PRP Records

Probable Primes Top 10000

(291910 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 ?
77512^336350-344291101252Enzo Doria07/2015
7752(17*10^101251-161)/9101252Robert Price02/2021
7753(56*10^101222-47)/9101223Robert Price02/2019
77542^336243-108777101220Enzo Doria03/2014
7755(31*2^336189-1)/19101204Lelio R Paula03/2014
775623535^19954+19954^23535101202Hans Havermann11/2018
7757(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
77582^336150-20393101192Enzo Doria06/2013
775923996^16473+16473^23996101186Hans Havermann11/2018
77602^336112-1865249101180Enzo Doria03/2016
77612^336103-109015101178Enzo Doria04/2014
7762(2^336095+2078)/2101175Stefano Morozzi09/2020
776313^90809-96101157Lelio R Paula10/2016
776426199^7258+7258^26199101150Hans Havermann11/2018
776519^79098-30101147Lelio R Paula10/2016
776619^79095+88101144Lelio R Paula10/2016
776712401^24702-24702^12401101117Norbert Schneider07/2022
776815^85976+32101116Lelio R Paula10/2016
77692^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
7770(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
7771(4^167933+17)/3101106Robert Price02/2017
77722^335858+153101104Lelio R Paula10/2009
7773(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
7774(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
7775(2^335839+2114)/2101098Stefano Morozzi09/2020
7776(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
77786^129918-35101096Lelio R Paula10/2016
7777(2*10^101096-107)/3101096Robert Price11/2020
77793^211885-70101095Lelio R Paula09/2016
7780(29*2^335835-1)/550599101093Lelio R Paula03/2014
7781(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
77822^335818-20033101092Enzo Doria06/2013
77832^335813-110083101090Enzo Doria04/2014
77842^335804+2155101088Lelio R Paula09/2016
7785(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
77862^335784-16145101082Enzo Doria04/2013
778711^97051+62101069Lelio R Paula10/2016
77883*10^101065+11101066Robert Price07/2018
778927820^4293+4293^27820101064Hans Havermann10/2018
7790(2^335714+3750)/2101060Stefano Morozzi01/2021
7791(2^335690+1038)/2101053Stefano Morozzi09/2020
7792(2^335691-3)/26515101049Lelio R Paula12/2013
77932^335658-94395101044Lelio R Paula09/2016
779424514^13215+13215^24514101024Hans Havermann11/2018
77952^335586+169101022Lelio R Paula10/2009
7796(56^57787-1)/55101021Paul Bourdelais08/2017
7797(2^335562+1258)/2101014Stefano Morozzi09/2020
77982^335541+4849845101008Paul Bourdelais04/2022
7799(38*10^100999+169)/9101000Robert Price11/2021
7800(19*10^100997+737)/9100998Robert Price07/2018
780147599!2+1024100991Robert Price02/2015
78022^335468-18629100986Enzo Doria05/2013
78032^335454-20961100982Enzo Doria06/2013
7804(2^335454+3258)/2100982Stefano Morozzi02/2021
780510^100978+61100979Lelio R Paula09/2016
780610^100978-156437100978Patrick De Geest11/2016
7807(2^335422+3114)/2100972Stefano Morozzi09/2020
7808(35*10^100970-89)/9100971Robert Price02/2022
7809(15*2^335417+1)/481100970Lelio R Paula12/2013
78102^335403-1859167100967Enzo Doria03/2016
781123599^18976+18976^23599100962Hans Havermann10/2018
78126*10^100958+43100959Robert Price07/2020
78139*2^335364-5100956Lelio R Paula08/2014
7814(7998^25867-1)/7997100955Serge Batalov06/2022
78152^335349+72287100951Enzo Doria04/2016
78162^335329+16095100945Lelio R Paula09/2016
7817232823#+233663100937Makoto Morimoto10/2017
7818(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
78192^335237-20893100917Enzo Doria06/2013
78202^335222-19337100912Enzo Doria05/2013
78212^335222-109985100912Enzo Doria04/2014
78222^335182-17237100900Enzo Doria05/2013
7823(2^335107+1634)/2100877Stefano Morozzi09/2020
78242^335043-16737100858Enzo Doria05/2013
7825(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
78262^335038-20633100857Enzo Doria06/2013
78272^335031+1873373100855Enzo Doria06/2016
782823489^19650+19650^23489100847Hans Havermann10/2018
78293^211354-8816100842Enzo Doria05/2014
78302^334984-112757100841Enzo Doria06/2014
7831(746*10^100827+1)/9100829Robert Price03/2020
783229451^2648+2648^29451100809Hans Havermann09/2018
783325583^8716+8716^25583100806Hans Havermann08/2018
78352^334857+48527100803Lelio R Paula08/2011
783412^93406+29100803Lelio R Paula10/2016
783628780^3179+3179^28780100796Hans Havermann09/2018
7837(5*2^334825+1)/47100792Lelio R Paula12/2013
7838(328^40063-1)/327100791Serge Batalov06/2022
78392^334809-13100788Lelio R Paula04/2011
7840(3552^28387-1)/3551100784Serge Batalov06/2022
7841(82*10^100780-1)/9100781Robert Price12/2014
784231395^1622+1622^31395100780Hans Havermann09/2018
7843(2^334779+47)/5100778Lelio R Paula12/2013
78442^334751+2049100771Lelio R Paula09/2016
784513^90443-98100749Lelio R Paula10/2016
7846(2^334674+3190)/2100747Stefano Morozzi09/2020
7847(2^334651+1050)/2100740Stefano Morozzi09/2020
7848(7*10^100737+71)/3100738Robert Price05/2018
7849(24737*2^334628+1)/3100737Lelio R Paula07/2014
785015^85639-28100720Lelio R Paula10/2016
785127068^5259+5259^27068100718Hans Havermann08/2018
78522^334562+577294575100711Lelio R Paula09/2016
78534*3^211077-5100710Lelio R Paula08/2014
78542^334524+145100702Lelio R Paula07/2009
7855(2^334451+714)/2100680Stefano Morozzi09/2020
785627648^4375+4375^27648100666Hans Havermann09/2018
7857(1017*2^334391-1)/3535100662Lelio R Paula05/2015
7858(2^334309+3122)/2100637Stefano Morozzi09/2020
78592^334294-113111100633Enzo Doria07/2014
786025581^8582+8582^25581100626Hans Havermann08/2018
78626^129308-17723100622Enzo Doria03/2013
7861(19*10^100627+287)/9/292157100622Alfred Reich11/2022
78636^129305+95100619Lelio R Paula10/2016
78642^334244-1167100618Lelio R Paula09/2016
7865(2^334233+3066)/2100614Stefano Morozzi09/2020
7866(76*10^100611+77)/9100612Robert Price10/2019
78677*10^100606-93100607Robert Price08/2020
7868(26*10^100566+49)/3100567Robert Price08/2019
7869(21*2^334050+1)/935100558Lelio R Paula12/2013
787024885^10984+10984^24885100555Hans Havermann07/2018
7871(1351^32119-1)/1350100551Serge Batalov06/2022
7872(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
7873(35*10^100542+1)/9100543Serge Batalov11/2010
787423578^18367+18367^23578100538Hans Havermann07/2018
787513^90251+24100535Lelio R Paula10/2016
78762^333963+789100533Lelio R Paula08/2011
78772^333919-1840087100520Enzo Doria06/2015
7878(2^333916+1698)/2100519Stefano Morozzi09/2020
78792^333911+72623100518Enzo Doria04/2016
788024605^12168+12168^24605100517Hans Havermann08/2018
788166*10^100502+7100504Robert Price07/2020
788218^80064-67100503Lelio R Paula10/2016
7883(13*10^100487+137)/3100488Robert Price06/2021
78845^143742-48100472Lelio R Paula10/2016
788524095^14784+14784^24095100472Hans Havermann08/2018
78862^333757-112123100471Enzo Doria06/2014
7887(7953^25759-1)/7952100470Serge Batalov06/2022
78887*10^100457-57100458Robert Price06/2020
788927358^4693+4693^27358100444Hans Havermann07/2018
78908*10^100439-51100440Robert Price08/2019
78912^333603-108861100425Enzo Doria03/2014
78929*7^118818-2100414Lelio R Paula11/2014
78932^333546-17097100408Enzo Doria05/2013
7894(19*10^100403+287)/9/3100403Alfred Reich11/2022
789517^81597+72100401Lelio R Paula10/2016
7896(3613^28219-1)/3612100396Serge Batalov06/2022
7897p(20559)#/2+8100384Robert Price01/2017
789811^96390-24100380Lelio R Paula10/2016
7899(2^333385+2730)/2100359Stefano Morozzi09/2020
79004832563059*2^333333+30029100353Donovan Johnson01/2008
790123565^18136+18136^23565100353Hans Havermann07/2018
79022^333354+763100350Lelio R Paula08/2011
7903(1608961*2^333333+1)/3100349Alex_soldier09/2022
7904(424517*2^333333+1)/5100349Alex_soldier09/2022
7905(887087*2^333333+1)/5100349Alex_soldier09/2022
7906(1159703*2^333333+1)/7100349Alex_soldier09/2022
7907(25*10^100343-67)/3100344Robert Price06/2019
79082^333289-109483100330Enzo Doria04/2014
79092^333240-2790209100316Enzo Doria03/2016
791023601^17798+17798^23601100314Hans Havermann05/2018
7912(2^333227-2^166614+1)/510031111/2006
79112^333225+719100311Lelio R Paula08/2011
79132^333221-2785333100310Enzo Doria10/2015
791476^53332-75100308Norbert Schneider02/2015
7915(29*10^100302+583)/9100303Robert Price06/2021
79166^128892-17573100298Enzo Doria03/2013
7917(47*10^100283-119)/9100284Robert Price05/2019
79182^333105-113215100275Enzo Doria07/2014
7919(31*2^333102+1)/2375100272Lelio R Paula11/2013
79204*10^100257-83100258Robert Price10/2018
792117^81476-74100253Lelio R Paula10/2016
792223392^19207+19207^23392100199Hans Havermann06/2018
7923(2^332830+750)/2100192Stefano Morozzi09/2020
7924(206*10^100189-17)/9100191Robert Price01/2020
792517^81417-16100180Theodore Burton11/2005
7926(2^332773+590)/2100175Stefano Morozzi09/2020
79272^332739-113215100165Enzo Doria07/2014
79282^332730-1865621100162Enzo Doria03/2016
792991^51127-2100160Lelio R Paula09/2013
793015^85159-32100155Lelio R Paula10/2016
79316^128661+97100118Lelio R Paula10/2016
793219^78285+40100108Lelio R Paula07/2016
79336^128640+5100102Lelio R Paula11/2014
793410^100095+89973100096Patrick De Geest10/2022
793510^100095-400001100095Robert Price09/2021
793610^100095-203693100095Patrick De Geest10/2022
793722779^22970-22970^22779100093Norbert Schneider08/2020
7938(2^332468+3130)/2100083Stefano Morozzi09/2020
7939(14*10^100075+61)/3100076Robert Price12/2018
7940(2^332435+3098)/2100073Stefano Morozzi09/2020
794128562^3189+3189^28562100072Hans Havermann05/2018
79426^128565-127100044Lelio R Paula08/2016
7943(2^332317+2106)/2100038Stefano Morozzi09/2020
79442^332309-133100035Lelio R Paula02/2011
79452^332307+731100035Lelio R Paula07/2011
79462^332301+12927100033Lelio R Paula04/2013
794723406^18781+18781^23406100031Hans Havermann04/2018
79482^332277-4573100026Yves Minet03/2019
794912^92684-13100023Lelio R Paula07/2016
795078557*2^332193+55669100005Jorge Menendez04/2019
795178557*2^332192+72689100005Jorge Menendez04/2019
795210^100003+45799100004Stefano Morozzi04/2019
795310^100003+155461100004Stefano Morozzi04/2019
795410^100003+211389100004Stefano Morozzi04/2019
795510^100003+381027100004Stefano Morozzi04/2019
795610^100003+540703100004Stefano Morozzi04/2019
795710^100003+823977100004Stefano Morozzi04/2019
796910^100002+236023100003Stefano Morozzi05/2018
797010^100002+433741100003Stefano Morozzi05/2018
79582^332202+104659100003Stefano Morozzi04/2019
79592^332202+857539100003Stefano Morozzi04/2019
79602^332202+181773100003Stefano Morozzi04/2019
79612^332202+687543100003Stefano Morozzi04/2019
79622^332202+941595100003Stefano Morozzi04/2019
79632^332202+445813100003Stefano Morozzi04/2019
79642^332202+1599727100003Stefano Morozzi04/2019
79652^332202+1389567100003Stefano Morozzi04/2019
79662^332202+1206315100003Stefano Morozzi04/2019
79672^332202+1958647100003Stefano Morozzi04/2019
796810^100003-562857100003Patrick De Geest07/2019
7971(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
7972(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
797310^100002-249519100002Patrick De Geest07/2018
797410^100001+314199100002Patrick De Geest07/2018
799410^100000+3938473100001Robert Price05/2015
799510^100000+3979761100001Robert Price05/2015
799610^100000+4293973100001Robert Price09/2015
799110^100000+4858267100001Robert Price12/2015
799210^100000+5113299100001Robert Price02/2016
799310^100000+5169411100001Robert Price02/2016
798310^100000+5354043100001Robert Price05/2016
798410^100000+5717979100001Robert Price05/2016
798510^100000+6080631100001Robert Price07/2016
798610^100000+6308469100001Robert Price07/2016
798710^100000+6512023100001Robert Price08/2016
798810^100000+6596557100001Robert Price08/2016
798910^100000+7115409100001Robert Price10/2016
799010^100000+7235803100001Robert Price10/2016
799710^100000+7867333100001Robert Price12/2016
799810^100000+8743093100001Robert Price02/2017
799910^100000+8955391100001Robert Price03/2017
800010^100000+9180019100001Robert Price03/2017
797510^100000+11187931100001Robert Price03/2018
797610^100000+11264721100001Robert Price04/2018
797710^100000+11477661100001Robert Price05/2018
797810^100000+11644653100001Robert Price07/2018
797910^100001-431439100001Patrick De Geest07/2018
798010^100000+11769399100001Robert Price08/2018
798110^100000+11848159100001Robert Price08/2018
798210^100000+11863467100001Robert Price08/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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