PRP Records

Probable Primes Top 10000

(271067 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 ?
80022^263032+8751779181Yves Minet11/2010
80016^101755+9579181Lelio R Paula03/2015
8003(2^263010+1738)/279174Stefano Morozzi01/2020
80044^131497-3^13149779170Jean-Louis Charton05/2004
80055*7^93674+879165Lelio R Paula10/2014
8006(2^262939+1326)/279153Stefano Morozzi01/2020
8007(2^262941+926)/279153Stefano Morozzi01/2020
8008lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
8009260^32768+179^3276879134Serge Batalov03/2018
801011^75978-4279123Lelio R Paula02/2015
80118*5^113180+979111Lelio R Paula10/2014
8012(2^262757+3222)/279098Stefano Morozzi01/2020
8013(6883*2^262741-1)/483579094Lelio R Paula04/2015
8014(9*2^262745+1)/13779093Lelio R Paula10/2012
801512^73285+8579088Lelio R Paula02/2015
801619^61840+5279079Lelio R Paula03/2015
8018(10^79067+77)/379067Robert Price01/2017
8017(2^262655+678)/279067Stefano Morozzi01/2020
8019(1017*2^262640-1)/1155779062Lelio R Paula04/2015
8020(2^262634+1674)/279061Stefano Morozzi01/2020
802110^79040+13794979041Patrick De Geest02/2016
802310^79040-100729779040Robert Price02/2015
802210^79040-7742779040Patrick De Geest02/2016
80242^262551-1729579036Lelio R Paula07/2013
8025(22973^18121-1)/2297279026Serge Batalov08/2020
80263^165597+34079010Lelio R Paula02/2015
802719620^10633+10633^1962079003Hans Havermann02/2020
8028(23*2^262435+1)/5579001Lelio R Paula10/2012
802911^75860-210079001Enzo Doria12/2012
80308*7^93463+978987Lelio R Paula10/2014
8031(2^262376+3942)/278983Stefano Morozzi01/2020
803267^43240-278960Lelio R Paula09/2013
80331000001^13159-1000000^1315978953Jean-Louis Charton10/2003
8034(2^262263+3410)/278949Stefano Morozzi01/2020
80352^262199-11028778930Enzo Doria05/2014
8036(19*2^262180-1)/17778924Lelio R Paula02/2014
8037(3^165403+4)/778917Lelio R Paula10/2012
80382^21068*(2^241076+1)-178914Makoto Morimoto03/2014
80392^29258*(2^232886+1)-178914Makoto Morimoto03/2014
80412^262144+1853178914Makoto Morimoto12/2015
80402^262144-23142578914Matthias Baur03/2020
8042(2^262137+1730)/278911Stefano Morozzi01/2020
8043(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
8044(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
804514^68837+7578897Lelio R Paula02/2015
8046(2^262055+1806)/278887Stefano Morozzi01/2020
8047(20450^18301-1)/2044978886Serge Batalov08/2020
8048(2^262049+1406)/278885Stefano Morozzi01/2020
8049106^38949+10578884Norbert Schneider12/2016
8050(2^262010+3778)/278873Stefano Morozzi01/2020
805118683^16636+16636^1868378862Hans Havermann03/2020
8052(2^261964+1450)/278859Stefano Morozzi01/2020
805323288^2433+2433^2328878857Hans Havermann03/2020
8054(70^42737+1)/7178853Paul Bourdelais08/2017
8055(2^261919+2474)/278846Stefano Morozzi01/2020
8056(25*2^261917-1)/2092778842Lelio R Paula02/2014
80572^261881-185971378835Enzo Doria03/2016
80592^261874+191578832Lelio R Paula07/2013
8058(2^261872+1582)/278832Stefano Morozzi01/2020
80602^261856+9876533178827Jason Earls01/2009
8061(5*2^261857-1)/2050127778821Lelio R Paula02/2014
8062(10493^19603-1)/1049278818Serge Batalov08/2020
806324586^1605+1605^2458678810Hans Havermann02/2020
8064(2^261786+3538)/278806Stefano Morozzi01/2020
8065(2^261780+2290)/278804Stefano Morozzi01/2020
80662^261724+9269178787Tony Prest / Never Odd Or Even03/2014
80672^261724+28511178787Tony Prest / Never Odd Or Even04/2014
80682^261724+29371378787Tony Prest / Never Odd Or Even04/2014
8069(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
80702^261724+57297178787Tony Prest / Never Odd Or Even05/2014
8071(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
8072(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
8073(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
8074(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
8075(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
8076(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
8077(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
8078(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
8079(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
808019473^11110+11110^1947378783Hans Havermann04/2020
8081(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
8082(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
8083(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
8084(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
8085(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
8086(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
8087(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
8088(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
8089(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
8090(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
8091(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
8092(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
8093(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
8094(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
8095(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
8096(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
8097(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
8098(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
8099(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
8100(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
8101(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
8102(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
8103(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
8104(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
8105(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
8106(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
8107(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
8108(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
8109(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
8110(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
8111(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
8112(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
8113(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
8114(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
8115(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
8116(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
8117(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
8118(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
8119(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
8120(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
8121(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
8122(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
8123(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
8124(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
8126(23*2^261642+1)/9378762Lelio R Paula10/2012
8125(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
8127(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
8128(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
812971293!4-478759Robert Price11/2019
8130(2^261630+3582)/278759Stefano Morozzi01/2020
8131(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
8132(2^261536+846)/278730Stefano Morozzi01/2020
81332^261507-228778722Yves Minet04/2009
81348*10^78717+3978718Robert Price01/2017
8135(78557*2^261440+1)/378706Lelio R Paula06/2014
8136(290^31963-1)/28978704Serge Batalov08/2020
8137(21323^18181-1)/2132278699Serge Batalov08/2020
81386^101128-1643378693Enzo Doria02/2013
813920^60482+9978689Lelio R Paula03/2015
81402^261348-11063378674Enzo Doria05/2014
8141191^34487+278666Lelio R Paula05/2013
81422^261305-11013978661Enzo Doria04/2014
8143(82*10^78635-1)/978636Robert Price12/2014
814410^78632+8178633Robert Price03/2011
814510^78632-40269378632Patrick De Geest07/2013
81463*10^78631+1778632Robert Price03/2017
81472^261174-391178622Yves Minet04/2017
81482^261167+7484378620Enzo Doria04/2016
814918810^15119+15119^1881078617Hans Havermann04/2020
8150L(376121)+F(376122)78605Henri Lifchitz01/2007
815114^68580-2978602Lelio R Paula02/2015
8152(4270^21649-1)/426978592Serge Batalov08/2020
815320603^6522+6522^2060378588Hans Havermann03/2020
8154(2^261056+646)/278586Stefano Morozzi01/2020
8155(73*10^78576-1)/978577Robert Price01/2015
8156(2^261020+2158)/278575Stefano Morozzi01/2020
8157(17*2^261026-1)/4045178574Lelio R Paula02/2014
8158(2415^23227-1)/241478572Serge Batalov08/2020
81602^261001-19578570Lelio R Paula05/2012
815918532^17365+17365^1853278570Hans Havermann02/2020
81615*2^260950+978555Lelio R Paula06/2014
81622^260931-760578549Lelio R Paula07/2013
816319863^9002+9002^1986378546Hans Havermann02/2020
816415^66778-3278538Lelio R Paula02/2015
8165(11*2^260896-1)/24578537Lelio R Paula02/2014
816630^53166+2978533Norbert Schneider03/2017
8168lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
816718729^15592+15592^1872978529Hans Havermann04/2020
81697*3^164574-278523Lelio R Paula06/2014
817018518^17385+17385^1851878520Hans Havermann03/2020
81712^260830-11213378518Enzo Doria06/2014
817213^70486+4278518Lelio R Paula03/2015
817311^75386-708078507Enzo Doria01/2013
8175(86^40583-1)/8578506Paul Bourdelais08/2017
8174(2^260790+1914)/278506Stefano Morozzi01/2020
81765*10^78504+1178505Robert Price08/2019
81772^260711-5869578482Lelio R Paula07/2013
8178(2^260695+2258)/278477Stefano Morozzi01/2020
81792^260678-11106578472Enzo Doria05/2014
818021560^4359+4359^2156078466Hans Havermann02/2020
818118^62501-9778456Lelio R Paula02/2015
818253^45498-278452Lelio R Paula08/2013
8183(8890^19867-1)/888978449Serge Batalov08/2020
8184(2^260549+642)/278433Stefano Morozzi01/2020
8185(2^260527+3906)/278427Stefano Morozzi01/2020
81862^260513-11112178423Enzo Doria05/2014
818737845!2-6478412Robert Price06/2015
81882^260469-11069578409Enzo Doria05/2014
8189(11*10^78408-113)/378409Robert Price01/2017
81902^260447+841578403Lelio R Paula07/2013
819137837!2-6478394Robert Price06/2015
8192(19*2^260379-1)/5378382Lelio R Paula02/2014
81932^260377-11323378382Enzo Doria07/2014
8194(2^260378+3750)/278382Stefano Morozzi01/2020
81969^82138+6^82138-2^8213878380Mike Oakes08/2010
819569^42624+278380Lelio R Paula05/2013
81972^260369-185971378379Enzo Doria03/2016
819818634^16067+16067^1863478374Hans Havermann02/2020
819914*10^78362+108978364Jens K. Andersen11/2007
8200(2^260317+3542)/278363Stefano Morozzi01/2020
8201(1942^23827-1)/194178346Serge Batalov08/2020
82025^112070-5478334Lelio R Paula02/2015
820320120^7821+7821^2012078333Hans Havermann03/2020
8204(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
8205(2^260195+3546)/278327Stefano Morozzi01/2020
82062^260182-11345378323Enzo Doria07/2014
8207f(16405)78319Robert Price09/2017
820818547^16678+16678^1854778309Hans Havermann02/2020
8209(78557*2^260084+1)/51978296Lelio R Paula06/2014
821110^78288+9^(78288+1)78289Robert Price08/2016
821010^78288+3910978289Patrick De Geest12/2016
821210^78288-21629978288Patrick De Geest12/2016
8213(2^260059+2430)/278286Stefano Morozzi01/2020
8214(2^260056+1662)/278285Stefano Morozzi01/2020
82155^111997+3678283Lelio R Paula02/2015
8216(2^260017+1602)/278273Stefano Morozzi01/2020
8217(2^260017+2162)/278273Stefano Morozzi01/2020
821823969^1842+1842^2396978266Hans Havermann05/2020
821919297^11370+11370^1929778265Hans Havermann05/2020
8220(21^59183+1)/2278252Paul Bourdelais03/2010
822119090^12561+12561^1909078251Hans Havermann04/2020
8222(88*10^78242-7)/978243Robert Price11/2014
82232*6^100547+778242Lelio R Paula10/2014
8224(2^259913+3470)/278242Stefano Morozzi01/2020
8225(2^259885+3726)/278233Stefano Morozzi01/2020
82262^259860-11108978226Enzo Doria05/2014
822718226^18359+18359^1822678223Norbert Schneider02/2020
8228(2^259833+3342)/278218Stefano Morozzi01/2020
822937^49875-278215Lelio R Paula09/2013
8230(13*10^78213+401)/978214Robert Price10/2017
82317*5^111893-478211Lelio R Paula10/2014
8232(11*2^259809-1)/143778209Lelio R Paula02/2014
82337^92511-678181Theodore Burton11/2005
8234(3^163859-4)/25378179Lelio R Paula10/2012
8235(2^259689+1346)/278174Stefano Morozzi01/2020
8236(27*2^259666-1)/62569178163Lelio R Paula02/2014
8237(2^259642+3202)/278160Stefano Morozzi01/2020
8238(2^259624+442)/278155Stefano Morozzi01/2020
82393*10^78146+1778147Robert Price03/2017
8240(2^259594+1558)/278146Stefano Morozzi01/2020
8241(576^28307+1)/57778137Richard Fischer01/2018
82422^259503+7433378119Enzo Doria04/2016
8243(2^259503+2438)/278118Stefano Morozzi01/2020
8244(31*2^259504-1)/1336578116Lelio R Paula02/2014
8246(58547^16384+1)/278111Lelio R Paula11/2011
82456^100379+1378111Lelio R Paula03/2015
82472^259469-10990978108Enzo Doria04/2014
824815^66413-2678108Lelio R Paula02/2015
824918550^16229+16229^1855078101Hans Havermann05/2020
82507^92410-926678096Mike Oakes02/2010


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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