PRP Records

Probable Primes Top 10000

(301692 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 ?
3501(76*10^164984+77)/9164985Robert Price10/2019
350231058^36715-36715^31058164931Frank Doornink01/2024
3503(4*10^164929-211)/9164929Robert Price03/2022
350410^164878-500001164878Robert Price03/2022
35059*10^164791-89164792Robert Price04/2020
3506(2^788414)%F(788414)164769Henri Lifchitz05/2025
35072^547178-1856501164717Enzo Doria10/2015
350811^158160-60164707Enzo Doria07/2012
3509(26*10^164643-167)/3164644Robert Price10/2019
3510(10^164643+83)/3164643Robert Price08/2021
35112^546398-59201164483Enzo Doria10/2015
35122^546332-114893164463Enzo Doria05/2015
351336087^36087-36080^36080164462Henri Lifchitz08/2024
351432003^36504-36504^32003164458Frank Doornink01/2024
3515(65*10^164427+277)/9164428Robert Price08/2021
35162^545958+1876189164350Enzo Doria07/2016
35172^545878-49841164326Enzo Doria10/2015
3518(10^164284+77)/3164284Robert Price01/2018
35192^545668-4019164263Yves Minet04/2017
352010^164216+780639164217Patrick De Geest08/2021
352210^164216-50000000001164216Robert Price12/2020
352110^164216-891051164216Patrick De Geest08/2021
3523(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
3524(16*10^164122+197)/3164123Robert Price04/2019
35252^545185+76757164118Enzo Doria05/2016
35262^545076-114329164085Enzo Doria01/2015
3527(2*10^164043-143)/3164043Robert Price03/2018
3528(33085^36481-1)/(33085^191-1)164018Ryan Propper11/2023
3529(29^112153+1)/30164011Lelio R Paula03/2017
35302^544757+1874777163989Enzo Doria06/2016
35312^544723+211193163978Enzo Doria08/2023
35322^544444-457199163894Enzo Doria01/2015
3533(32804^36481-1)/(32804^191-1)163883Ryan Propper11/2023
35342^544264-343529163840Enzo Doria07/2015
35357*10^163780+9163781Robert Price09/2015
3536(2^783598)%L(783598)163761Henri Lifchitz05/2025
35372^543989+2793047163758Enzo Doria02/2016
3538(28*10^163709+113)/3163710Robert Price03/2020
3539(2^543398)/(543398^2)163568Henri Lifchitz05/2025
3540(2013^49729-1)/(2013^223-1)163561Ryan Propper11/2023
3541(23*10^163523+301)/9163524Robert Price06/2021
3542(68*10^163521-329)/9163522Robert Price03/2021
354335820^35899+35899^35820163489Norbert Schneider11/2021
35442^542870-69551163421Enzo Doria12/2015
35452^542502+24799163310Enzo Doria10/2023
35462^542395+72533163278Enzo Doria04/2016
35472^542258+216949163236Enzo Doria12/2023
35482^542072-3683163180Yves Minet03/2017
3549fibonacci(780566)-4163129Jon Grantham08/2023
3550(682*10^163106-7)/9163108Robert Price08/2021
35512^541779-1867357163092Enzo Doria04/2016
3552(29*10^163056+313)/9163057Robert Price04/2021
35532^541476+214743163001Enzo Doria11/2023
355413^142159+14^142159-2162933Harsh Aggarwal05/2024
35558*10^162924+9162925Robert Price12/2015
35562^540905+81557162829Enzo Doria08/2016
35572^540628-2939162746Yves Minet09/2014
3558919^54919-918^54919162743Jean-Louis Charton01/2013
3559(203*10^162689+1)/3162691Robert Price03/2020
35603*10^162620-59162621Robert Price09/2018
35612^540180+26791162611Enzo Doria12/2023
35623^340694-112960162553Enzo Doria07/2014
35632^539925+81162534Henri Lifchitz11/2024
35642^539807-114081162499Enzo Doria12/2014
3565414^62093+62093^414162498Norbert Schneider03/2022
35662^539654-114893162453Enzo Doria05/2015
35679*10^162449-71162450Robert Price11/2020
35682^539617-1851583162441Enzo Doria08/2015
3569(509*10^162422+31)/9162424Robert Price08/2022
3570(91*10^162410+11)/3162412Robert Price02/2020
35712^539346+81049162360Enzo Doria07/2016
35722^539220-115499162322Enzo Doria07/2015
35732^539217-113713162321Enzo Doria09/2014
35749^170099-8^170099162316Jean-Louis Charton05/2005
35754*10^162263-39162264Robert Price09/2020
357631243^36098-36098^31243162252Frank Doornink01/2024
357731987^36000-36000^31987162180Frank Doornink01/2024
3578(115*10^162153-1)/3162155Serge Batalov12/2014
3579(10^162138+11)/3162138Serge Batalov07/2015
3580(61*10^162100-403)/9162101Robert Price10/2021
35812^538473-112723162097Enzo Doria06/2014
35822^538157+79337162002Enzo Doria06/2016
35832^538136-114749161996Enzo Doria05/2015
35842^538104+1531161986Lelio R Paula01/2013
3585(9*29^110727-1199)/14161927Curtis Bright05/2015
3586((2^179294-1)^3+2)/11161918Serge Batalov03/2023
358731198^36027-36027^31198161910Frank Doornink01/2024
35882^537815-22737161899Enzo Doria07/2013
35892^537804-39839161896Enzo Doria09/2015
3590(754*10^161816-7)/9161818Robert Price05/2020
35912^537461+29867161792Enzo Doria03/2024
35922^537458-59201161791Enzo Doria10/2015
35932*10^161766+51161767Robert Price05/2018
3594(7*10^161760+131)/3161761Robert Price06/2020
35952^537209-49849161717Enzo Doria10/2015
3596(58*10^161691+329)/9161692Robert Price05/2019
359723*10^161668-3161670Robert Price10/2021
35982^536937+1879397161635Enzo Doria09/2016
35993*2^536868-5161614Jon Grantham07/2023
360034*10^161593-9161595Robert Price06/2020
3601(31*10^161582-1)/3161584Robert Price02/2020
360224494^36813+36813^24494161575Norbert Schneider11/2023
36032^536569-22881161524Enzo Doria07/2013
3604(46*10^161505+593)/9161506Robert Price04/2022
360510^161253+573493161254Patrick De Geest07/2018
360610^161253-8001161253Robert Price03/2018
360797*10^161247-3161249Robert Price05/2020
36087*10^161192-9161193Robert Price10/2015
36092^535415-19161176Stefano Morozzi07/2022
36102^535269-113803161133Enzo Doria09/2014
36112^535205-23295161113Enzo Doria08/2013
3612(49*10^161105+437)/9161106Robert Price09/2021
36132^534961+6561161040Henri Lifchitz11/2024
3614(89^82609+1)/90161036Paul Bourdelais10/2017
361535385^35385-17692^17692160960Henri Lifchitz10/2024
36162^534429-19160880Stefano Morozzi07/2022
36172^534359-23229160859Enzo Doria08/2013
361810^160836-1001160836Robert Price10/2022
3619457^60454+60454^457160803Norbert Schneider07/2021
36208*10^160782+53160783Robert Price08/2020
362167^88037-66^88037160763Robert Price10/2013
3622(88*10^160761-637)/9160762Robert Price11/2020
36232^533981+81160745Henri Lifchitz11/2024
36242^533948-1852559160735Enzo Doria08/2015
3625(2^769082)%F(769082)160728Henri Lifchitz05/2025
36262^533665-23335160650Enzo Doria08/2013
36272^533600+217981160630Enzo Doria01/2024
3628(19*10^160619+77)/3160620Robert Price05/2019
36292^533350-5160555Stefano Morozzi07/2022
3630(38*10^160508+151)/9160509Robert Price03/2022
36313^336353-2^336353160482Mike Oakes10/2007
363226134^36315-36315^26134160411Frank Doornink03/2024
363325821^36358-36358^25821160411Frank Doornink03/2024
36342*10^160339-63160340Robert Price01/2022
363524419^36532+36532^24419160293Norbert Schneider10/2023
3636(91*10^160249+11)/3160251Robert Price02/2020
3637(772*10^160239-7)/9160241Robert Price06/2022
3638(2*10^160226+187)/9160226Robert Price06/2022
36392^532253+1868417160225Enzo Doria04/2016
36402^532108-291989160181Enzo Doria07/2015
3641(28*10^160171-79)/3160172Robert Price02/2021
3642(26*10^160166-131)/3160167Robert Price10/2019
364355*10^160145+9160147Robert Price03/2022
3644(17*10^160143+67)/3160144Robert Price01/2019
3645(394^61637-1)/393159977Jinyuan Wang04/2023
3646(19*10^159921-49)/3159922Robert Price05/2019
36472^531110-1853771159881Enzo Doria09/2015
3648(275^65536+53^65536)/2159864Kellen Shenton11/2020
36492^530992-1845299159845Enzo Doria07/2015
36502^530810+25159790Stefano Morozzi04/2021
365125590^36241-36241^25590159753Frank Doornink02/2024
3652(136*10^159736-1)/9159738Serge Batalov12/2014
36532^530417-113833159672Enzo Doria09/2014
36542^530406-69701159669Enzo Doria02/2016
36555*10^159656+41159657Robert Price03/2019
36568*10^159614+29159615Robert Price11/2021
36577^188858-188858^7159604Norbert Schneider05/2018
365828^110278+27159590Alfred Reich02/2024
3659(45^96517-2^96517)/43159562Robert Price11/2024
36607*10^159553-27159554Robert Price11/2022
36613^334409-5*2^334409159554Jon Grantham08/2023
3662(24^115597-1)/23159547Paul Bourdelais09/2017
366325472^36209-36209^25472159540Frank Doornink01/2024
3664(17*10^159438-377)/9159439Robert Price03/2018
3665(49^94321+2^94321)/51159420Robert Price06/2025
3666(203*10^159381+1)/3159383Robert Price03/2020
366732282^35343-35343^32282159361Frank Doornink02/2024
36682^529215+219383159310Enzo Doria02/2024
366989*10^159258-9159260Robert Price05/2020
36702^528944-461315159229Enzo Doria07/2015
3671(13*10^159147+161)/3159148Robert Price11/2018
36722^528620-113879159131Enzo Doria10/2014
367332125^35306-35306^32125159119Frank Doornink02/2024
3674(47*10^159083+259)/9159084Robert Price03/2022
3675(861^54181-1)/860159019Jinyuan Wang11/2023
36762^528000-23307158944Enzo Doria08/2013
3677(29*10^158909+61)/9158910Robert Price08/2018
36782^527817+1876817158889Enzo Doria07/2016
36792^527774-49451158876Enzo Doria10/2015
36802^527745-291553158868Enzo Doria07/2015
3681(91*10^158862+11)/3158864Robert Price02/2020
36822^527644-1856999158837Enzo Doria10/2015
3683(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
3684(17*10^158819+7)/3158820Robert Price06/2023
36852^527573-1863253158816Enzo Doria12/2015
36862^527553-23401158810Enzo Doria08/2013
3687(49*10^158783+437)/9158784Robert Price09/2021
368810^158755+310207158756Patrick De Geest08/2021
368910^158755-50001158755Robert Price08/2020
3690(61*10^158748-619)/9158749Robert Price03/2022
369111^152420-210158730Enzo Doria09/2012
3692(13*10^158694+401)/9158695Robert Price01/2018
36932^527052-69059158659Enzo Doria11/2015
36942^526849-113233158598Enzo Doria07/2014
369524286^36161+36161^24286158579Norbert Schneider08/2023
3696(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
3697(299*10^158544-17)/3158546Robert Price04/2020
36982^526658-3551158540Yves Minet03/2017
36997*10^158465-11158466Robert Price06/2019
3700(7^187507-3^187507)/4158462Jon Grantham08/2023
37012^526375-23115158455Enzo Doria08/2013
3702(77*10^158407-293)/9158408Robert Price09/2019
370331209^35242-35242^31209158388Frank Doornink01/2024
370432071^35144-35144^32071158363Frank Doornink01/2024
37052^526028-112793158351Enzo Doria07/2014
3706(229*10^158339-1)/3158341Robert Price07/2020
370732042^35123-35123^32042158255Frank Doornink01/2024
37082^525690-9221158249Lelio R Paula01/2013
37092*10^158242-7158243Robert Price10/2015
37102^525667-525667^2158242Henri Lifchitz12/2017
3711(56*10^158230+187)/9158231Robert Price10/2021
371210^158209-7000000001158209Robert Price12/2021
371331050^35207-35207^31050158153Frank Doornink01/2024
37142^525186-1857431158097Enzo Doria10/2015
371531527^35108-35108^31527157940Frank Doornink01/2024
37162^524515-23245157895Enzo Doria08/2013
37172^524499-109087157890Enzo Doria04/2014
37182^524384-219533157856Enzo Doria03/2024
37202^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
37212^524288+189093157827Makoto Morimoto01/2016
37192^524288-164073157827Matthias Baur03/2020
3722(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
3723(10^157792+359)/9157792Serge Batalov12/2014
37242^524154+25157787Stefano Morozzi04/2021
37252^523924+1876591157717Enzo Doria07/2016
3726(17*10^157705+67)/3157706Robert Price01/2019
3727(46^94841+1)/47157696Robert Price01/2014
37282^523774+77839157672Enzo Doria05/2016
37292^523587+2799143157616Enzo Doria04/2016
37302^523496+220141157588Enzo Doria03/2024
37312^523371+1872113157551Enzo Doria05/2016
37328*10^157477+27157478Robert Price09/2021
3733p(30987)#-p(30987+1)157417Henri Lifchitz11/2024
373432268^34909-34909^32268157397Frank Doornink02/2024
3735(8*10^157368+49)/3157369Robert Price05/2020
3736(82*10^157319+449)/9157320Robert Price11/2019
37372^522535-351457157299Enzo Doria07/2015
373825401^35704-35704^25401157271Frank Doornink01/2024
37392^522226+2799079157206Enzo Doria04/2016
3740(134*10^157191-11)/3157193Robert Price01/2022
37412^522134-1849451157178Enzo Doria08/2015
37429*10^157152+71157153Robert Price08/2020
37434*10^157150+93157151Robert Price08/2018
374431227^34952-34952^31227157093Frank Doornink01/2024
3745(32^104347+5^104347)/37157057Anonymous12/2023
3746fibonacci(751442)-2157042Jon Grantham08/2023
37472^521401-29593156958Enzo Doria08/2015
37487*10^156956+87156957Robert Price07/2019
37492^521348-23397156942Enzo Doria08/2013
375010^156902+34509156903Patrick De Geest08/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 05 2025 13:49 (Time in France)

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