robert Price09/2021
712422779^22970-22970^22779100093Norbert Schneider08/2020
7125(2^332468+3130)/2100083Stefano Morozzi09/2020
7126(14*10^100075+61)/3100076Robert Price12/2018
7127(2^332435+3098)/2100073Stefano Morozzi09/2020
712828562^3189+3189^28562100072Hans Havermann05/2018
71296^128565-127100044Lelio R Paula08/2016
7130(2^332317+2106)/2100038Stefano Morozzi09/2020
71312^332309-133100035Lelio R Paula02/2011
71322^332307+731100035Lelio R Paula07/2011
71332^332301+12927100033Lelio R Paula04/2013
713423406^18781+18781^23406100031Hans Havermann04/2018
71352^332277-4573100026Yves Minet03/2019
713612^92684-13100023Lelio R Paula07/2016
713778557*2^332193+55669100005Jorge Menendez04/2019
713878557*2^332192+72689100005Jorge Menendez04/2019
713910^100003+45799100004Stefano Morozzi04/2019
714010^100003+155461100004Stefano Morozzi04/2019
714110^100003+211389100004Stefano Morozzi04/2019
714210^100003+381027100004Stefano Morozzi04/2019
714310^100003+540703100004Stefano Morozzi04/2019
714410^100003+823977100004Stefano Morozzi04/2019
715610^100002+236023100003Stefano Morozzi05/2018
715710^100002+433741100003Stefano Morozzi05/2018
71452^332202+104659100003Stefano Morozzi04/2019
71462^332202+857539100003Stefano Morozzi04/2019
71472^332202+181773100003Stefano Morozzi04/2019
71482^332202+687543100003Stefano Morozzi04/2019
71492^332202+941595100003Stefano Morozzi04/2019
71502^332202+445813100003Stefano Morozzi04/2019
71512^332202+1599727100003Stefano Morozzi04/2019
71522^332202+1389567100003Stefano Morozzi04/2019
71532^332202+1206315100003Stefano Morozzi04/2019
71542^332202+1958647100003Stefano Morozzi04/2019
715510^100003-562857100003Patrick De Geest07/2019
7158(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
7159(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
716010^100002-249519100002Patrick De Geest07/2018
716110^100001+314199100002Patrick De Geest07/2018
718110^100000+3938473100001Robert Price05/2015
718210^100000+3979761100001Robert Price05/2015
718310^100000+4293973100001Robert Price09/2015
717810^100000+4858267100001Robert Price12/2015
717910^100000+5113299100001Robert Price02/2016
718010^100000+5169411100001Robert Price02/2016
717010^100000+5354043100001Robert Price05/2016
717110^100000+5717979100001Robert Price05/2016
717210^100000+6080631100001Robert Price07/2016
717310^100000+6308469100001Robert Price07/2016
717410^100000+6512023100001Robert Price08/2016
717510^100000+6596557100001Robert Price08/2016
717610^100000+7115409100001Robert Price10/2016
717710^100000+7235803100001Robert Price10/2016
718410^100000+7867333100001Robert Price12/2016
718510^100000+8743093100001Robert Price02/2017
718610^100000+8955391100001Robert Price03/2017
718710^100000+9180019100001Robert Price03/2017
718810^100000+9225987100001Robert Price04/2017
718910^100000+9265587100001Robert Price04/2017
719010^100000+9287049100001Robert Price04/2017
719110^100000+9425053100001Robert Price05/2017
719210^100000+9450769100001Robert Price05/2017
719310^100000+9528747100001Robert Smith05/2017
719410^100000+9548071100001Robert Price06/2017
719510^100000+10064287100001Robert Price08/2017
719610^100000+10229569100001Robert Price10/2017
716210^100000+11187931100001Robert Price03/2018
716310^100000+11264721100001Robert Price04/2018
716410^100000+11477661100001Robert Price05/2018
716510^100000+11644653100001Robert Price07/2018
716610^100001-431439100001Patrick De Geest07/2018
716710^100000+11769399100001Robert Price08/2018
716810^100000+11848159100001Robert Price08/2018
716910^100000+11863467100001Robert Price08/2018
719710^100000+11992051100001Robert Price09/2018
71982^332196-1-2*29696100001Matt Stath11/2018
719910^100000+12363957100001Robert Price11/2018
72002^332196+1+2*17152100001Matt Stath12/2018
720110^100000+12778033100001Robert Price02/2019
720210^100000+13581679100001Robert Price05/2019
720310^100000+13613199100001Robert Price05/2019
720410^100000+13752327100001Robert Price05/2019
720510^100000+14139243100001Robert Price06/2019
720610^100000+14151057100001Robert Price06/2019
720710^100000+14218923100001Robert Price06/2019
723210^100000+19956229100001Robert Price09/2020
723310^100000+3*(10^37093-1)/9*10^31454+1100001Makoto Morimoto09/2020
723410^100000+4*(10^36149-1)/9*10^31926+1100001Makoto Morimoto09/2020
723510^100000+6*(10^41029-1)/9*10^29486+1100001Makoto Morimoto09/2020
723610^100000+7*(10^55505-1)/9*10^22248+1100001Makoto Morimoto09/2020
723710^100000+20234607100001Robert Price10/2020
723810^100000+20752303100001Robert Price11/2020
723910^100000+20774041100001Robert Price11/2020
724010^100000+20854741100001Robert Price11/2020
724110^100000+20908917100001Robert Price11/2020
724210^100000+20994793100001Robert Price11/2020
724310^100000+21354249100001Robert Price12/2020
724410^100000+21455559100001Robert Price12/2020
724510^100000+21538873100001Robert Price12/2020
724610^100000+21830901100001Robert Price01/2021
724710^100000+21842629100001Robert Price01/2021
724810^100000+21930861100001Robert Price01/2021
724910^100000+22092943100001Robert Price03/2021
725010^100000+22278417100001Robert Price03/2021
720810^100000+24543147100001Robert Price08/2021
720910^100000+24781659100001Robert Price08/2021
721010^100000+24906153100001Robert Price08/2021
721110^100000+25682679100001Robert Price10/2021
721210^100000+25905301100001Robert Price10/2021
721310^100000+25923967100001Robert Price10/2021
721410^100000+26061691100001Robert Price10/2021
721510^100000+26173351100001Robert Price11/2021
721610^100000+26673487100001Robert Price11/2021
721710^100000+26849359100001Robert Price12/2021
721810^100000+26893887100001Robert Price12/2021
721910^100000+26954551100001Robert Price12/2021
722010^100000+27024543100001Robert Price12/2021
722110^100000+27060877100001Robert Price12/2021
722210^100000+27617577100001Robert Price03/2022
722310^100000+27869671100001Robert Price03/2022
722410^100000+27956481100001Robert Price03/2022
722510^100000+28078261100001Robert Price03/2022
722610^100000+28150203100001Robert Price03/2022
722710^100000+28626021100001Robert Price05/2022
722810^100000+28649299100001Robert Price05/2022
722910^100000+29409799100001Robert Price06/2022
723010^100000+29415577100001Robert Price06/2022
723110^100000+29424201100001Robert Price06/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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