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 ?
6751(191*10^112903-17)/3112905Robert Price11/2021
6752(2^375022+1210)/2112893Stefano Morozzi09/2020
675325992^22039+22039^25992112889Hans Havermann02/2021
67542^374993-2787163112885Enzo Doria11/2015
6755(697*10^112869+23)/9112871Robert Price04/2021
6756(19*10^112851+377)/9112852Alfred Reich11/2022
675730420^5111+5111^30420112813Hans Havermann02/2021
675813699^27268+27268^13699112800Norbert Schneider12/2020
6759123^53970+2112793Lelio R Paula06/2013
676012308*27^78796+23112790Eric Chen07/2023
676128942^7887+7887^28942112785Hans Havermann01/2021
67622^374640-4685112778Yves Minet05/2019
676312^104501-11112776Riley Fisher12/2023
676457290^93+93^57290112775Hans Havermann01/2021
6765115^54726-54726^115112774Norman Luhn09/2024
676613608^27277-27277^13608112758Norbert Schneider12/2022
6767(2^374556+682)/2112753Stefano Morozzi09/2020
6768p(22852)#/2+512112745Robert Price05/2017
6769(11*10^112742-131)/3112743Robert Price09/2018
67702^374441-21049112718Enzo Doria06/2013
67714*10^112706-93112707Robert Price07/2020
6772(2^374321+1)/3112682H.&R. Lifchitz12/2000
6773(2^374213+1766)/2112650Stefano Morozzi09/2020
6774(2^374094+2674)/2112614Stefano Morozzi09/2020
6775(13^101089-1)/12112607Paul Bourdelais03/2010
67763^236011-8828112606Enzo Doria05/2014
677731854^3427+3427^31854112602Hans Havermann02/2021
6778(85*10^112530-373)/9112531Robert Price05/2021
6779(2^373748+1090)/2112510Stefano Morozzi09/2020
6780(2^373727+1806)/2112503Stefano Morozzi01/2021
678127618^11821+11821^27618112479Hans Havermann01/2021
6782U(602921)/4823369112479Serge Batalov07/2024
678326343^18580+18580^26343112460Hans Havermann01/2021
678439^70666+2112435Lelio R Paula11/2013
6785(134*10^112400+7)/3112402Robert Price02/2020
6786(2^373365+326)/2112394Stefano Morozzi09/2020
6787(2^373350-7)/3112390Lelio R Paula03/2014
67882^373306-1840931112377Enzo Doria06/2015
67898*10^112371-37112372Robert Price03/2022
6790(2^373262+270)/2112363Stefano Morozzi09/2020
67916*10^112359-79112360Robert Price03/2022
679234409^1842+1842^34409112356Hans Havermann02/2021
6793(142*10^112352-7)/9112354Robert Price12/2019
679425580^24633+24633^25580112336Hans Havermann01/2021
67952^373117+1872107112320Enzo Doria05/2016
6796(2^373083+2226)/2112309Stefano Morozzi01/2021
6797(35*10^112308+37)/9112309Robert Price05/2022
679827963^10376+10376^27963112301Hans Havermann01/2021
67992^373040+2792761112297Enzo Doria03/2016
6800(156^51203-1)/155112293Anonymous06/2024
6801EPrime(112280)112280Eric W. Weisstein10/2010
68022^372950+7112270Lelio R Paula03/2013
68032^372945+1872167112268Enzo Doria05/2016
680436274^1243+1243^36274112249Hans Havermann02/2021
6805(55*10^112246+629)/9112247Robert Price01/2022
6806(2^372872+3798)/2112246Stefano Morozzi02/2021
680725513^25060+25060^25513112232Hans Havermann02/2021
6808(53*10^112229-611)/9112230Robert Price02/2022
6809(2^372754+3094)/2112210Stefano Morozzi09/2020
68106*10^112208+43112209Robert Price07/2020
6811(2^372728+3058)/2112203Stefano Morozzi09/2020
681232061^3158+3158^32061112195Hans Havermann02/2021
68132^372695+72113112193Enzo Doria04/2016
68142^372689-2563112191Yves Minet07/2014
68152^372638-1859441112176Enzo Doria03/2016
68163^235074-113056112159Enzo Doria07/2014
6817-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
6818(2^372514+1822)/2112138Stefano Morozzi02/2021
681929468^6387+6387^29468112135Hans Havermann02/2021
6820(2^372428+3742)/2112112Stefano Morozzi01/2021
682125375^25454-25454^25375112110Norbert Schneider01/2021
6822131^52949-130112108Norbert Schneider02/2019
6823(91*10^112098-1)/9112100Robert Price04/2015
6824(68*10^112087-149)/9112088Robert Price07/2022
68252^372314+212419112078Enzo Doria08/2023
68262^372310-85061112077Paul Bourdelais02/2012
6827(10^112067+53)/9112067Serge Batalov07/2015
6828(2^372237+2082)/2112055Stefano Morozzi09/2020
682975^59760+2112054Lelio R Paula08/2013
6830(2^372200+1710)/2112044Stefano Morozzi09/2020
6831(10^112048+7)/8747/373157112039Alfred Reich06/2021
6832(2^372181+2250)/2112038Stefano Morozzi01/2021
6833F(536233)/825798821/1102495049/5641839306317112036Serge Batalov07/2024
6834(2^372161+2574)/2112032Stefano Morozzi09/2020
68358*10^112018-49112019Robert Price08/2019
68372^372108+74221112016Enzo Doria04/2016
6836(2^372109+2046)/2112016Stefano Morozzi09/2020
68388*10^112011-73112012Robert Price01/2022
6839(184*10^112007-1)/3112009Robert Price02/2020
68405*10^112003+81112004Robert Price03/2019
6841215^48018+48018^215112000Norbert Schneider10/2018
684225549^24148+24148^25549111979Hans Havermann02/2021
68432^371970-459491111975Enzo Doria05/2015
684441^69427-40^69427111971Robert Price07/2012
6845(2^371782+358)/2111918Stefano Morozzi01/2021
684615*25^80056+446111915Eric Chen10/2023
6847(34*10^111902-547)/9111903Robert Price03/2021
6848(10^111902+71)/9111902Serge Batalov07/2015
6849(2^371625+1610)/2111870Stefano Morozzi09/2020
685029080^7027+7027^29080111865Hans Havermann01/2021
685131307^3730+3730^31307111820Hans Havermann02/2021
68522^371440-112865111815Enzo Doria06/2014
68532^371426-459161111811Enzo Doria05/2015
685425768^21771+21771^25768111779Hans Havermann02/2021
685528022^9747+9747^28022111777Hans Havermann02/2021
6856(94*10^111770+11)/3111772Robert Price04/2020
68572^371276-461267111766Enzo Doria07/2015
68586*10^111760+43111761Robert Price07/2020
685998079!4-1024111747Robert Price11/2019
6860(2^371186+3162)/2111738Stefano Morozzi09/2020
686110^(2*55862+1)-4*10^55862-1111725Robert Price07/2023
68622^371098-113261111712Enzo Doria07/2014
6863(7*10^111706-61)/9111706Erik Branger01/2011
68642^371044+1869391111696Enzo Doria05/2016
686526310^17581+17581^26310111688Hans Havermann01/2021
686688^57416+87111645Norbert Schneider11/2015
68672^370829-109693111631Enzo Doria04/2014
686815^94906-2111619Lelio R Paula11/2013
686925835^20904+20904^25835111614Hans Havermann02/2021
6870(2^370726+1198)/2111600Stefano Morozzi09/2020
687127758^10479+10479^27758111597Hans Havermann02/2021
68722^370695-4627111591Yves Minet05/2019
68737*10^111579-87111580Robert Price06/2020
68742^370643-37111575Yves Minet01/2012
6875(2^370655-5)/2439111575Lelio R Paula03/2014
68762^370610-3911111565Yves Minet04/2017
6877(154*10^111549+17)/9111551Robert Price06/2022
687826200^18097+18097^26200111550Hans Havermann01/2021
6879286^45405+45405^286111532Norbert Schneider04/2015
68804*5^159563-9111531Lelio R Paula11/2014
68815*10^111528-21111529Robert Price12/2021
6882(4^185225+23)/3111517Robert Price10/2018
68832^370393-2797093111500Enzo Doria03/2016
6884(21*2^370382-1)/629111495Lelio R Paula03/2014
6885(2^370371+554)/2111493Stefano Morozzi09/2020
68866^143273-5111489Paul Bourdelais01/2021
68872^370292-2791979111469Enzo Doria03/2016
6888(14*10^111443-11)/3111444Robert Price08/2022
68892^370177-461551111435Enzo Doria07/2015
6890(2^370169+1706)/2111432Stefano Morozzi09/2020
6891109^54683-108111413Norbert Schneider02/2017
6893(83*10^111406-173)/9111407Robert Price04/2021
6892959^37362-37362^959111407Henri Lifchitz10/2024
6894(2^370043+1010)/2111394Stefano Morozzi09/2020
689532961^2396+2396^32961111392Hans Havermann10/2020
6896numbpart(10^10+76282)111391Serge Batalov04/2015
6897(19*10^111385+11)/3111386Robert Price07/2023
6898(23*10^111380-29)/3111381Robert Price03/2022
68992^369974+733111374Lelio R Paula05/2013
6900121^53470+120111367Norbert Schneider10/2018
69012^369915-286267111356Enzo Doria07/2015
6902(62*10^111347-629)/9111348Robert Price07/2021
69032^369855-1615111338Lelio R Paula05/2017
69047*10^111325+3111326Robert Price08/2015
690551^65176+2111293Lelio R Paula08/2013
6906Phi(43329,-43329)111283Henri Lifchitz06/2025
69072^369643-1865767111274Enzo Doria03/2016
69082^369603+885111262Lelio R Paula05/2017
690925555^22564+22564^25555111252Hans Havermann10/2020
6910F(532391)/89441689/1425422598617111243Serge Batalov07/2024
6911L(532277)111240Renaud Lifchitz03/2004
6912105^55033-2111233Lelio R Paula10/2017
6913(35*10^111232-737)/9111233Robert Price07/2018
691426970^13307+13307^26970111227Hans Havermann10/2020
691525419^23716+23716^25419111210Hans Havermann10/2020
6916(26^78593-3^78593)/23111206Robert Price02/2025
69179*10^111201-29111202Robert Price09/2019
69182^369392+29835111199Lelio R Paula05/2017
69193^233059+16111198Robert Price03/2020
69202^369354-3413111187Yves Minet12/2016
69212^369296-27111170Lelio R Paula02/2013
6922(2468^40960+1)/(2468^8192+1)111161Martin Hopf08/2024
69232^369239-109837111153Enzo Doria05/2014
69242^369224-291839111148Enzo Doria07/2015
69252^369216+2798881111146Enzo Doria04/2016
692626842^13817+13817^26842111137Hans Havermann11/2020
6927(5*10^111119-191)/3111120Robert Price05/2021
6928(29*10^111112-23)/3111113Robert Price03/2022
692910^111111+163849111112Patrick De Geest03/2017
693010^111111-312911111111Patrick De Geest03/2017
69312^369092-216923111108Enzo Doria05/2014
69322^369081-55111105Lelio R Paula02/2013
6933(2^369047+3618)/2111094Stefano Morozzi09/2020
693488^57124-87111077Norbert Schneider11/2015
69352^368980+753111075Lelio R Paula05/2013
69362^368946-3623111064Yves Minet03/2017
69372^368929+29835111059Lelio R Paula05/2017
69384^184463-3^184463111058Jean-Louis Charton12/2004
6939111^54298+110111057Norbert Schneider04/2017
6940(4*10^111032-7)/3111033Ray Chandler04/2011
6941(29*10^111020-41)/3111021Tyler Busby03/2024
694235799^1262+1262^35799111015Hans Havermann10/2020
6943(298*10^111004+11)/3111006Robert Price11/2020
694427648^10349+10349^27648111004Hans Havermann11/2020
694528899^6932+6932^28899110997Hans Havermann11/2020
6946(749^38809+1)/(749^197+1)110990Martin Hopf11/2023
69472^368641-460303110972Enzo Doria06/2015
69482^368619-109087110966Enzo Doria04/2014
6949(74*10^110961+313)/9110962Robert Price06/2019
695025258^24711+24711^25258110956Hans Havermann11/2020
6951(2^368539+1290)/2110941Stefano Morozzi01/2021
69523*2^368489+7110927Lelio R Paula09/2014
6953(14*10^110922+61)/3110923Robert Price12/2018
695497411!4-2110913Robert Price07/2017
6955(301*10^110903+23)/9110905Robert Price06/2021
6956(9179*2^368330-1)/35110881Lelio R Paula05/2015
695725830^19619+19619^25830110880Hans Havermann10/2020
6958(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
695926022^18191+18191^26022110850Hans Havermann10/2020
6960(2^368211+2250)/2110843Stefano Morozzi01/2021
6961(37*10^110813+251)/9110814Robert Price09/2021
69622^368050-64875110795Lelio R Paula05/2017
69632^368048+25110794Lelio R Paula02/2013
6964(2^368017+2262)/2110784Stefano Morozzi02/2021
696569^60239-2110771Lelio R Paula10/2013
6966(23*2^367952+1)/15717110762Lelio R Paula03/2014
69672^367924-69110757Lelio R Paula02/2013
6968(23*10^110738+61)/3110739Robert Price01/2022
6969(2^367779+3750)/2110713Stefano Morozzi01/2021
69702^367709-109723110692Enzo Doria04/2014
69712^367687+213413110685Enzo Doria09/2023
6972(3*2^367644-1)/107110671Lelio R Paula03/2014
6973(2^367626+3514)/2110667Stefano Morozzi09/2020
6974(1288676*34^72242-455)/33110642Eric Chen03/2023
6975379*10^110616+9110619Jason Yuen01/2025
6976(23*2^367398+1)/57963110595Lelio R Paula03/2014
6977140^51515-139110558Norbert Schneider04/2019
69782^367215+1879223110543Enzo Doria09/2016
697925782^19375+19375^25782110534Hans Havermann10/2020
698026117^17058+17058^26117110526Hans Havermann10/2020
69812^367141+41110521Lelio R Paula02/2013
69822^367126+29835110516Lelio R Paula05/2017
6983(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
6984(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
6985(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
6986(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
6987(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
6988(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
6989(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
6990(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
6991(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
6992(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
6993(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
69943*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
69953*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
69963*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
69973*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
69983*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
69993*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
70003*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020


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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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