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 ?
57512^342966-16995103244Lelio R Paula11/2016
575223797^21774+21774^23797103230Hans Havermann09/2020
575325388^11637+11637^25388103224Hans Havermann09/2020
5754(2^342876+2086)/2103216Stefano Morozzi09/2020
5755(16*10^103214-31)/3103215Robert Price03/2019
5757(37*10^103211+611)/9103212Robert Price11/2018
5756(238*10^103210-1)/3103212Robert Price04/2020
57585^147650+16103203Lelio R Paula11/2016
5759gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
57602^342817+2707067103199Enzo Doria03/2016
576143^63177-42103198Theodore Burton02/2007
57622^342805-21025103195Enzo Doria06/2013
576324129^18890+18890^24129103182Hans Havermann09/2020
5764(622*10^103171-1)/9103173Robert Price11/2021
57652^342714+12285103168Lelio R Paula11/2016
576618^82178-4481103156Enzo Doria03/2013
57672^342665-17349103153Enzo Doria05/2013
576830408^2467+2467^30408103150Hans Havermann09/2020
5769(5^147571-3^147571)/2103148Kellen Shenton05/2022
5770(2^342615+3090)/2103138Stefano Morozzi09/2020
57712^342612+175103137Lelio R Paula08/2011
57725*2^342585-3103130Lelio R Paula09/2014
5773(16*10^103127+77)/3103128Robert Price03/2019
5774(2^342527+3774)/2103111Stefano Morozzi02/2021
57752^342503-19209103104Enzo Doria05/2013
5776(2^342484+2586)/2103098Stefano Morozzi09/2020
57772^342476+51103096Lelio R Paula08/2011
57782^342460-18885103091Enzo Doria05/2013
5779(2^342442+862)/2103086Stefano Morozzi02/2021
5780(194*10^103074-17)/3103076Robert Price09/2020
57817^121968+82103075Lelio R Paula10/2016
57822^342392-108863103071Enzo Doria03/2014
5783(2^342389+806)/2103070Stefano Morozzi01/2021
57843^216014+28103065Lelio R Paula11/2016
57852^342353-108879103059Enzo Doria03/2014
578610^103055+276081103056Patrick De Geest12/2016
578710^103055-53103055Lelio R Paula11/2016
5788(58*10^103046+419)/9103047Robert Price05/2019
57897^121933+4103046Lelio R Paula11/2014
5790(71*10^103028-143)/9103029Robert Price10/2021
5791(2^342235+3618)/2103023Stefano Morozzi09/2020
579219^80560-68103017Lelio R Paula10/2016
57932^342209+76607103016Enzo Doria05/2016
5795328^40945+40945^328103013Norbert Schneider12/2014
579412^95454-91103013Lelio R Paula10/2016
579625833^9716+9716^25833103009Hans Havermann01/2019
5797(893*10^103004+7)/9103006Robert Price06/2021
5798(1475^32503-1)/1474102993Serge Batalov06/2022
579965^56809-64^56809102990Robert Price08/2013
58005^147338-6102985Lelio R Paula11/2014
58012^342084-112739102978Enzo Doria06/2014
58029*6^132330+7102974Lelio R Paula11/2014
58032^342034-16737102963Enzo Doria05/2013
5804(9787*2^342011-1)/25102959Lelio R Paula05/2015
5805(3^215802-5)/124343756102956Lelio R Paula12/2013
58062^341991-17421102950Enzo Doria05/2013
58072^341969-112225102943Enzo Doria06/2014
5808(9787*2^341864-1)/3102915Lelio R Paula05/2015
58092^341859+1869413102910Enzo Doria05/2016
581010^102909+61102910Lelio R Paula11/2016
581110^102909-67049102909Patrick De Geest12/2016
581223814^20935+20935^23814102898Hans Havermann02/2019
581328345^4264+4264^28345102888Hans Havermann02/2019
581425665^10204+10204^25665102886Hans Havermann02/2019
581526288^8181+8181^26288102860Hans Havermann02/2019
58162^341659+1836773102850Enzo Doria03/2016
58172^341608-110639102835Enzo Doria05/2014
581810^102824+49102825Lelio R Paula11/2016
581910^102824-168011102824Patrick De Geest12/2016
582011^98708-8102794Lelio R Paula10/2016
58212^341466+4429102792Lelio R Paula09/2011
58222^341460-107102790Lelio R Paula08/2011
5823(2^341388+47)/21014943102761Lelio R Paula12/2013
58242^341355+21102759Lelio R Paula08/2011
5825(6496^26947-1)/6495102736Serge Batalov06/2022
58262^341246+40755102726Lelio R Paula11/2016
5827(2^341256-5)/991699102723Lelio R Paula12/2013
58287^121547+78102720Lelio R Paula10/2016
58292^341223-461197102719Enzo Doria06/2015
583027838^4893+4893^27838102711Hans Havermann03/2019
58322^341190-20577102709Enzo Doria06/2013
5831(27*2^341212+1)/84674449102709Lelio R Paula12/2013
58336^131976-65102698Lelio R Paula10/2016
58342^341134+2533102692Henri Lifchitz09/2005
583513^92184-54102688Lelio R Paula10/2016
58362^341116-20873102687Enzo Doria06/2013
58372^341094-19953102680Enzo Doria06/2013
583823761^20950+20950^23761102676Hans Havermann03/2019
58402^341053+129102668Lelio R Paula08/2011
5839(4724^27943-1)/4723102668Serge Batalov06/2022
5842(31*2^341006-1)/3102655Lelio R Paula03/2014
58417^121471+94102655Lelio R Paula10/2016
58442^341004-173102653Lelio R Paula08/2011
584320^78901+3102653Lelio R Paula10/2016
5845(2^341001+1674)/2102652Stefano Morozzi09/2020
58465^146853-52102646Lelio R Paula10/2016
58472^340969-216931102642Enzo Doria05/2014
5848122^49196+121102641Norbert Schneider10/2018
58492^340952+1870021102637Enzo Doria05/2016
58505*2^340940-3102634Lelio R Paula08/2014
5851(6^131891+1)/7102631Paul Bourdelais01/2010
5852(11*10^102629-23)/3102630Robert Price09/2021
585325876^9239+9239^25876102615Hans Havermann02/2019
5854(4*10^102612+83)/3102613Robert Price02/2018
585575^54717+74102598Norbert Schneider01/2015
5856(17*10^102597+13)/3102598Robert Price01/2019
58572^340806-20393102593Enzo Doria06/2013
5858(2^340790+5)/138267102583Lelio R Paula12/2013
58596^131821+77102577Lelio R Paula10/2016
5860(203*10^102561-11)/3102563Robert Price12/2020
58612^340688-29102558Henri Lifchitz05/2005
58622^340685-109101102557Enzo Doria04/2014
586365^56567-64102552Norbert Schneider11/2014
586426230^8121+8121^26230102550Hans Havermann03/2019
5865(8*10^102541+49)/3102542Robert Price05/2020
5866(536*10^102533-23)/9102535Robert Price02/2020
58672^340547-108897102515Enzo Doria03/2014
5868(2^340536+778)/2102512Stefano Morozzi09/2020
586925592^10119+10119^25592102500Hans Havermann02/2019
58707^121268+82102484Lelio R Paula10/2016
5871(6883*2^340443-1)/162401102483Lelio R Paula05/2015
58722^340434-5955102481Lelio R Paula11/2016
5873(7*10^102480-19)/3102481Robert Price10/2020
5874(2^340381+47)/7102465Lelio R Paula12/2013
5875111^50095+110102461Norbert Schneider04/2017
58762^340291-20301102438Enzo Doria06/2013
587712^94915+89102431Lelio R Paula10/2016
5878(106*10^102422+17)/3102424Robert Price04/2021
587924466^15349+15349^24466102417Hans Havermann03/2019
58802^340212+111546435102415Paul Bourdelais10/2021
58812^340208-20373102413Enzo Doria06/2013
58826^131598-17273102404Enzo Doria02/2013
5883(2^340132+1182)/2102390Stefano Morozzi09/2020
5884(2^340133+1166)/2102390Stefano Morozzi09/2020
58852^340115-21181102385Enzo Doria06/2013
5886(55459*2^340090+1)/1591102379Lelio R Paula07/2014
5887(2^340064+3630)/2102370Stefano Morozzi09/2020
588889^52511-88^52511102365Robert Price06/2015
58893^214539-112756102362Enzo Doria07/2014
589023159^23450-23450^23159102353Norbert Schneider12/2019
58912^340000-19877102351Enzo Doria06/2013
58922^339990-114845102348Enzo Doria05/2015
5893(3^214516-2)/51383102346Lelio R Paula12/2013
589420^78661-99102341Lelio R Paula09/2016
58952^339951-19585102336Enzo Doria05/2013
5896(17*10^102335-167)/3102336Robert Price05/2022
5897(13*2^339943+1)/45102333Lelio R Paula12/2013
5898(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
58995*10^102323-91102324Robert Price03/2021
59012^339889+29327102317Yves Minet06/2010
5900(167*10^102315-17)/3102317Robert Price03/2020
590226348^7641+7641^26348102314Hans Havermann03/2019
5903Phi(239414,10)/6333218543102303Makoto Kamada08/2019
59042^339834-109493102301Enzo Doria04/2014
5905(16*10^102299-19)/3102300Robert Price02/2019
5906(11^98221-5^98221)/6102286Robert Price01/2013
59073^214365+1820102279Lelio R Paula10/2016
590831978^1579+1579^31978102278Hans Havermann03/2019
5909(89*10^102262-467)/9102263Robert Price04/2022
5910(11*2^339705-1)/183102261Lelio R Paula03/2014
59112^339694-16995102259Lelio R Paula09/2016
5912(56*10^102255+691)/9102256Robert Price05/2019
5913122^49008+121102249Norbert Schneider10/2018
5914(2^339652+3178)/2102246Stefano Morozzi09/2020
59157^120985-38102245Lelio R Paula10/2016
591610^102244+122961102245Patrick De Geest12/2016
591710^102244-27102244Lelio R Paula09/2016
59187^120982-62102242Lelio R Paula10/2016
5919(2^339640+2670)/2102242Stefano Morozzi09/2020
59204*6^131382-5102236Lelio R Paula11/2014
5921(2^339607+3290)/2102232Stefano Morozzi02/2021
59222^339586-1091102226Yves Minet11/2012
592311^98161-3072000102225Enzo Doria12/2012
59249*7^120961-4102225Lelio R Paula11/2014
59255*3^214250+2102224Serge Batalov10/2010
592612^94713-59102213Lelio R Paula10/2016
592712^94705+89102204Lelio R Paula10/2016
59282^339407-177102172Lelio R Paula08/2011
59294*10^102163-57102164Robert Price10/2018
59302^339355+65102157Lelio R Paula07/2011
5931(28*10^102142-31)/3102143Robert Price12/2019
5932(2^339323+47)/880715102141Lelio R Paula12/2013
5933(2^339268+1758)/2102130Stefano Morozzi09/2020
5934s(178551)102122Robert Price05/2020
5935(797*10^102112-23)/9102114Robert Price01/2022
5936(2^339175+2790)/2102102Stefano Morozzi02/2021
59382^339168+21102100Lelio R Paula07/2011
59392^339167-108807102100Enzo Doria03/2014
5937(2^339169+42)/2102100Stefano Morozzi09/2020
59402^339156+163102097Lelio R Paula08/2011
5941(2^339149+746)/2102094Stefano Morozzi09/2020
5942(25*10^102076-67)/3102077Robert Price06/2019
59432^339081-4543102074Yves Minet03/2019
5944(3435^28867-1)/3434102069Serge Batalov06/2022
59452*10^102062+77102063Robert Price08/2020
594624327^15668+15668^24327102053Hans Havermann02/2019
594710^102052-7000001102052Robert Price06/2021
59482^339000-175635102050Stefano Morozzi12/2021
59492^339000-151667102050Stefano Morozzi12/2021
59502^338999+79289102049Stefano Morozzi01/2022
59512^338994+188757102048Stefano Morozzi05/2022
59522^338992+181591102047Stefano Morozzi01/2022
59532^338992+136171102047Stefano Morozzi03/2022
59542^338991-109435102047Stefano Morozzi04/2022
59552^338988-134619102046Stefano Morozzi04/2022
59562^338981+106391102044Stefano Morozzi01/2022
59572^338982+34069102044Stefano Morozzi03/2022
59582^338982-58781102044Stefano Morozzi04/2022
59592^338977+83007102043Stefano Morozzi02/2022
59602^338979-83601102043Stefano Morozzi04/2022
59612^338975+28355102042Stefano Morozzi01/2022
59622^338973+134619102042Stefano Morozzi03/2022
59632^338974+183777102042Stefano Morozzi03/2022
596825080^11711+11711^25080102041Hans Havermann02/2019
59642^338972+152343102041Stefano Morozzi12/2021
59652^338972-180623102041Stefano Morozzi02/2022
59662^338972+84441102041Stefano Morozzi03/2022
59672^338971+64875102041Stefano Morozzi05/2022
59692^338968+53461102040Stefano Morozzi01/2022
59702^338969+160175102040Stefano Morozzi03/2022
59712^338967+13409102040Stefano Morozzi04/2022
59722^338963-127455102039Stefano Morozzi12/2021
59732^338963+132195102039Stefano Morozzi02/2022
59742^338966+137919102039Stefano Morozzi04/2022
5979(2^338982-7)/1754517102038Lelio R Paula12/2013
59752^338960+53935102038Stefano Morozzi01/2022
59762^338962+83157102038Stefano Morozzi02/2022
59772^338961+12341102038Stefano Morozzi04/2022
59782^338960+63933102038Stefano Morozzi05/2022
59802^338959-30919102037Stefano Morozzi02/2022
59812^338959+164769102037Stefano Morozzi05/2022
59822^338954-177003102036Stefano Morozzi12/2021
59832^338954+154207102036Stefano Morozzi01/2022
59842^338956+182493102036Stefano Morozzi02/2022
59852^338954+162715102036Stefano Morozzi04/2022
59862^338955-158241102036Stefano Morozzi04/2022
59872^338956-33395102036Stefano Morozzi04/2022
59882^338950+175077102035Stefano Morozzi12/2021
59892^338951-51687102035Stefano Morozzi12/2021
59902^338949+85449102034Stefano Morozzi03/2022
59912^338949-184585102034Stefano Morozzi04/2022
59922^338943+127103102033Stefano Morozzi12/2021
59932^338944-84003102033Stefano Morozzi04/2022
59942^338945+138605102033Stefano Morozzi05/2022
59952^338940+78607102032Stefano Morozzi01/2022
59962^338939+151569102031Stefano Morozzi12/2021
59972^338938+183975102031Stefano Morozzi03/2022
59982^338937-33429102031Stefano Morozzi04/2022
59992^338939-183259102031Stefano Morozzi04/2022
60002^338935+179999102030Stefano Morozzi01/2022


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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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