PRP Records

Probable Primes Top 10000

(291192 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 ?
72512^336112-1865249101180Enzo Doria03/2016
72522^336103-109015101178Enzo Doria04/2014
7253(2^336095+2078)/2101175Stefano Morozzi09/2020
725413^90809-96101157Lelio R Paula10/2016
725526199^7258+7258^26199101150Hans Havermann11/2018
725619^79098-30101147Lelio R Paula10/2016
725719^79095+88101144Lelio R Paula10/2016
725812401^24702-24702^12401101117Norbert Schneider07/2022
725915^85976+32101116Lelio R Paula10/2016
72602^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
7261(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
7262(4^167933+17)/3101106Robert Price02/2017
72632^335858+153101104Lelio R Paula10/2009
7264(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
7265(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
7266(2^335839+2114)/2101098Stefano Morozzi09/2020
7267(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
72696^129918-35101096Lelio R Paula10/2016
7268(2*10^101096-107)/3101096Robert Price11/2020
72703^211885-70101095Lelio R Paula09/2016
7271(29*2^335835-1)/550599101093Lelio R Paula03/2014
7272(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
72732^335818-20033101092Enzo Doria06/2013
72742^335813-110083101090Enzo Doria04/2014
72752^335804+2155101088Lelio R Paula09/2016
7276(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
72772^335784-16145101082Enzo Doria04/2013
727811^97051+62101069Lelio R Paula10/2016
72793*10^101065+11101066Robert Price07/2018
728027820^4293+4293^27820101064Hans Havermann10/2018
7281(2^335714+3750)/2101060Stefano Morozzi01/2021
7282(2^335690+1038)/2101053Stefano Morozzi09/2020
7283(2^335691-3)/26515101049Lelio R Paula12/2013
72842^335658-94395101044Lelio R Paula09/2016
728524514^13215+13215^24514101024Hans Havermann11/2018
72862^335586+169101022Lelio R Paula10/2009
7287(56^57787-1)/55101021Paul Bourdelais08/2017
7288(2^335562+1258)/2101014Stefano Morozzi09/2020
72892^335541+4849845101008Paul Bourdelais04/2022
7290(38*10^100999+169)/9101000Robert Price11/2021
7291(19*10^100997+737)/9100998Robert Price07/2018
729247599!2+1024100991Robert Price02/2015
72932^335468-18629100986Enzo Doria05/2013
72942^335454-20961100982Enzo Doria06/2013
7295(2^335454+3258)/2100982Stefano Morozzi02/2021
729610^100978+61100979Lelio R Paula09/2016
729710^100978-156437100978Patrick De Geest11/2016
7298(2^335422+3114)/2100972Stefano Morozzi09/2020
7299(35*10^100970-89)/9100971Robert Price02/2022
7300(15*2^335417+1)/481100970Lelio R Paula12/2013
73012^335403-1859167100967Enzo Doria03/2016
730223599^18976+18976^23599100962Hans Havermann10/2018
73036*10^100958+43100959Robert Price07/2020
73049*2^335364-5100956Lelio R Paula08/2014
7305(7998^25867-1)/7997100955Serge Batalov06/2022
73062^335349+72287100951Enzo Doria04/2016
73072^335329+16095100945Lelio R Paula09/2016
7308232823#+233663100937Makoto Morimoto10/2017
7309(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
73102^335237-20893100917Enzo Doria06/2013
73112^335222-19337100912Enzo Doria05/2013
73122^335222-109985100912Enzo Doria04/2014
73132^335182-17237100900Enzo Doria05/2013
7314(2^335107+1634)/2100877Stefano Morozzi09/2020
73152^335043-16737100858Enzo Doria05/2013
7316(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
73172^335038-20633100857Enzo Doria06/2013
73182^335031+1873373100855Enzo Doria06/2016
731923489^19650+19650^23489100847Hans Havermann10/2018
73203^211354-8816100842Enzo Doria05/2014
73212^334984-112757100841Enzo Doria06/2014
7322(746*10^100827+1)/9100829Robert Price03/2020
732329451^2648+2648^29451100809Hans Havermann09/2018
732425583^8716+8716^25583100806Hans Havermann08/2018
73262^334857+48527100803Lelio R Paula08/2011
732512^93406+29100803Lelio R Paula10/2016
732728780^3179+3179^28780100796Hans Havermann09/2018
7328(5*2^334825+1)/47100792Lelio R Paula12/2013
7329(328^40063-1)/327100791Serge Batalov06/2022
73302^334809-13100788Lelio R Paula04/2011
7331(3552^28387-1)/3551100784Serge Batalov06/2022
7332(82*10^100780-1)/9100781Robert Price12/2014
733331395^1622+1622^31395100780Hans Havermann09/2018
7334(2^334779+47)/5100778Lelio R Paula12/2013
73352^334751+2049100771Lelio R Paula09/2016
733613^90443-98100749Lelio R Paula10/2016
7337(2^334674+3190)/2100747Stefano Morozzi09/2020
7338(2^334651+1050)/2100740Stefano Morozzi09/2020
7339(7*10^100737+71)/3100738Robert Price05/2018
7340(24737*2^334628+1)/3100737Lelio R Paula07/2014
734115^85639-28100720Lelio R Paula10/2016
734227068^5259+5259^27068100718Hans Havermann08/2018
73432^334562+577294575100711Lelio R Paula09/2016
73444*3^211077-5100710Lelio R Paula08/2014
73452^334524+145100702Lelio R Paula07/2009
7346(2^334451+714)/2100680Stefano Morozzi09/2020
734727648^4375+4375^27648100666Hans Havermann09/2018
7348(1017*2^334391-1)/3535100662Lelio R Paula05/2015
7349(2^334309+3122)/2100637Stefano Morozzi09/2020
73502^334294-113111100633Enzo Doria07/2014
735125581^8582+8582^25581100626Hans Havermann08/2018
73526^129308-17723100622Enzo Doria03/2013
73536^129305+95100619Lelio R Paula10/2016
73542^334244-1167100618Lelio R Paula09/2016
7355(2^334233+3066)/2100614Stefano Morozzi09/2020
7356(76*10^100611+77)/9100612Robert Price10/2019
73577*10^100606-93100607Robert Price08/2020
7358(26*10^100566+49)/3100567Robert Price08/2019
7359(21*2^334050+1)/935100558Lelio R Paula12/2013
736024885^10984+10984^24885100555Hans Havermann07/2018
7361(1351^32119-1)/1350100551Serge Batalov06/2022
7362(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
7363(35*10^100542+1)/9100543Serge Batalov11/2010
736423578^18367+18367^23578100538Hans Havermann07/2018
736513^90251+24100535Lelio R Paula10/2016
73662^333963+789100533Lelio R Paula08/2011
73672^333919-1840087100520Enzo Doria06/2015
7368(2^333916+1698)/2100519Stefano Morozzi09/2020
73692^333911+72623100518Enzo Doria04/2016
737024605^12168+12168^24605100517Hans Havermann08/2018
737166*10^100502+7100504Robert Price07/2020
737218^80064-67100503Lelio R Paula10/2016
7373(13*10^100487+137)/3100488Robert Price06/2021
73745^143742-48100472Lelio R Paula10/2016
737524095^14784+14784^24095100472Hans Havermann08/2018
73762^333757-112123100471Enzo Doria06/2014
7377(7953^25759-1)/7952100470Serge Batalov06/2022
73787*10^100457-57100458Robert Price06/2020
737927358^4693+4693^27358100444Hans Havermann07/2018
73808*10^100439-51100440Robert Price08/2019
73812^333603-108861100425Enzo Doria03/2014
73829*7^118818-2100414Lelio R Paula11/2014
73832^333546-17097100408Enzo Doria05/2013
738417^81597+72100401Lelio R Paula10/2016
7385(3613^28219-1)/3612100396Serge Batalov06/2022
7386p(20559)#/2+8100384Robert Price01/2017
738711^96390-24100380Lelio R Paula10/2016
7388(2^333385+2730)/2100359Stefano Morozzi09/2020
73894832563059*2^333333+30029100353Donovan Johnson01/2008
739023565^18136+18136^23565100353Hans Havermann07/2018
73912^333354+763100350Lelio R Paula08/2011
7392(25*10^100343-67)/3100344Robert Price06/2019
73932^333289-109483100330Enzo Doria04/2014
73942^333240-2790209100316Enzo Doria03/2016
739523601^17798+17798^23601100314Hans Havermann05/2018
7397(2^333227-2^166614+1)/510031111/2006
73962^333225+719100311Lelio R Paula08/2011
73982^333221-2785333100310Enzo Doria10/2015
739976^53332-75100308Norbert Schneider02/2015
7400(29*10^100302+583)/9100303Robert Price06/2021
74016^128892-17573100298Enzo Doria03/2013
7402(47*10^100283-119)/9100284Robert Price05/2019
74032^333105-113215100275Enzo Doria07/2014
7404(31*2^333102+1)/2375100272Lelio R Paula11/2013
74054*10^100257-83100258Robert Price10/2018
740617^81476-74100253Lelio R Paula10/2016
740723392^19207+19207^23392100199Hans Havermann06/2018
7408(2^332830+750)/2100192Stefano Morozzi09/2020
7409(206*10^100189-17)/9100191Robert Price01/2020
741017^81417-16100180Theodore Burton11/2005
7411(2^332773+590)/2100175Stefano Morozzi09/2020
74122^332739-113215100165Enzo Doria07/2014
74132^332730-1865621100162Enzo Doria03/2016
741491^51127-2100160Lelio R Paula09/2013
741515^85159-32100155Lelio R Paula10/2016
74166^128661+97100118Lelio R Paula10/2016
741719^78285+40100108Lelio R Paula07/2016
74186^128640+5100102Lelio R Paula11/2014
741910^100095-400001100095Robert Price09/2021
742022779^22970-22970^22779100093Norbert Schneider08/2020
7421(2^332468+3130)/2100083Stefano Morozzi09/2020
7422(14*10^100075+61)/3100076Robert Price12/2018
7423(2^332435+3098)/2100073Stefano Morozzi09/2020
742428562^3189+3189^28562100072Hans Havermann05/2018
74256^128565-127100044Lelio R Paula08/2016
7426(2^332317+2106)/2100038Stefano Morozzi09/2020
74272^332309-133100035Lelio R Paula02/2011
74282^332307+731100035Lelio R Paula07/2011
74292^332301+12927100033Lelio R Paula04/2013
743023406^18781+18781^23406100031Hans Havermann04/2018
74312^332277-4573100026Yves Minet03/2019
743212^92684-13100023Lelio R Paula07/2016
743378557*2^332193+55669100005Jorge Menendez04/2019
743478557*2^332192+72689100005Jorge Menendez04/2019
743510^100003+45799100004Stefano Morozzi04/2019
743610^100003+155461100004Stefano Morozzi04/2019
743710^100003+211389100004Stefano Morozzi04/2019
743810^100003+381027100004Stefano Morozzi04/2019
743910^100003+540703100004Stefano Morozzi04/2019
744010^100003+823977100004Stefano Morozzi04/2019
745210^100002+236023100003Stefano Morozzi05/2018
745310^100002+433741100003Stefano Morozzi05/2018
74412^332202+104659100003Stefano Morozzi04/2019
74422^332202+857539100003Stefano Morozzi04/2019
74432^332202+181773100003Stefano Morozzi04/2019
74442^332202+687543100003Stefano Morozzi04/2019
74452^332202+941595100003Stefano Morozzi04/2019
74462^332202+445813100003Stefano Morozzi04/2019
74472^332202+1599727100003Stefano Morozzi04/2019
74482^332202+1389567100003Stefano Morozzi04/2019
74492^332202+1206315100003Stefano Morozzi04/2019
74502^332202+1958647100003Stefano Morozzi04/2019
745110^100003-562857100003Patrick De Geest07/2019
7454(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
7455(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
745610^100002-249519100002Patrick De Geest07/2018
745710^100001+314199100002Patrick De Geest07/2018
747710^100000+3938473100001Robert Price05/2015
747810^100000+3979761100001Robert Price05/2015
747910^100000+4293973100001Robert Price09/2015
747410^100000+4858267100001Robert Price12/2015
747510^100000+5113299100001Robert Price02/2016
747610^100000+5169411100001Robert Price02/2016
746610^100000+5354043100001Robert Price05/2016
746710^100000+5717979100001Robert Price05/2016
746810^100000+6080631100001Robert Price07/2016
746910^100000+6308469100001Robert Price07/2016
747010^100000+6512023100001Robert Price08/2016
747110^100000+6596557100001Robert Price08/2016
747210^100000+7115409100001Robert Price10/2016
747310^100000+7235803100001Robert Price10/2016
748010^100000+7867333100001Robert Price12/2016
748110^100000+8743093100001Robert Price02/2017
748210^100000+8955391100001Robert Price03/2017
748310^100000+9180019100001Robert Price03/2017
748410^100000+9225987100001Robert Price04/2017
748510^100000+9265587100001Robert Price04/2017
748610^100000+9287049100001Robert Price04/2017
748710^100000+9425053100001Robert Price05/2017
748810^100000+9450769100001Robert Price05/2017
748910^100000+9528747100001Robert Smith05/2017
749010^100000+9548071100001Robert Price06/2017
749110^100000+10064287100001Robert Price08/2017
749210^100000+10229569100001Robert Price10/2017
745810^100000+11187931100001Robert Price03/2018
745910^100000+11264721100001Robert Price04/2018
746010^100000+11477661100001Robert Price05/2018
746110^100000+11644653100001Robert Price07/2018
746210^100001-431439100001Patrick De Geest07/2018
746310^100000+11769399100001Robert Price08/2018
746410^100000+11848159100001Robert Price08/2018
746510^100000+11863467100001Robert Price08/2018
749310^100000+11992051100001Robert Price09/2018
74942^332196-1-2*29696100001Matt Stath11/2018
749510^100000+12363957100001Robert Price11/2018
74962^332196+1+2*17152100001Matt Stath12/2018
749710^100000+12778033100001Robert Price02/2019
749810^100000+13581679100001Robert Price05/2019
749910^100000+13613199100001Robert Price05/2019
750010^100000+13752327100001Robert Price05/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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