PRP Records

Probable Primes Top 10000

(301668 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 ?
8751(8766^26227-1)/8765103404Serge Batalov06/2022
8752(509203*2^343491-1)/16147103403Lelio R Paula05/2015
87533^216685-113056103386Enzo Doria07/2014
875424829^14580+14580^24829103382Hans Havermann08/2020
875591355!4+1024103381Robert Price09/2019
875644^62903-43^62903103379Jean-Louis Charton08/2012
875711^99262-20103371Lelio R Paula12/2016
8758(509203*2^343357-1)/5103366Lelio R Paula05/2015
8759(2^343363+3570)/2103363Stefano Morozzi09/2020
87602^343356-2791889103361Enzo Doria03/2016
8761(25*10^103360-241)/9103361Robert Price05/2018
8762Phi(104989,10)/2939693103350Maksym Voznyy09/2015
8763(371*33^68040-19)/32103321Eric Chen05/2023
876424826^14511+14511^24826103319Hans Havermann09/2020
87652^343182-171103309Lelio R Paula08/2011
8766(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
8767(16487^24649-1)/(16487^157-1)103287Ryan Propper11/2023
8768(10680^25639-1)/10679103285Serge Batalov06/2022
8769(7427^26683-1)/7426103282Serge Batalov06/2022
87702^343079-1835611103278Enzo Doria05/2015
87712^343063-1147103273Yves Minet06/2013
877224741^14930+14930^24741103271Hans Havermann09/2020
8773(16*10^103255-73)/3103256Robert Price07/2020
8774(219^44119-1)/218103256Serge Batalov06/2022
87759*6^132689+7103254Lelio R Paula11/2014
87762^342979-18085103247Enzo Doria05/2013
8777(16*10^103244-31)/3103245Robert Price03/2019
87782^342966-16995103244Lelio R Paula11/2016
877923797^21774+21774^23797103230Hans Havermann09/2020
878025388^11637+11637^25388103224Hans Havermann09/2020
8781(2^342876+2086)/2103216Stefano Morozzi09/2020
8782(16*10^103214-31)/3103215Robert Price03/2019
8784(37*10^103211+611)/9103212Robert Price11/2018
8783(238*10^103210-1)/3103212Robert Price04/2020
87855^147650+16103203Lelio R Paula11/2016
8786gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
8787Phi(852060L,10)103201Anonymous03/2025
87882^342817+2707067103199Enzo Doria03/2016
878943^63177-42103198Theodore Burton02/2007
87902^342805-21025103195Enzo Doria06/2013
879124129^18890+18890^24129103182Hans Havermann09/2020
8792(622*10^103171-1)/9103173Robert Price11/2021
87932^342714+12285103168Lelio R Paula11/2016
8794(2*10^103161-17)/3103161Serge Batalov11/2022
879518^82178-4481103156Enzo Doria03/2013
87962^342665-17349103153Enzo Doria05/2013
879730408^2467+2467^30408103150Hans Havermann09/2020
8798(5^147571-3^147571)/2103148Kellen Shenton05/2022
8799(2^342615+3090)/2103138Stefano Morozzi09/2020
88002^342612+175103137Lelio R Paula08/2011
88015*2^342585-3103130Lelio R Paula09/2014
8802(16*10^103127+77)/3103128Robert Price03/2019
8803(2^342527+3774)/2103111Stefano Morozzi02/2021
88042^342503-19209103104Enzo Doria05/2013
8805(2^342484+2586)/2103098Stefano Morozzi09/2020
88062^342476+51103096Lelio R Paula08/2011
88072^342460-18885103091Enzo Doria05/2013
8808(2^342442+862)/2103086Stefano Morozzi02/2021
8809(194*10^103074-17)/3103076Robert Price09/2020
88107^121968+82103075Lelio R Paula10/2016
88112^342392-108863103071Enzo Doria03/2014
8812(2^342389+806)/2103070Stefano Morozzi01/2021
88133^216014+28103065Lelio R Paula11/2016
88142^342353-108879103059Enzo Doria03/2014
881510^103055+276081103056Patrick De Geest12/2016
881610^103055-53103055Lelio R Paula11/2016
8817(58*10^103046+419)/9103047Robert Price05/2019
88187^121933+4103046Lelio R Paula11/2014
8819(71*10^103028-143)/9103029Robert Price10/2021
8820(2^342235+3618)/2103023Stefano Morozzi09/2020
882119^80560-68103017Lelio R Paula10/2016
88222^342209+76607103016Enzo Doria05/2016
8824328^40945+40945^328103013Norbert Schneider12/2014
882312^95454-91103013Lelio R Paula10/2016
882525833^9716+9716^25833103009Hans Havermann01/2019
8826(893*10^103004+7)/9103006Robert Price06/2021
8827(1475^32503-1)/1474102993Serge Batalov06/2022
882865^56809-64^56809102990Robert Price08/2013
88295^147338-6102985Lelio R Paula11/2014
88302^342084-112739102978Enzo Doria06/2014
88319*6^132330+7102974Lelio R Paula11/2014
88322^342034-16737102963Enzo Doria05/2013
8833(9787*2^342011-1)/25102959Lelio R Paula05/2015
8834(3^215802-5)/124343756102956Lelio R Paula12/2013
88352^341991-17421102950Enzo Doria05/2013
88362^341969-112225102943Enzo Doria06/2014
8837(9787*2^341864-1)/3102915Lelio R Paula05/2015
88382^341859+1869413102910Enzo Doria05/2016
883910^102909+61102910Lelio R Paula11/2016
884010^102909-67049102909Patrick De Geest12/2016
884123814^20935+20935^23814102898Hans Havermann02/2019
884228345^4264+4264^28345102888Hans Havermann02/2019
884325665^10204+10204^25665102886Hans Havermann02/2019
884426288^8181+8181^26288102860Hans Havermann02/2019
88452^341659+1836773102850Enzo Doria03/2016
88462^341608-110639102835Enzo Doria05/2014
884710^102824+49102825Lelio R Paula11/2016
884810^102824-168011102824Patrick De Geest12/2016
8849(156^46877-1)/155102805Anonymous06/2024
885011^98708-8102794Lelio R Paula10/2016
88512^341466+4429102792Lelio R Paula09/2011
88522^341460-107102790Lelio R Paula08/2011
8853(2^341388+47)/21014943102761Lelio R Paula12/2013
88542^341355+21102759Lelio R Paula08/2011
88552^341319+224885102748Enzo Doria07/2024
8856(419^39181-1)/418102739Tom Wu07/2024
8857(6496^26947-1)/6495102736Serge Batalov06/2022
88582^341246+40755102726Lelio R Paula11/2016
8859(2^341256-5)/991699102723Lelio R Paula12/2013
88607^121547+78102720Lelio R Paula10/2016
88612^341223-461197102719Enzo Doria06/2015
886227838^4893+4893^27838102711Hans Havermann03/2019
88642^341190-20577102709Enzo Doria06/2013
8863(27*2^341212+1)/84674449102709Lelio R Paula12/2013
8865(25*10^102698+77)/3102699Robert Price09/2022
88666^131976-65102698Lelio R Paula10/2016
88672^341134+2533102692Henri Lifchitz09/2005
886813^92184-54102688Lelio R Paula10/2016
88692^341116-20873102687Enzo Doria06/2013
88702^341094-19953102680Enzo Doria06/2013
887123761^20950+20950^23761102676Hans Havermann03/2019
88732^341053+129102668Lelio R Paula08/2011
8872(4724^27943-1)/4723102668Serge Batalov06/2022
8875(31*2^341006-1)/3102655Lelio R Paula03/2014
88747^121471+94102655Lelio R Paula10/2016
88772^341004-173102653Lelio R Paula08/2011
887620^78901+3102653Lelio R Paula10/2016
8878(2^341001+1674)/2102652Stefano Morozzi09/2020
88795^146853-52102646Lelio R Paula10/2016
88802^340969-216931102642Enzo Doria05/2014
8881122^49196+121102641Norbert Schneider10/2018
88822^340952+1870021102637Enzo Doria05/2016
88835*2^340940-3102634Lelio R Paula08/2014
8884(6^131891+1)/7102631Paul Bourdelais01/2010
8885(11*10^102629-23)/3102630Robert Price09/2021
88863^215094+5*2^215094102626Jon Grantham08/2023
888725876^9239+9239^25876102615Hans Havermann02/2019
8888(4*10^102612+83)/3102613Robert Price02/2018
8889(234^43313-1)/20184091102611Aurel Gibier03/2025
889175^54717+74102598Norbert Schneider01/2015
8890(17*10^102597+13)/3102598Robert Price01/2019
88922^340806-20393102593Enzo Doria06/2013
8893(2^340790+5)/138267102583Lelio R Paula12/2013
88946^131821+77102577Lelio R Paula10/2016
8895(203*10^102561-11)/3102563Robert Price12/2020
8896(67^56171-1)/2053280351166102561Paul Vanderveen05/2025
88972^340688-29102558Henri Lifchitz05/2005
88982^340685-109101102557Enzo Doria04/2014
889965^56567-64102552Norbert Schneider11/2014
890026230^8121+8121^26230102550Hans Havermann03/2019
8901(64*10^102547+161)/9102548Robert Price08/2022
8902(8*10^102541+49)/3102542Robert Price05/2020
8903(536*10^102533-23)/9102535Robert Price02/2020
89042^340547-108897102515Enzo Doria03/2014
8905(2^340536+778)/2102512Stefano Morozzi09/2020
890625592^10119+10119^25592102500Hans Havermann02/2019
8907(5*10^102492-23)/9102492Serge Batalov11/2022
89087^121268+82102484Lelio R Paula10/2016
8909(6883*2^340443-1)/162401102483Lelio R Paula05/2015
89102^340434-5955102481Lelio R Paula11/2016
8911(7*10^102480-19)/3102481Robert Price10/2020
8912(2^340381+47)/7102465Lelio R Paula12/2013
8913111^50095+110102461Norbert Schneider04/2017
8914180^45427-45427^180102451Norman Luhn09/2024
89152^340291-20301102438Enzo Doria06/2013
891612^94915+89102431Lelio R Paula10/2016
8917(106*10^102422+17)/3102424Robert Price04/2021
891824466^15349+15349^24466102417Hans Havermann03/2019
89192^340212+111546435102415Paul Bourdelais10/2021
89202^340208-20373102413Enzo Doria06/2013
89216^131598-17273102404Enzo Doria02/2013
8922(2^340132+1182)/2102390Stefano Morozzi09/2020
8923(2^340133+1166)/2102390Stefano Morozzi09/2020
89242^340115-21181102385Enzo Doria06/2013
8925(55459*2^340090+1)/1591102379Lelio R Paula07/2014
8926(2^340064+3630)/2102370Stefano Morozzi09/2020
89279348*31^68638+13102369Eric Chen04/2024
892889^52511-88^52511102365Robert Price06/2015
89293^214539-112756102362Enzo Doria07/2014
8930Phi(562221,2)/53723397926257372614541581386770268796893300042857102361Anonymous06/2025
893123159^23450-23450^23159102353Norbert Schneider12/2019
89322^340000-19877102351Enzo Doria06/2013
89342^339990-114845102348Enzo Doria05/2015
8933311^41058-41058^311102348Norman Luhn09/2024
8935(3^214516-2)/51383102346Lelio R Paula12/2013
893620^78661-99102341Lelio R Paula09/2016
89372^339951-19585102336Enzo Doria05/2013
8938(17*10^102335-167)/3102336Robert Price05/2022
8939(13*2^339943+1)/45102333Lelio R Paula12/2013
8940(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
89415*10^102323-91102324Robert Price03/2021
89432^339889+29327102317Yves Minet06/2010
8942(167*10^102315-17)/3102317Robert Price03/2020
894426348^7641+7641^26348102314Hans Havermann03/2019
8945Phi(239414,10)/6333218543102303Makoto Kamada08/2019
89462^339834-109493102301Enzo Doria04/2014
8947(16*10^102299-19)/3102300Robert Price02/2019
8948(11^98221-5^98221)/6102286Robert Price01/2013
89493^214365+1820102279Lelio R Paula10/2016
895031978^1579+1579^31978102278Hans Havermann03/2019
8951(89*10^102262-467)/9102263Robert Price04/2022
8952(11*2^339705-1)/183102261Lelio R Paula03/2014
89532^339694-16995102259Lelio R Paula09/2016
8954(56*10^102255+691)/9102256Robert Price05/2019
8955122^49008+121102249Norbert Schneider10/2018
8956(2^339652+3178)/2102246Stefano Morozzi09/2020
89577^120985-38102245Lelio R Paula10/2016
895810^102244+122961102245Patrick De Geest12/2016
895910^102244-27102244Lelio R Paula09/2016
89607^120982-62102242Lelio R Paula10/2016
8961(2^339640+2670)/2102242Stefano Morozzi09/2020
89624*6^131382-5102236Lelio R Paula11/2014
8963(2^339607+3290)/2102232Stefano Morozzi02/2021
89642^339586-1091102226Yves Minet11/2012
896511^98161-3072000102225Enzo Doria12/2012
89669*7^120961-4102225Lelio R Paula11/2014
89675*3^214250+2102224Serge Batalov10/2010
896812^94713-59102213Lelio R Paula10/2016
896912^94705+89102204Lelio R Paula10/2016
8970L(2*339475)%(2^339475)102193Henri Lifchitz06/2025
89712^339407-177102172Lelio R Paula08/2011
89724*10^102163-57102164Robert Price10/2018
89732^339355+65102157Lelio R Paula07/2011
8974(28*10^102142-31)/3102143Robert Price12/2019
8975(2^339323+47)/880715102141Lelio R Paula12/2013
8976(2^339268+1758)/2102130Stefano Morozzi09/2020
8977U(610865)102130Serge Batalov07/2024
8978s(178551)102122Robert Price05/2020
8979(797*10^102112-23)/9102114Robert Price01/2022
8980(5*10^102107+7)/3102108Tyler Busby02/2023
8981(2^339175+2790)/2102102Stefano Morozzi02/2021
89842^339168+21102100Lelio R Paula07/2011
89832^339167-108807102100Enzo Doria03/2014
8982(2^339169+42)/2102100Stefano Morozzi09/2020
89852^339156+163102097Lelio R Paula08/2011
8986(2^339149+746)/2102094Stefano Morozzi09/2020
8987(25*10^102076-67)/3102077Robert Price06/2019
89882^339081-4543102074Yves Minet03/2019
8989(3435^28867-1)/3434102069Serge Batalov06/2022
89902*10^102062+77102063Robert Price08/2020
899124327^15668+15668^24327102053Hans Havermann02/2019
899210^102052+66793102053Patrick De Geest09/2022
899410^102052-7000001102052Robert Price06/2021
899310^102052-618623102052Patrick De Geest09/2022
89952^339000-175635102050Stefano Morozzi12/2021
89962^339000-151667102050Stefano Morozzi12/2021
89972^338999+79289102049Stefano Morozzi01/2022
89982^338998-63897102049Stefano Morozzi12/2022
89992^338997+99659102049Stefano Morozzi02/2023
90002^338994+188757102048Stefano Morozzi05/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2025 15:18 (Time in France)

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