PRP Records

Probable Primes Top 10000

(301723 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(148*10^103718-1)/3103720Robert Price03/2020
87522^344541-19561103718Enzo Doria05/2013
8753(1017*2^344529-1)/569103714Lelio R Paula05/2015
8754(8896^26263-1)/8895103714Serge Batalov06/2022
8755(2^344503+1758)/2103706Stefano Morozzi09/2020
8756(4*10^103703-1)/3103704Serge Batalov08/2009
87572^344444-455103688Yves Minet03/2012
8758(4*10^103678-43)/3103679Robert Price01/2022
8759(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
8760(2^344367+2738)/2103665Stefano Morozzi01/2021
87622^344317-109933103650Enzo Doria04/2014
876126055^9508+9508^26055103650Hans Havermann09/2020
87632^344309-1852033103648Enzo Doria08/2015
876425729^10672+10672^25729103643Hans Havermann09/2020
8765(2^344289+1166)/2103642Stefano Morozzi09/2020
87663*10^103637+61103638Robert Price09/2020
8767(2^344246+1614)/2103629Stefano Morozzi09/2020
87682^344213-21253103619Enzo Doria06/2013
87692^344196-465103614Lelio R Paula11/2016
87702^344187-20001103611Enzo Doria06/2013
8771(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
8772(237^43627-1)/236103601Serge Batalov06/2022
877320^79621-19^79621103590Jean-Louis Charton03/2011
8774Phi(155391,10)/1243129103586Maksym Voznyy09/2015
8775(9^108553-2^108553)/7103586Jon Grantham07/2023
87762^344085-20365103580Enzo Doria06/2013
87775^148169+54103566Lelio R Paula11/2016
87782^344017-108795103560Enzo Doria03/2014
8779(2^343974+2670)/2103547Stefano Morozzi09/2020
87802^343971-5077103546Lelio R Paula09/2011
8781(7*10^103531+71)/3103532Robert Price05/2018
87822^343899+141103524Lelio R Paula08/2011
8783(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
87846^133029-67103517Lelio R Paula11/2016
8785(17*2^343877+1)/13625103515Lelio R Paula12/2013
878666*10^103507+7103509Robert Price07/2020
878726297^8614+8614^26297103485Hans Havermann09/2020
8788(2^343764+2658)/2103483Stefano Morozzi09/2020
878926499^8036+8036^26499103480Hans Havermann09/2020
8790(103^51413-1)/4478483706103477Paul Vanderveen06/2025
8791(136*10^103474-1)/9103476Serge Batalov12/2014
87925^148014-24103458Lelio R Paula11/2016
879325^74007-24103458Anonymous09/2024
879428316^4503+4503^28316103453Hans Havermann09/2020
8795(22*10^103450+53)/3103451Robert Price07/2019
87962^343604+9931103436Yves Minet01/2011
87972^343601-21189103435Enzo Doria06/2013
8798(10^103423+173)/3103423Robert Price05/2021
87992^343508-115229103407Enzo Doria06/2015
8800(8766^26227-1)/8765103404Serge Batalov06/2022
8801(509203*2^343491-1)/16147103403Lelio R Paula05/2015
88023^216685-113056103386Enzo Doria07/2014
880324829^14580+14580^24829103382Hans Havermann08/2020
880491355!4+1024103381Robert Price09/2019
880544^62903-43^62903103379Jean-Louis Charton08/2012
880611^99262-20103371Lelio R Paula12/2016
8807(509203*2^343357-1)/5103366Lelio R Paula05/2015
8808(2^343363+3570)/2103363Stefano Morozzi09/2020
88092^343356-2791889103361Enzo Doria03/2016
8810(25*10^103360-241)/9103361Robert Price05/2018
8811Phi(104989,10)/2939693103350Maksym Voznyy09/2015
8812(371*33^68040-19)/32103321Eric Chen05/2023
881324826^14511+14511^24826103319Hans Havermann09/2020
88142^343182-171103309Lelio R Paula08/2011
8815(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
8816(16487^24649-1)/(16487^157-1)103287Ryan Propper11/2023
8817(10680^25639-1)/10679103285Serge Batalov06/2022
8818(7427^26683-1)/7426103282Serge Batalov06/2022
88192^343079-1835611103278Enzo Doria05/2015
88202^343063-1147103273Yves Minet06/2013
882124741^14930+14930^24741103271Hans Havermann09/2020
8822(16*10^103255-73)/3103256Robert Price07/2020
8823(219^44119-1)/218103256Serge Batalov06/2022
88249*6^132689+7103254Lelio R Paula11/2014
88252^342979-18085103247Enzo Doria05/2013
8826(16*10^103244-31)/3103245Robert Price03/2019
88272^342966-16995103244Lelio R Paula11/2016
882823797^21774+21774^23797103230Hans Havermann09/2020
882925388^11637+11637^25388103224Hans Havermann09/2020
8830(2^342876+2086)/2103216Stefano Morozzi09/2020
8831(16*10^103214-31)/3103215Robert Price03/2019
8833(37*10^103211+611)/9103212Robert Price11/2018
8832(238*10^103210-1)/3103212Robert Price04/2020
88345^147650+16103203Lelio R Paula11/2016
8835gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
8836Phi(852060L,10)103201Anonymous03/2025
88372^342817+2707067103199Enzo Doria03/2016
883843^63177-42103198Theodore Burton02/2007
88392^342805-21025103195Enzo Doria06/2013
884024129^18890+18890^24129103182Hans Havermann09/2020
8841(622*10^103171-1)/9103173Robert Price11/2021
88422^342714+12285103168Lelio R Paula11/2016
8843(2*10^103161-17)/3103161Serge Batalov11/2022
884418^82178-4481103156Enzo Doria03/2013
88452^342665-17349103153Enzo Doria05/2013
884630408^2467+2467^30408103150Hans Havermann09/2020
8847(5^147571-3^147571)/2103148Kellen Shenton05/2022
8848(2^342615+3090)/2103138Stefano Morozzi09/2020
88492^342612+175103137Lelio R Paula08/2011
88505*2^342585-3103130Lelio R Paula09/2014
8851(16*10^103127+77)/3103128Robert Price03/2019
8852(2^342527+3774)/2103111Stefano Morozzi02/2021
88532^342503-19209103104Enzo Doria05/2013
8854(2^342484+2586)/2103098Stefano Morozzi09/2020
88552^342476+51103096Lelio R Paula08/2011
88562^342460-18885103091Enzo Doria05/2013
8857(2^342442+862)/2103086Stefano Morozzi02/2021
8858(194*10^103074-17)/3103076Robert Price09/2020
88597^121968+82103075Lelio R Paula10/2016
88602^342392-108863103071Enzo Doria03/2014
8861(2^342389+806)/2103070Stefano Morozzi01/2021
88623^216014+28103065Lelio R Paula11/2016
88632^342353-108879103059Enzo Doria03/2014
886410^103055+276081103056Patrick De Geest12/2016
886510^103055-53103055Lelio R Paula11/2016
8866(58*10^103046+419)/9103047Robert Price05/2019
88677^121933+4103046Lelio R Paula11/2014
8868(71*10^103028-143)/9103029Robert Price10/2021
8869(2^342235+3618)/2103023Stefano Morozzi09/2020
887019^80560-68103017Lelio R Paula10/2016
88712^342209+76607103016Enzo Doria05/2016
8873328^40945+40945^328103013Norbert Schneider12/2014
887212^95454-91103013Lelio R Paula10/2016
887425833^9716+9716^25833103009Hans Havermann01/2019
8875(893*10^103004+7)/9103006Robert Price06/2021
8876(1475^32503-1)/1474102993Serge Batalov06/2022
887765^56809-64^56809102990Robert Price08/2013
88785^147338-6102985Lelio R Paula11/2014
88792^342084-112739102978Enzo Doria06/2014
88809*6^132330+7102974Lelio R Paula11/2014
88812^342034-16737102963Enzo Doria05/2013
8882(9787*2^342011-1)/25102959Lelio R Paula05/2015
8883(3^215802-5)/124343756102956Lelio R Paula12/2013
88842^341991-17421102950Enzo Doria05/2013
88852^341969-112225102943Enzo Doria06/2014
8886(9787*2^341864-1)/3102915Lelio R Paula05/2015
88872^341859+1869413102910Enzo Doria05/2016
888810^102909+61102910Lelio R Paula11/2016
888910^102909-67049102909Patrick De Geest12/2016
889023814^20935+20935^23814102898Hans Havermann02/2019
889128345^4264+4264^28345102888Hans Havermann02/2019
889225665^10204+10204^25665102886Hans Havermann02/2019
889326288^8181+8181^26288102860Hans Havermann02/2019
88942^341659+1836773102850Enzo Doria03/2016
88952^341608-110639102835Enzo Doria05/2014
889610^102824+49102825Lelio R Paula11/2016
889710^102824-168011102824Patrick De Geest12/2016
8898(156^46877-1)/155102805Anonymous06/2024
889911^98708-8102794Lelio R Paula10/2016
89002^341466+4429102792Lelio R Paula09/2011
89012^341460-107102790Lelio R Paula08/2011
8902(2^341388+47)/21014943102761Lelio R Paula12/2013
89032^341355+21102759Lelio R Paula08/2011
89042^341319+224885102748Enzo Doria07/2024
8905(419^39181-1)/418102739Tom Wu07/2024
8906(6496^26947-1)/6495102736Serge Batalov06/2022
89072^341246+40755102726Lelio R Paula11/2016
8908(2^341256-5)/991699102723Lelio R Paula12/2013
89097^121547+78102720Lelio R Paula10/2016
89102^341223-461197102719Enzo Doria06/2015
891127838^4893+4893^27838102711Hans Havermann03/2019
89132^341190-20577102709Enzo Doria06/2013
8912(27*2^341212+1)/84674449102709Lelio R Paula12/2013
8914(25*10^102698+77)/3102699Robert Price09/2022
89156^131976-65102698Lelio R Paula10/2016
89162^341134+2533102692Henri Lifchitz09/2005
891713^92184-54102688Lelio R Paula10/2016
89182^341116-20873102687Enzo Doria06/2013
89192^341094-19953102680Enzo Doria06/2013
892023761^20950+20950^23761102676Hans Havermann03/2019
89222^341053+129102668Lelio R Paula08/2011
8921(4724^27943-1)/4723102668Serge Batalov06/2022
8924(31*2^341006-1)/3102655Lelio R Paula03/2014
89237^121471+94102655Lelio R Paula10/2016
89262^341004-173102653Lelio R Paula08/2011
892520^78901+3102653Lelio R Paula10/2016
8927(2^341001+1674)/2102652Stefano Morozzi09/2020
89285^146853-52102646Lelio R Paula10/2016
89292^340969-216931102642Enzo Doria05/2014
8930122^49196+121102641Norbert Schneider10/2018
89312^340952+1870021102637Enzo Doria05/2016
89325*2^340940-3102634Lelio R Paula08/2014
8933(6^131891+1)/7102631Paul Bourdelais01/2010
8934(11*10^102629-23)/3102630Robert Price09/2021
89353^215094+5*2^215094102626Jon Grantham08/2023
893625876^9239+9239^25876102615Hans Havermann02/2019
8937(4*10^102612+83)/3102613Robert Price02/2018
8938(234^43313-1)/20184091102611Aurel Gibier03/2025
894075^54717+74102598Norbert Schneider01/2015
8939(17*10^102597+13)/3102598Robert Price01/2019
89412^340806-20393102593Enzo Doria06/2013
8942(2^340790+5)/138267102583Lelio R Paula12/2013
89436^131821+77102577Lelio R Paula10/2016
8944(203*10^102561-11)/3102563Robert Price12/2020
8945(67^56171-1)/2053280351166102561Paul Vanderveen05/2025
89462^340688-29102558Henri Lifchitz05/2005
89472^340685-109101102557Enzo Doria04/2014
894865^56567-64102552Norbert Schneider11/2014
894926230^8121+8121^26230102550Hans Havermann03/2019
8950(64*10^102547+161)/9102548Robert Price08/2022
8951(8*10^102541+49)/3102542Robert Price05/2020
8952(536*10^102533-23)/9102535Robert Price02/2020
89532^340547-108897102515Enzo Doria03/2014
8954(2^340536+778)/2102512Stefano Morozzi09/2020
895525592^10119+10119^25592102500Hans Havermann02/2019
8956(5*10^102492-23)/9102492Serge Batalov11/2022
89577^121268+82102484Lelio R Paula10/2016
8958(6883*2^340443-1)/162401102483Lelio R Paula05/2015
89592^340434-5955102481Lelio R Paula11/2016
8960(7*10^102480-19)/3102481Robert Price10/2020
8961(2^340381+47)/7102465Lelio R Paula12/2013
8962111^50095+110102461Norbert Schneider04/2017
8963180^45427-45427^180102451Norman Luhn09/2024
89642^340291-20301102438Enzo Doria06/2013
896512^94915+89102431Lelio R Paula10/2016
8966(106*10^102422+17)/3102424Robert Price04/2021
896724466^15349+15349^24466102417Hans Havermann03/2019
89682^340212+111546435102415Paul Bourdelais10/2021
89692^340208-20373102413Enzo Doria06/2013
89706^131598-17273102404Enzo Doria02/2013
8971(2^340132+1182)/2102390Stefano Morozzi09/2020
8972(2^340133+1166)/2102390Stefano Morozzi09/2020
89732^340115-21181102385Enzo Doria06/2013
8974(55459*2^340090+1)/1591102379Lelio R Paula07/2014
8975(2^340064+3630)/2102370Stefano Morozzi09/2020
89769348*31^68638+13102369Eric Chen04/2024
897789^52511-88^52511102365Robert Price06/2015
89783^214539-112756102362Enzo Doria07/2014
8979Phi(562221,2)/53723397926257372614541581386770268796893300042857102361Anonymous06/2025
898023159^23450-23450^23159102353Norbert Schneider12/2019
89812^340000-19877102351Enzo Doria06/2013
89832^339990-114845102348Enzo Doria05/2015
8982311^41058-41058^311102348Norman Luhn09/2024
8984(3^214516-2)/51383102346Lelio R Paula12/2013
898520^78661-99102341Lelio R Paula09/2016
89862^339951-19585102336Enzo Doria05/2013
8987(17*10^102335-167)/3102336Robert Price05/2022
8988(13*2^339943+1)/45102333Lelio R Paula12/2013
8989(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
89905*10^102323-91102324Robert Price03/2021
89922^339889+29327102317Yves Minet06/2010
8991(167*10^102315-17)/3102317Robert Price03/2020
899326348^7641+7641^26348102314Hans Havermann03/2019
8994Phi(239414,10)/6333218543102303Makoto Kamada08/2019
89952^339834-109493102301Enzo Doria04/2014
8996(16*10^102299-19)/3102300Robert Price02/2019
8997(11^98221-5^98221)/6102286Robert Price01/2013
89983^214365+1820102279Lelio R Paula10/2016
899931978^1579+1579^31978102278Hans Havermann03/2019
9000(89*10^102262-467)/9102263Robert Price04/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 10 2025 14:11 (Time in France)

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