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 ?
675125580^24633+24633^25580112336Hans Havermann01/2021
67522^373117+1872107112320Enzo Doria05/2016
6753(2^373083+2226)/2112309Stefano Morozzi01/2021
6754(35*10^112308+37)/9112309Robert Price05/2022
675527963^10376+10376^27963112301Hans Havermann01/2021
67562^373040+2792761112297Enzo Doria03/2016
6757(156^51203-1)/155112293Anonymous06/2024
6758EPrime(112280)112280Eric W. Weisstein10/2010
67592^372950+7112270Lelio R Paula03/2013
67602^372945+1872167112268Enzo Doria05/2016
676136274^1243+1243^36274112249Hans Havermann02/2021
6762(55*10^112246+629)/9112247Robert Price01/2022
6763(2^372872+3798)/2112246Stefano Morozzi02/2021
676425513^25060+25060^25513112232Hans Havermann02/2021
6765(53*10^112229-611)/9112230Robert Price02/2022
6766(2^372754+3094)/2112210Stefano Morozzi09/2020
67676*10^112208+43112209Robert Price07/2020
6768(2^372728+3058)/2112203Stefano Morozzi09/2020
676932061^3158+3158^32061112195Hans Havermann02/2021
67702^372695+72113112193Enzo Doria04/2016
67712^372689-2563112191Yves Minet07/2014
67722^372638-1859441112176Enzo Doria03/2016
67733^235074-113056112159Enzo Doria07/2014
6774-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
6775(2^372514+1822)/2112138Stefano Morozzi02/2021
677629468^6387+6387^29468112135Hans Havermann02/2021
6777(2^372428+3742)/2112112Stefano Morozzi01/2021
677825375^25454-25454^25375112110Norbert Schneider01/2021
6779131^52949-130112108Norbert Schneider02/2019
6780(91*10^112098-1)/9112100Robert Price04/2015
6781(68*10^112087-149)/9112088Robert Price07/2022
67822^372314+212419112078Enzo Doria08/2023
67832^372310-85061112077Paul Bourdelais02/2012
6784(10^112067+53)/9112067Serge Batalov07/2015
6785(2^372237+2082)/2112055Stefano Morozzi09/2020
678675^59760+2112054Lelio R Paula08/2013
6787(2^372200+1710)/2112044Stefano Morozzi09/2020
6788(10^112048+7)/8747/373157112039Alfred Reich06/2021
6789(2^372181+2250)/2112038Stefano Morozzi01/2021
6790F(536233)/825798821/1102495049/5641839306317112036Serge Batalov07/2024
6791(2^372161+2574)/2112032Stefano Morozzi09/2020
67928*10^112018-49112019Robert Price08/2019
67942^372108+74221112016Enzo Doria04/2016
6793(2^372109+2046)/2112016Stefano Morozzi09/2020
67958*10^112011-73112012Robert Price01/2022
6796(184*10^112007-1)/3112009Robert Price02/2020
67975*10^112003+81112004Robert Price03/2019
6798215^48018+48018^215112000Norbert Schneider10/2018
679925549^24148+24148^25549111979Hans Havermann02/2021
68002^371970-459491111975Enzo Doria05/2015
680141^69427-40^69427111971Robert Price07/2012
6802(2^371782+358)/2111918Stefano Morozzi01/2021
680315*25^80056+446111915Eric Chen10/2023
6804(34*10^111902-547)/9111903Robert Price03/2021
6805(10^111902+71)/9111902Serge Batalov07/2015
6806(2^371625+1610)/2111870Stefano Morozzi09/2020
680729080^7027+7027^29080111865Hans Havermann01/2021
680831307^3730+3730^31307111820Hans Havermann02/2021
68092^371440-112865111815Enzo Doria06/2014
68102^371426-459161111811Enzo Doria05/2015
681125768^21771+21771^25768111779Hans Havermann02/2021
681228022^9747+9747^28022111777Hans Havermann02/2021
6813(94*10^111770+11)/3111772Robert Price04/2020
68142^371276-461267111766Enzo Doria07/2015
68156*10^111760+43111761Robert Price07/2020
681698079!4-1024111747Robert Price11/2019
6817(2^371186+3162)/2111738Stefano Morozzi09/2020
681810^(2*55862+1)-4*10^55862-1111725Robert Price07/2023
68192^371098-113261111712Enzo Doria07/2014
6820(7*10^111706-61)/9111706Erik Branger01/2011
68212^371044+1869391111696Enzo Doria05/2016
682226310^17581+17581^26310111688Hans Havermann01/2021
682388^57416+87111645Norbert Schneider11/2015
68242^370829-109693111631Enzo Doria04/2014
682515^94906-2111619Lelio R Paula11/2013
682625835^20904+20904^25835111614Hans Havermann02/2021
6827(2^370726+1198)/2111600Stefano Morozzi09/2020
682827758^10479+10479^27758111597Hans Havermann02/2021
68292^370695-4627111591Yves Minet05/2019
68307*10^111579-87111580Robert Price06/2020
68312^370643-37111575Yves Minet01/2012
6832(2^370655-5)/2439111575Lelio R Paula03/2014
68332^370610-3911111565Yves Minet04/2017
6834(154*10^111549+17)/9111551Robert Price06/2022
683526200^18097+18097^26200111550Hans Havermann01/2021
6836286^45405+45405^286111532Norbert Schneider04/2015
68374*5^159563-9111531Lelio R Paula11/2014
68385*10^111528-21111529Robert Price12/2021
6839(4^185225+23)/3111517Robert Price10/2018
68402^370393-2797093111500Enzo Doria03/2016
6841(21*2^370382-1)/629111495Lelio R Paula03/2014
6842(2^370371+554)/2111493Stefano Morozzi09/2020
68436^143273-5111489Paul Bourdelais01/2021
68442^370292-2791979111469Enzo Doria03/2016
6845(14*10^111443-11)/3111444Robert Price08/2022
68462^370177-461551111435Enzo Doria07/2015
6847(2^370169+1706)/2111432Stefano Morozzi09/2020
6848109^54683-108111413Norbert Schneider02/2017
6850(83*10^111406-173)/9111407Robert Price04/2021
6849959^37362-37362^959111407Henri Lifchitz10/2024
6851(2^370043+1010)/2111394Stefano Morozzi09/2020
685232961^2396+2396^32961111392Hans Havermann10/2020
6853numbpart(10^10+76282)111391Serge Batalov04/2015
6854(19*10^111385+11)/3111386Robert Price07/2023
6855(23*10^111380-29)/3111381Robert Price03/2022
68562^369974+733111374Lelio R Paula05/2013
6857121^53470+120111367Norbert Schneider10/2018
68582^369915-286267111356Enzo Doria07/2015
6859(62*10^111347-629)/9111348Robert Price07/2021
68602^369855-1615111338Lelio R Paula05/2017
68617*10^111325+3111326Robert Price08/2015
686251^65176+2111293Lelio R Paula08/2013
6863Phi(43329,-43329)111283Henri Lifchitz06/2025
68642^369643-1865767111274Enzo Doria03/2016
68652^369603+885111262Lelio R Paula05/2017
686625555^22564+22564^25555111252Hans Havermann10/2020
6867F(532391)/89441689/1425422598617111243Serge Batalov07/2024
6868L(532277)111240Renaud Lifchitz03/2004
6869105^55033-2111233Lelio R Paula10/2017
6870(35*10^111232-737)/9111233Robert Price07/2018
687126970^13307+13307^26970111227Hans Havermann10/2020
687225419^23716+23716^25419111210Hans Havermann10/2020
6873(26^78593-3^78593)/23111206Robert Price02/2025
68749*10^111201-29111202Robert Price09/2019
68752^369392+29835111199Lelio R Paula05/2017
68763^233059+16111198Robert Price03/2020
68772^369354-3413111187Yves Minet12/2016
68782^369296-27111170Lelio R Paula02/2013
6879(2468^40960+1)/(2468^8192+1)111161Martin Hopf08/2024
68802^369239-109837111153Enzo Doria05/2014
68812^369224-291839111148Enzo Doria07/2015
68822^369216+2798881111146Enzo Doria04/2016
688326842^13817+13817^26842111137Hans Havermann11/2020
6884(5*10^111119-191)/3111120Robert Price05/2021
6885(29*10^111112-23)/3111113Robert Price03/2022
688610^111111+163849111112Patrick De Geest03/2017
688710^111111-312911111111Patrick De Geest03/2017
68882^369092-216923111108Enzo Doria05/2014
68892^369081-55111105Lelio R Paula02/2013
6890(2^369047+3618)/2111094Stefano Morozzi09/2020
689188^57124-87111077Norbert Schneider11/2015
68922^368980+753111075Lelio R Paula05/2013
68932^368946-3623111064Yves Minet03/2017
68942^368929+29835111059Lelio R Paula05/2017
68954^184463-3^184463111058Jean-Louis Charton12/2004
6896111^54298+110111057Norbert Schneider04/2017
6897(4*10^111032-7)/3111033Ray Chandler04/2011
6898(29*10^111020-41)/3111021Tyler Busby03/2024
689935799^1262+1262^35799111015Hans Havermann10/2020
6900(298*10^111004+11)/3111006Robert Price11/2020
690127648^10349+10349^27648111004Hans Havermann11/2020
690228899^6932+6932^28899110997Hans Havermann11/2020
6903(749^38809+1)/(749^197+1)110990Martin Hopf11/2023
69042^368641-460303110972Enzo Doria06/2015
69052^368619-109087110966Enzo Doria04/2014
6906(74*10^110961+313)/9110962Robert Price06/2019
690725258^24711+24711^25258110956Hans Havermann11/2020
6908(2^368539+1290)/2110941Stefano Morozzi01/2021
69093*2^368489+7110927Lelio R Paula09/2014
6910(14*10^110922+61)/3110923Robert Price12/2018
691197411!4-2110913Robert Price07/2017
6912(301*10^110903+23)/9110905Robert Price06/2021
6913(9179*2^368330-1)/35110881Lelio R Paula05/2015
691425830^19619+19619^25830110880Hans Havermann10/2020
6915(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
691626022^18191+18191^26022110850Hans Havermann10/2020
6917(2^368211+2250)/2110843Stefano Morozzi01/2021
6918(37*10^110813+251)/9110814Robert Price09/2021
69192^368050-64875110795Lelio R Paula05/2017
69202^368048+25110794Lelio R Paula02/2013
6921(2^368017+2262)/2110784Stefano Morozzi02/2021
692269^60239-2110771Lelio R Paula10/2013
6923(23*2^367952+1)/15717110762Lelio R Paula03/2014
69242^367924-69110757Lelio R Paula02/2013
6925(23*10^110738+61)/3110739Robert Price01/2022
6926(2^367779+3750)/2110713Stefano Morozzi01/2021
69272^367709-109723110692Enzo Doria04/2014
69282^367687+213413110685Enzo Doria09/2023
6929(3*2^367644-1)/107110671Lelio R Paula03/2014
6930(2^367626+3514)/2110667Stefano Morozzi09/2020
6931(1288676*34^72242-455)/33110642Eric Chen03/2023
6932379*10^110616+9110619Jason Yuen01/2025
6933(23*2^367398+1)/57963110595Lelio R Paula03/2014
6934140^51515-139110558Norbert Schneider04/2019
69352^367215+1879223110543Enzo Doria09/2016
693625782^19375+19375^25782110534Hans Havermann10/2020
693726117^17058+17058^26117110526Hans Havermann10/2020
69382^367141+41110521Lelio R Paula02/2013
69392^367126+29835110516Lelio R Paula05/2017
6940(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
6941(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
6942(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
6943(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
6944(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
6945(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
6946(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
6947(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
6948(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
6949(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
6950(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
69513*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
69523*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
69533*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
69543*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
69553*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
69563*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
69573*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
69587*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
69597*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
69607*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
69617*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
69627*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
69637*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
69647*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
69657*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
69667*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
69677*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
69687*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
69697*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
69707*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
69717*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
69727*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
6973(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
6974(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
6975(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
6976(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
6977(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
6978(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
6979(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
6980(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
6981(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
6982(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
6983(11*10^110496+49)/3110497Robert Price07/2018
698425447^21958+21958^25447110481Hans Havermann11/2020
6985(31*2^366976+1)/7110472Lelio R Paula03/2014
69867*10^110468-23110469Robert Price07/2019
69875*3^231464-2^231464110438Jon Grantham08/2023
69882^366853+5711110434Lelio R Paula05/2017
6989(21181*2^366833+1)/3110432Lelio R Paula07/2014
6990(4^231439)%(3^231439)110425Henri Lifchitz06/2025
69912^366816+315110423Lelio R Paula05/2017
6992(11^2667520)/(10^2667520)110416Henri Lifchitz06/2025
69932^366775-2787037110411Enzo Doria03/2016
6994(112*10^110405-1)/3110407Serge Batalov12/2014
69952^366751+2797553110404Enzo Doria03/2016
699625276^23331+23331^25276110404Hans Havermann10/2020
69972^366748+255110403Lelio R Paula05/2017
69982^366738-2985110400Yves Minet09/2014
6999(23*2^366739+1)/74575110396Lelio R Paula03/2014
7000(2^366722+1314)/2110395Stefano Morozzi02/2021


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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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