PRP Records

Probable Primes Top 10000

(301678 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 ?
875128316^4503+4503^28316103453Hans Havermann09/2020
8752(22*10^103450+53)/3103451Robert Price07/2019
87532^343604+9931103436Yves Minet01/2011
87542^343601-21189103435Enzo Doria06/2013
8755(10^103423+173)/3103423Robert Price05/2021
87562^343508-115229103407Enzo Doria06/2015
8757(8766^26227-1)/8765103404Serge Batalov06/2022
8758(509203*2^343491-1)/16147103403Lelio R Paula05/2015
87593^216685-113056103386Enzo Doria07/2014
876024829^14580+14580^24829103382Hans Havermann08/2020
876191355!4+1024103381Robert Price09/2019
876244^62903-43^62903103379Jean-Louis Charton08/2012
876311^99262-20103371Lelio R Paula12/2016
8764(509203*2^343357-1)/5103366Lelio R Paula05/2015
8765(2^343363+3570)/2103363Stefano Morozzi09/2020
87662^343356-2791889103361Enzo Doria03/2016
8767(25*10^103360-241)/9103361Robert Price05/2018
8768Phi(104989,10)/2939693103350Maksym Voznyy09/2015
8769(371*33^68040-19)/32103321Eric Chen05/2023
877024826^14511+14511^24826103319Hans Havermann09/2020
87712^343182-171103309Lelio R Paula08/2011
8772(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
8773(16487^24649-1)/(16487^157-1)103287Ryan Propper11/2023
8774(10680^25639-1)/10679103285Serge Batalov06/2022
8775(7427^26683-1)/7426103282Serge Batalov06/2022
87762^343079-1835611103278Enzo Doria05/2015
87772^343063-1147103273Yves Minet06/2013
877824741^14930+14930^24741103271Hans Havermann09/2020
8779(16*10^103255-73)/3103256Robert Price07/2020
8780(219^44119-1)/218103256Serge Batalov06/2022
87819*6^132689+7103254Lelio R Paula11/2014
87822^342979-18085103247Enzo Doria05/2013
8783(16*10^103244-31)/3103245Robert Price03/2019
87842^342966-16995103244Lelio R Paula11/2016
878523797^21774+21774^23797103230Hans Havermann09/2020
878625388^11637+11637^25388103224Hans Havermann09/2020
8787(2^342876+2086)/2103216Stefano Morozzi09/2020
8788(16*10^103214-31)/3103215Robert Price03/2019
8790(37*10^103211+611)/9103212Robert Price11/2018
8789(238*10^103210-1)/3103212Robert Price04/2020
87915^147650+16103203Lelio R Paula11/2016
8792gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
8793Phi(852060L,10)103201Anonymous03/2025
87942^342817+2707067103199Enzo Doria03/2016
879543^63177-42103198Theodore Burton02/2007
87962^342805-21025103195Enzo Doria06/2013
879724129^18890+18890^24129103182Hans Havermann09/2020
8798(622*10^103171-1)/9103173Robert Price11/2021
87992^342714+12285103168Lelio R Paula11/2016
8800(2*10^103161-17)/3103161Serge Batalov11/2022
880118^82178-4481103156Enzo Doria03/2013
88022^342665-17349103153Enzo Doria05/2013
880330408^2467+2467^30408103150Hans Havermann09/2020
8804(5^147571-3^147571)/2103148Kellen Shenton05/2022
8805(2^342615+3090)/2103138Stefano Morozzi09/2020
88062^342612+175103137Lelio R Paula08/2011
88075*2^342585-3103130Lelio R Paula09/2014
8808(16*10^103127+77)/3103128Robert Price03/2019
8809(2^342527+3774)/2103111Stefano Morozzi02/2021
88102^342503-19209103104Enzo Doria05/2013
8811(2^342484+2586)/2103098Stefano Morozzi09/2020
88122^342476+51103096Lelio R Paula08/2011
88132^342460-18885103091Enzo Doria05/2013
8814(2^342442+862)/2103086Stefano Morozzi02/2021
8815(194*10^103074-17)/3103076Robert Price09/2020
88167^121968+82103075Lelio R Paula10/2016
88172^342392-108863103071Enzo Doria03/2014
8818(2^342389+806)/2103070Stefano Morozzi01/2021
88193^216014+28103065Lelio R Paula11/2016
88202^342353-108879103059Enzo Doria03/2014
882110^103055+276081103056Patrick De Geest12/2016
882210^103055-53103055Lelio R Paula11/2016
8823(58*10^103046+419)/9103047Robert Price05/2019
88247^121933+4103046Lelio R Paula11/2014
8825(71*10^103028-143)/9103029Robert Price10/2021
8826(2^342235+3618)/2103023Stefano Morozzi09/2020
882719^80560-68103017Lelio R Paula10/2016
88282^342209+76607103016Enzo Doria05/2016
8830328^40945+40945^328103013Norbert Schneider12/2014
882912^95454-91103013Lelio R Paula10/2016
883125833^9716+9716^25833103009Hans Havermann01/2019
8832(893*10^103004+7)/9103006Robert Price06/2021
8833(1475^32503-1)/1474102993Serge Batalov06/2022
883465^56809-64^56809102990Robert Price08/2013
88355^147338-6102985Lelio R Paula11/2014
88362^342084-112739102978Enzo Doria06/2014
88379*6^132330+7102974Lelio R Paula11/2014
88382^342034-16737102963Enzo Doria05/2013
8839(9787*2^342011-1)/25102959Lelio R Paula05/2015
8840(3^215802-5)/124343756102956Lelio R Paula12/2013
88412^341991-17421102950Enzo Doria05/2013
88422^341969-112225102943Enzo Doria06/2014
8843(9787*2^341864-1)/3102915Lelio R Paula05/2015
88442^341859+1869413102910Enzo Doria05/2016
884510^102909+61102910Lelio R Paula11/2016
884610^102909-67049102909Patrick De Geest12/2016
884723814^20935+20935^23814102898Hans Havermann02/2019
884828345^4264+4264^28345102888Hans Havermann02/2019
884925665^10204+10204^25665102886Hans Havermann02/2019
885026288^8181+8181^26288102860Hans Havermann02/2019
88512^341659+1836773102850Enzo Doria03/2016
88522^341608-110639102835Enzo Doria05/2014
885310^102824+49102825Lelio R Paula11/2016
885410^102824-168011102824Patrick De Geest12/2016
8855(156^46877-1)/155102805Anonymous06/2024
885611^98708-8102794Lelio R Paula10/2016
88572^341466+4429102792Lelio R Paula09/2011
88582^341460-107102790Lelio R Paula08/2011
8859(2^341388+47)/21014943102761Lelio R Paula12/2013
88602^341355+21102759Lelio R Paula08/2011
88612^341319+224885102748Enzo Doria07/2024
8862(419^39181-1)/418102739Tom Wu07/2024
8863(6496^26947-1)/6495102736Serge Batalov06/2022
88642^341246+40755102726Lelio R Paula11/2016
8865(2^341256-5)/991699102723Lelio R Paula12/2013
88667^121547+78102720Lelio R Paula10/2016
88672^341223-461197102719Enzo Doria06/2015
886827838^4893+4893^27838102711Hans Havermann03/2019
88702^341190-20577102709Enzo Doria06/2013
8869(27*2^341212+1)/84674449102709Lelio R Paula12/2013
8871(25*10^102698+77)/3102699Robert Price09/2022
88726^131976-65102698Lelio R Paula10/2016
88732^341134+2533102692Henri Lifchitz09/2005
887413^92184-54102688Lelio R Paula10/2016
88752^341116-20873102687Enzo Doria06/2013
88762^341094-19953102680Enzo Doria06/2013
887723761^20950+20950^23761102676Hans Havermann03/2019
88792^341053+129102668Lelio R Paula08/2011
8878(4724^27943-1)/4723102668Serge Batalov06/2022
8881(31*2^341006-1)/3102655Lelio R Paula03/2014
88807^121471+94102655Lelio R Paula10/2016
88832^341004-173102653Lelio R Paula08/2011
888220^78901+3102653Lelio R Paula10/2016
8884(2^341001+1674)/2102652Stefano Morozzi09/2020
88855^146853-52102646Lelio R Paula10/2016
88862^340969-216931102642Enzo Doria05/2014
8887122^49196+121102641Norbert Schneider10/2018
88882^340952+1870021102637Enzo Doria05/2016
88895*2^340940-3102634Lelio R Paula08/2014
8890(6^131891+1)/7102631Paul Bourdelais01/2010
8891(11*10^102629-23)/3102630Robert Price09/2021
88923^215094+5*2^215094102626Jon Grantham08/2023
889325876^9239+9239^25876102615Hans Havermann02/2019
8894(4*10^102612+83)/3102613Robert Price02/2018
8895(234^43313-1)/20184091102611Aurel Gibier03/2025
889775^54717+74102598Norbert Schneider01/2015
8896(17*10^102597+13)/3102598Robert Price01/2019
88982^340806-20393102593Enzo Doria06/2013
8899(2^340790+5)/138267102583Lelio R Paula12/2013
89006^131821+77102577Lelio R Paula10/2016
8901(203*10^102561-11)/3102563Robert Price12/2020
8902(67^56171-1)/2053280351166102561Paul Vanderveen05/2025
89032^340688-29102558Henri Lifchitz05/2005
89042^340685-109101102557Enzo Doria04/2014
890565^56567-64102552Norbert Schneider11/2014
890626230^8121+8121^26230102550Hans Havermann03/2019
8907(64*10^102547+161)/9102548Robert Price08/2022
8908(8*10^102541+49)/3102542Robert Price05/2020
8909(536*10^102533-23)/9102535Robert Price02/2020
89102^340547-108897102515Enzo Doria03/2014
8911(2^340536+778)/2102512Stefano Morozzi09/2020
891225592^10119+10119^25592102500Hans Havermann02/2019
8913(5*10^102492-23)/9102492Serge Batalov11/2022
89147^121268+82102484Lelio R Paula10/2016
8915(6883*2^340443-1)/162401102483Lelio R Paula05/2015
89162^340434-5955102481Lelio R Paula11/2016
8917(7*10^102480-19)/3102481Robert Price10/2020
8918(2^340381+47)/7102465Lelio R Paula12/2013
8919111^50095+110102461Norbert Schneider04/2017
8920180^45427-45427^180102451Norman Luhn09/2024
89212^340291-20301102438Enzo Doria06/2013
892212^94915+89102431Lelio R Paula10/2016
8923(106*10^102422+17)/3102424Robert Price04/2021
892424466^15349+15349^24466102417Hans Havermann03/2019
89252^340212+111546435102415Paul Bourdelais10/2021
89262^340208-20373102413Enzo Doria06/2013
89276^131598-17273102404Enzo Doria02/2013
8928(2^340132+1182)/2102390Stefano Morozzi09/2020
8929(2^340133+1166)/2102390Stefano Morozzi09/2020
89302^340115-21181102385Enzo Doria06/2013
8931(55459*2^340090+1)/1591102379Lelio R Paula07/2014
8932(2^340064+3630)/2102370Stefano Morozzi09/2020
89339348*31^68638+13102369Eric Chen04/2024
893489^52511-88^52511102365Robert Price06/2015
89353^214539-112756102362Enzo Doria07/2014
8936Phi(562221,2)/53723397926257372614541581386770268796893300042857102361Anonymous06/2025
893723159^23450-23450^23159102353Norbert Schneider12/2019
89382^340000-19877102351Enzo Doria06/2013
89402^339990-114845102348Enzo Doria05/2015
8939311^41058-41058^311102348Norman Luhn09/2024
8941(3^214516-2)/51383102346Lelio R Paula12/2013
894220^78661-99102341Lelio R Paula09/2016
89432^339951-19585102336Enzo Doria05/2013
8944(17*10^102335-167)/3102336Robert Price05/2022
8945(13*2^339943+1)/45102333Lelio R Paula12/2013
8946(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
89475*10^102323-91102324Robert Price03/2021
89492^339889+29327102317Yves Minet06/2010
8948(167*10^102315-17)/3102317Robert Price03/2020
895026348^7641+7641^26348102314Hans Havermann03/2019
8951Phi(239414,10)/6333218543102303Makoto Kamada08/2019
89522^339834-109493102301Enzo Doria04/2014
8953(16*10^102299-19)/3102300Robert Price02/2019
8954(11^98221-5^98221)/6102286Robert Price01/2013
89553^214365+1820102279Lelio R Paula10/2016
895631978^1579+1579^31978102278Hans Havermann03/2019
8957(89*10^102262-467)/9102263Robert Price04/2022
8958(11*2^339705-1)/183102261Lelio R Paula03/2014
89592^339694-16995102259Lelio R Paula09/2016
8960(56*10^102255+691)/9102256Robert Price05/2019
8961122^49008+121102249Norbert Schneider10/2018
8962(2^339652+3178)/2102246Stefano Morozzi09/2020
89637^120985-38102245Lelio R Paula10/2016
896410^102244+122961102245Patrick De Geest12/2016
896510^102244-27102244Lelio R Paula09/2016
89667^120982-62102242Lelio R Paula10/2016
8967(2^339640+2670)/2102242Stefano Morozzi09/2020
89684*6^131382-5102236Lelio R Paula11/2014
8969(2^339607+3290)/2102232Stefano Morozzi02/2021
89702^339586-1091102226Yves Minet11/2012
897111^98161-3072000102225Enzo Doria12/2012
89729*7^120961-4102225Lelio R Paula11/2014
89735*3^214250+2102224Serge Batalov10/2010
897412^94713-59102213Lelio R Paula10/2016
897512^94705+89102204Lelio R Paula10/2016
8976L(2*339475)%(2^339475)102193Henri Lifchitz06/2025
89772^339407-177102172Lelio R Paula08/2011
89784*10^102163-57102164Robert Price10/2018
89792^339355+65102157Lelio R Paula07/2011
8980(28*10^102142-31)/3102143Robert Price12/2019
8981(2^339323+47)/880715102141Lelio R Paula12/2013
8982(2^339268+1758)/2102130Stefano Morozzi09/2020
8983U(610865)102130Serge Batalov07/2024
8984s(178551)102122Robert Price05/2020
8985(797*10^102112-23)/9102114Robert Price01/2022
8986(5*10^102107+7)/3102108Tyler Busby02/2023
8987(2^339175+2790)/2102102Stefano Morozzi02/2021
89902^339168+21102100Lelio R Paula07/2011
89892^339167-108807102100Enzo Doria03/2014
8988(2^339169+42)/2102100Stefano Morozzi09/2020
89912^339156+163102097Lelio R Paula08/2011
8992(2^339149+746)/2102094Stefano Morozzi09/2020
8993(25*10^102076-67)/3102077Robert Price06/2019
89942^339081-4543102074Yves Minet03/2019
8995(3435^28867-1)/3434102069Serge Batalov06/2022
89962*10^102062+77102063Robert Price08/2020
899724327^15668+15668^24327102053Hans Havermann02/2019
899810^102052+66793102053Patrick De Geest09/2022
900010^102052-7000001102052Robert Price06/2021
899910^102052-618623102052Patrick De Geest09/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 28 2025 10:26 (Time in France)

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