PRP Records

Probable Primes Top 10000

(294613 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 ?
875113^90809-96101157Lelio R Paula10/2016
875226199^7258+7258^26199101150Hans Havermann11/2018
875319^79098-30101147Lelio R Paula10/2016
875419^79095+88101144Lelio R Paula10/2016
8755(30826*34^66040-59)/11101143Eric Chen03/2023
875612401^24702-24702^12401101117Norbert Schneider07/2022
875715^85976+32101116Lelio R Paula10/2016
87582^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
8759(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
8760(4^167933+17)/3101106Robert Price02/2017
87612^335858+153101104Lelio R Paula10/2009
8762(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
8763(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
8764(2^335839+2114)/2101098Stefano Morozzi09/2020
8765(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
87676^129918-35101096Lelio R Paula10/2016
8766(2*10^101096-107)/3101096Robert Price11/2020
87683^211885-70101095Lelio R Paula09/2016
8769(29*2^335835-1)/550599101093Lelio R Paula03/2014
8770(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
87712^335818-20033101092Enzo Doria06/2013
87722^335813-110083101090Enzo Doria04/2014
87732^335804+2155101088Lelio R Paula09/2016
8774(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
87752^335784-16145101082Enzo Doria04/2013
877611^97051+62101069Lelio R Paula10/2016
87773*10^101065+11101066Robert Price07/2018
877827820^4293+4293^27820101064Hans Havermann10/2018
8779(2^335714+3750)/2101060Stefano Morozzi01/2021
8780(2^335690+1038)/2101053Stefano Morozzi09/2020
8781(2^335691-3)/26515101049Lelio R Paula12/2013
87822^335658-94395101044Lelio R Paula09/2016
878324514^13215+13215^24514101024Hans Havermann11/2018
87842^335586+169101022Lelio R Paula10/2009
8785(56^57787-1)/55101021Paul Bourdelais08/2017
8786(2^335562+1258)/2101014Stefano Morozzi09/2020
87872^335541+4849845101008Paul Bourdelais04/2022
8788(38*10^100999+169)/9101000Robert Price11/2021
8789(19*10^100997+737)/9100998Robert Price07/2018
879047599!2+1024100991Robert Price02/2015
87912^335468-18629100986Enzo Doria05/2013
87922^335454-20961100982Enzo Doria06/2013
8793(2^335454+3258)/2100982Stefano Morozzi02/2021
879410^100978+61100979Lelio R Paula09/2016
879510^100978-156437100978Patrick De Geest11/2016
8796(2^335422+3114)/2100972Stefano Morozzi09/2020
8797(35*10^100970-89)/9100971Robert Price02/2022
8798(15*2^335417+1)/481100970Lelio R Paula12/2013
87992^335403-1859167100967Enzo Doria03/2016
880023599^18976+18976^23599100962Hans Havermann10/2018
88016*10^100958+43100959Robert Price07/2020
88029*2^335364-5100956Lelio R Paula08/2014
8803(7998^25867-1)/7997100955Serge Batalov06/2022
88042^335349+72287100951Enzo Doria04/2016
88052^335329+16095100945Lelio R Paula09/2016
8806232823#+233663100937Makoto Morimoto10/2017
8807(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
88082^335237-20893100917Enzo Doria06/2013
88092^335222-19337100912Enzo Doria05/2013
88102^335222-109985100912Enzo Doria04/2014
88112^335182-17237100900Enzo Doria05/2013
8812(2^335107+1634)/2100877Stefano Morozzi09/2020
88132^335043-16737100858Enzo Doria05/2013
8814(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
88152^335038-20633100857Enzo Doria06/2013
88162^335031+1873373100855Enzo Doria06/2016
881723489^19650+19650^23489100847Hans Havermann10/2018
88183^211354-8816100842Enzo Doria05/2014
88192^334984-112757100841Enzo Doria06/2014
8820(746*10^100827+1)/9100829Robert Price03/2020
882129451^2648+2648^29451100809Hans Havermann09/2018
882225583^8716+8716^25583100806Hans Havermann08/2018
88242^334857+48527100803Lelio R Paula08/2011
882312^93406+29100803Lelio R Paula10/2016
882528780^3179+3179^28780100796Hans Havermann09/2018
8826(5*2^334825+1)/47100792Lelio R Paula12/2013
8827(328^40063-1)/327100791Serge Batalov06/2022
88282^334809-13100788Lelio R Paula04/2011
8829(3552^28387-1)/3551100784Serge Batalov06/2022
8830(82*10^100780-1)/9100781Robert Price12/2014
883131395^1622+1622^31395100780Hans Havermann09/2018
8832(2^334779+47)/5100778Lelio R Paula12/2013
88332^334751+2049100771Lelio R Paula09/2016
883413^90443-98100749Lelio R Paula10/2016
8835(2^334674+3190)/2100747Stefano Morozzi09/2020
8836(2^334651+1050)/2100740Stefano Morozzi09/2020
8837(7*10^100737+71)/3100738Robert Price05/2018
8838(24737*2^334628+1)/3100737Lelio R Paula07/2014
883915^85639-28100720Lelio R Paula10/2016
884027068^5259+5259^27068100718Hans Havermann08/2018
88412^334562+577294575100711Lelio R Paula09/2016
88424*3^211077-5100710Lelio R Paula08/2014
88432^334524+145100702Lelio R Paula07/2009
8844(2^334451+714)/2100680Stefano Morozzi09/2020
884527648^4375+4375^27648100666Hans Havermann09/2018
8846(1017*2^334391-1)/3535100662Lelio R Paula05/2015
8847(2^334309+3122)/2100637Stefano Morozzi09/2020
88482^334294-113111100633Enzo Doria07/2014
884925581^8582+8582^25581100626Hans Havermann08/2018
88516^129308-17723100622Enzo Doria03/2013
8850(19*10^100627+287)/9/292157100622Alfred Reich11/2022
88526^129305+95100619Lelio R Paula10/2016
88532^334244-1167100618Lelio R Paula09/2016
8854(2^334233+3066)/2100614Stefano Morozzi09/2020
8855(76*10^100611+77)/9100612Robert Price10/2019
88567*10^100606-93100607Robert Price08/2020
8857(26*10^100566+49)/3100567Robert Price08/2019
8858(21*2^334050+1)/935100558Lelio R Paula12/2013
885924885^10984+10984^24885100555Hans Havermann07/2018
8860(1351^32119-1)/1350100551Serge Batalov06/2022
8861(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
8862(35*10^100542+1)/9100543Serge Batalov11/2010
886323578^18367+18367^23578100538Hans Havermann07/2018
886413^90251+24100535Lelio R Paula10/2016
88652^333963+789100533Lelio R Paula08/2011
88662^333919-1840087100520Enzo Doria06/2015
8867(2^333916+1698)/2100519Stefano Morozzi09/2020
88682^333911+72623100518Enzo Doria04/2016
886924605^12168+12168^24605100517Hans Havermann08/2018
887066*10^100502+7100504Robert Price07/2020
887118^80064-67100503Lelio R Paula10/2016
8872(13*10^100487+137)/3100488Robert Price06/2021
88735^143742-48100472Lelio R Paula10/2016
887424095^14784+14784^24095100472Hans Havermann08/2018
88752^333757-112123100471Enzo Doria06/2014
8876(7953^25759-1)/7952100470Serge Batalov06/2022
88777*10^100457-57100458Robert Price06/2020
887827358^4693+4693^27358100444Hans Havermann07/2018
88798*10^100439-51100440Robert Price08/2019
88802^333603-108861100425Enzo Doria03/2014
88819*7^118818-2100414Lelio R Paula11/2014
88822^333546-17097100408Enzo Doria05/2013
8883(19*10^100403+287)/9/3100403Alfred Reich11/2022
888417^81597+72100401Lelio R Paula10/2016
8885(3613^28219-1)/3612100396Serge Batalov06/2022
8886p(20559)#/2+8100384Robert Price01/2017
888711^96390-24100380Lelio R Paula10/2016
8888(2^333385+2730)/2100359Stefano Morozzi09/2020
88894832563059*2^333333+30029100353Donovan Johnson01/2008
889023565^18136+18136^23565100353Hans Havermann07/2018
88912^333354+763100350Lelio R Paula08/2011
8892(1608961*2^333333+1)/3100349Alex_soldier09/2022
8893(424517*2^333333+1)/5100349Alex_soldier09/2022
8894(887087*2^333333+1)/5100349Alex_soldier09/2022
8895(1159703*2^333333+1)/7100349Alex_soldier09/2022
8896(25*10^100343-67)/3100344Robert Price06/2019
88972^333289-109483100330Enzo Doria04/2014
88982^333240-2790209100316Enzo Doria03/2016
889923601^17798+17798^23601100314Hans Havermann05/2018
8901(2^333227-2^166614+1)/510031111/2006
89002^333225+719100311Lelio R Paula08/2011
89022^333221-2785333100310Enzo Doria10/2015
890376^53332-75100308Norbert Schneider02/2015
8904(29*10^100302+583)/9100303Robert Price06/2021
89056^128892-17573100298Enzo Doria03/2013
8906(47*10^100283-119)/9100284Robert Price05/2019
89072^333105-113215100275Enzo Doria07/2014
8908(31*2^333102+1)/2375100272Lelio R Paula11/2013
89094*10^100257-83100258Robert Price10/2018
891017^81476-74100253Lelio R Paula10/2016
891123392^19207+19207^23392100199Hans Havermann06/2018
8912(2^332830+750)/2100192Stefano Morozzi09/2020
8913(206*10^100189-17)/9100191Robert Price01/2020
891417^81417-16100180Theodore Burton11/2005
8915(2^332773+590)/2100175Stefano Morozzi09/2020
89162*23^73562+215100172Eric Chen08/2023
89172^332739-113215100165Enzo Doria07/2014
89182^332730-1865621100162Enzo Doria03/2016
891991^51127-2100160Lelio R Paula09/2013
892015^85159-32100155Lelio R Paula10/2016
89216^128661+97100118Lelio R Paula10/2016
892219^78285+40100108Lelio R Paula07/2016
89236^128640+5100102Lelio R Paula11/2014
892410^100095+89973100096Patrick De Geest10/2022
892510^100095-400001100095Robert Price09/2021
892610^100095-203693100095Patrick De Geest10/2022
892722779^22970-22970^22779100093Norbert Schneider08/2020
8928(2^332468+3130)/2100083Stefano Morozzi09/2020
8929(14*10^100075+61)/3100076Robert Price12/2018
8930(2^332435+3098)/2100073Stefano Morozzi09/2020
893128562^3189+3189^28562100072Hans Havermann05/2018
89326^128565-127100044Lelio R Paula08/2016
8933(2^332317+2106)/2100038Stefano Morozzi09/2020
89352^332309-133100035Lelio R Paula02/2011
89362^332307+731100035Lelio R Paula07/2011
8934937^33662-33662^937100035Norbert Schneider05/2023
89372^332301+12927100033Lelio R Paula04/2013
893823406^18781+18781^23406100031Hans Havermann04/2018
89392^332277-4573100026Yves Minet03/2019
894012^92684-13100023Lelio R Paula07/2016
894170^54207-54207^70100018Norbert Schneider04/2023
894278557*2^332193+55669100005Jorge Menendez04/2019
894378557*2^332192+72689100005Jorge Menendez04/2019
894410^100003+45799100004Stefano Morozzi04/2019
894510^100003+155461100004Stefano Morozzi04/2019
894610^100003+211389100004Stefano Morozzi04/2019
894710^100003+381027100004Stefano Morozzi04/2019
894810^100003+540703100004Stefano Morozzi04/2019
894910^100003+823977100004Stefano Morozzi04/2019
896110^100002+236023100003Stefano Morozzi05/2018
896210^100002+433741100003Stefano Morozzi05/2018
89502^332202+104659100003Stefano Morozzi04/2019
89512^332202+857539100003Stefano Morozzi04/2019
89522^332202+181773100003Stefano Morozzi04/2019
89532^332202+687543100003Stefano Morozzi04/2019
89542^332202+941595100003Stefano Morozzi04/2019
89552^332202+445813100003Stefano Morozzi04/2019
89562^332202+1599727100003Stefano Morozzi04/2019
89572^332202+1389567100003Stefano Morozzi04/2019
89582^332202+1206315100003Stefano Morozzi04/2019
89592^332202+1958647100003Stefano Morozzi04/2019
896010^100003-562857100003Patrick De Geest07/2019
8963(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
8964(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
896510^100002-249519100002Patrick De Geest07/2018
896610^100001+314199100002Patrick De Geest07/2018
898610^100000+3938473100001Robert Price05/2015
898710^100000+3979761100001Robert Price05/2015
898810^100000+4293973100001Robert Price09/2015
898310^100000+4858267100001Robert Price12/2015
898410^100000+5113299100001Robert Price02/2016
898510^100000+5169411100001Robert Price02/2016
897510^100000+5354043100001Robert Price05/2016
897610^100000+5717979100001Robert Price05/2016
897710^100000+6080631100001Robert Price07/2016
897810^100000+6308469100001Robert Price07/2016
897910^100000+6512023100001Robert Price08/2016
898010^100000+6596557100001Robert Price08/2016
898110^100000+7115409100001Robert Price10/2016
898210^100000+7235803100001Robert Price10/2016
899210^100000+7867333100001Robert Price12/2016
899310^100000+8743093100001Robert Price02/2017
899410^100000+8955391100001Robert Price03/2017
899510^100000+9180019100001Robert Price03/2017
899610^100000+9225987100001Robert Price04/2017
899710^100000+9265587100001Robert Price04/2017
899810^100000+9287049100001Robert Price04/2017
899910^100000+9425053100001Robert Price05/2017
900010^100000+9450769100001Robert Price05/2017
896710^100000+11187931100001Robert Price03/2018
896810^100000+11264721100001Robert Price04/2018
896910^100000+11477661100001Robert Price05/2018
897010^100000+11644653100001Robert Price07/2018
897110^100001-431439100001Patrick De Geest07/2018
897210^100000+11769399100001Robert Price08/2018
897310^100000+11848159100001Robert Price08/2018
897410^100000+11863467100001Robert Price08/2018
898910^100000+11992051100001Robert Price09/2018
89902^332196-1-2*29696100001Matt Stath11/2018
899110^100000+12363957100001Robert Price11/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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