PRP Records

Probable Primes Top 10000

(301668 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(10^164284+77)/3164284Robert Price01/2018
35022^545668-4019164263Yves Minet04/2017
350310^164216+780639164217Patrick De Geest08/2021
350510^164216-50000000001164216Robert Price12/2020
350410^164216-891051164216Patrick De Geest08/2021
3506(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
3507(16*10^164122+197)/3164123Robert Price04/2019
35082^545185+76757164118Enzo Doria05/2016
35092^545076-114329164085Enzo Doria01/2015
3510(2*10^164043-143)/3164043Robert Price03/2018
3511(33085^36481-1)/(33085^191-1)164018Ryan Propper11/2023
3512(29^112153+1)/30164011Lelio R Paula03/2017
35132^544757+1874777163989Enzo Doria06/2016
35142^544723+211193163978Enzo Doria08/2023
35152^544444-457199163894Enzo Doria01/2015
3516(32804^36481-1)/(32804^191-1)163883Ryan Propper11/2023
35172^544264-343529163840Enzo Doria07/2015
35187*10^163780+9163781Robert Price09/2015
3519(2^783598)%L(783598)163761Henri Lifchitz05/2025
35202^543989+2793047163758Enzo Doria02/2016
3521(28*10^163709+113)/3163710Robert Price03/2020
3522(2^543398)/(543398^2)163568Henri Lifchitz05/2025
3523(2013^49729-1)/(2013^223-1)163561Ryan Propper11/2023
3524(23*10^163523+301)/9163524Robert Price06/2021
3525(68*10^163521-329)/9163522Robert Price03/2021
352635820^35899+35899^35820163489Norbert Schneider11/2021
35272^542870-69551163421Enzo Doria12/2015
35282^542502+24799163310Enzo Doria10/2023
35292^542395+72533163278Enzo Doria04/2016
35302^542258+216949163236Enzo Doria12/2023
35312^542072-3683163180Yves Minet03/2017
3532fibonacci(780566)-4163129Jon Grantham08/2023
3533(682*10^163106-7)/9163108Robert Price08/2021
35342^541779-1867357163092Enzo Doria04/2016
3535(29*10^163056+313)/9163057Robert Price04/2021
35362^541476+214743163001Enzo Doria11/2023
353713^142159+14^142159-2162933Harsh Aggarwal05/2024
35388*10^162924+9162925Robert Price12/2015
35392^540905+81557162829Enzo Doria08/2016
35402^540628-2939162746Yves Minet09/2014
3541919^54919-918^54919162743Jean-Louis Charton01/2013
3542(203*10^162689+1)/3162691Robert Price03/2020
35433*10^162620-59162621Robert Price09/2018
35442^540180+26791162611Enzo Doria12/2023
35453^340694-112960162553Enzo Doria07/2014
35462^539925+81162534Henri Lifchitz11/2024
35472^539807-114081162499Enzo Doria12/2014
3548414^62093+62093^414162498Norbert Schneider03/2022
35492^539654-114893162453Enzo Doria05/2015
35509*10^162449-71162450Robert Price11/2020
35512^539617-1851583162441Enzo Doria08/2015
3552(509*10^162422+31)/9162424Robert Price08/2022
3553(91*10^162410+11)/3162412Robert Price02/2020
35542^539346+81049162360Enzo Doria07/2016
35552^539220-115499162322Enzo Doria07/2015
35562^539217-113713162321Enzo Doria09/2014
35579^170099-8^170099162316Jean-Louis Charton05/2005
35584*10^162263-39162264Robert Price09/2020
355931243^36098-36098^31243162252Frank Doornink01/2024
356031987^36000-36000^31987162180Frank Doornink01/2024
3561(115*10^162153-1)/3162155Serge Batalov12/2014
3562(10^162138+11)/3162138Serge Batalov07/2015
3563(61*10^162100-403)/9162101Robert Price10/2021
35642^538473-112723162097Enzo Doria06/2014
35652^538157+79337162002Enzo Doria06/2016
35662^538136-114749161996Enzo Doria05/2015
35672^538104+1531161986Lelio R Paula01/2013
3568(9*29^110727-1199)/14161927Curtis Bright05/2015
3569((2^179294-1)^3+2)/11161918Serge Batalov03/2023
357031198^36027-36027^31198161910Frank Doornink01/2024
35712^537815-22737161899Enzo Doria07/2013
35722^537804-39839161896Enzo Doria09/2015
3573(754*10^161816-7)/9161818Robert Price05/2020
35742^537461+29867161792Enzo Doria03/2024
35752^537458-59201161791Enzo Doria10/2015
35762*10^161766+51161767Robert Price05/2018
3577(7*10^161760+131)/3161761Robert Price06/2020
35782^537209-49849161717Enzo Doria10/2015
3579(58*10^161691+329)/9161692Robert Price05/2019
358023*10^161668-3161670Robert Price10/2021
35812^536937+1879397161635Enzo Doria09/2016
35823*2^536868-5161614Jon Grantham07/2023
358334*10^161593-9161595Robert Price06/2020
3584(31*10^161582-1)/3161584Robert Price02/2020
358524494^36813+36813^24494161575Norbert Schneider11/2023
35862^536569-22881161524Enzo Doria07/2013
3587(46*10^161505+593)/9161506Robert Price04/2022
358810^161253+573493161254Patrick De Geest07/2018
358910^161253-8001161253Robert Price03/2018
359097*10^161247-3161249Robert Price05/2020
35917*10^161192-9161193Robert Price10/2015
35922^535415-19161176Stefano Morozzi07/2022
35932^535269-113803161133Enzo Doria09/2014
35942^535205-23295161113Enzo Doria08/2013
3595(49*10^161105+437)/9161106Robert Price09/2021
35962^534961+6561161040Henri Lifchitz11/2024
3597(89^82609+1)/90161036Paul Bourdelais10/2017
359835385^35385-17692^17692160960Henri Lifchitz10/2024
35992^534429-19160880Stefano Morozzi07/2022
36002^534359-23229160859Enzo Doria08/2013
360110^160836-1001160836Robert Price10/2022
3602457^60454+60454^457160803Norbert Schneider07/2021
36038*10^160782+53160783Robert Price08/2020
360467^88037-66^88037160763Robert Price10/2013
3605(88*10^160761-637)/9160762Robert Price11/2020
36062^533981+81160745Henri Lifchitz11/2024
36072^533948-1852559160735Enzo Doria08/2015
3608(2^769082)%F(769082)160728Henri Lifchitz05/2025
36092^533665-23335160650Enzo Doria08/2013
36102^533600+217981160630Enzo Doria01/2024
3611(19*10^160619+77)/3160620Robert Price05/2019
36122^533350-5160555Stefano Morozzi07/2022
3613(38*10^160508+151)/9160509Robert Price03/2022
36143^336353-2^336353160482Mike Oakes10/2007
361526134^36315-36315^26134160411Frank Doornink03/2024
361625821^36358-36358^25821160411Frank Doornink03/2024
36172*10^160339-63160340Robert Price01/2022
361824419^36532+36532^24419160293Norbert Schneider10/2023
3619(91*10^160249+11)/3160251Robert Price02/2020
3620(772*10^160239-7)/9160241Robert Price06/2022
3621(2*10^160226+187)/9160226Robert Price06/2022
36222^532253+1868417160225Enzo Doria04/2016
36232^532108-291989160181Enzo Doria07/2015
3624(28*10^160171-79)/3160172Robert Price02/2021
3625(26*10^160166-131)/3160167Robert Price10/2019
362655*10^160145+9160147Robert Price03/2022
3627(17*10^160143+67)/3160144Robert Price01/2019
3628(394^61637-1)/393159977Jinyuan Wang04/2023
3629(19*10^159921-49)/3159922Robert Price05/2019
36302^531110-1853771159881Enzo Doria09/2015
3631(275^65536+53^65536)/2159864Kellen Shenton11/2020
36322^530992-1845299159845Enzo Doria07/2015
36332^530810+25159790Stefano Morozzi04/2021
363425590^36241-36241^25590159753Frank Doornink02/2024
3635(136*10^159736-1)/9159738Serge Batalov12/2014
36362^530417-113833159672Enzo Doria09/2014
36372^530406-69701159669Enzo Doria02/2016
36385*10^159656+41159657Robert Price03/2019
36398*10^159614+29159615Robert Price11/2021
36407^188858-188858^7159604Norbert Schneider05/2018
364128^110278+27159590Alfred Reich02/2024
3642(45^96517-2^96517)/43159562Robert Price11/2024
36437*10^159553-27159554Robert Price11/2022
36443^334409-5*2^334409159554Jon Grantham08/2023
3645(24^115597-1)/23159547Paul Bourdelais09/2017
364625472^36209-36209^25472159540Frank Doornink01/2024
3647(17*10^159438-377)/9159439Robert Price03/2018
3648(49^94321+2^94321)/51159420Robert Price06/2025
3649(203*10^159381+1)/3159383Robert Price03/2020
365032282^35343-35343^32282159361Frank Doornink02/2024
36512^529215+219383159310Enzo Doria02/2024
365289*10^159258-9159260Robert Price05/2020
36532^528944-461315159229Enzo Doria07/2015
3654(13*10^159147+161)/3159148Robert Price11/2018
36552^528620-113879159131Enzo Doria10/2014
365632125^35306-35306^32125159119Frank Doornink02/2024
3657(47*10^159083+259)/9159084Robert Price03/2022
3658(861^54181-1)/860159019Jinyuan Wang11/2023
36592^528000-23307158944Enzo Doria08/2013
3660(29*10^158909+61)/9158910Robert Price08/2018
36612^527817+1876817158889Enzo Doria07/2016
36622^527774-49451158876Enzo Doria10/2015
36632^527745-291553158868Enzo Doria07/2015
3664(91*10^158862+11)/3158864Robert Price02/2020
36652^527644-1856999158837Enzo Doria10/2015
3666(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
3667(17*10^158819+7)/3158820Robert Price06/2023
36682^527573-1863253158816Enzo Doria12/2015
36692^527553-23401158810Enzo Doria08/2013
3670(49*10^158783+437)/9158784Robert Price09/2021
367110^158755+310207158756Patrick De Geest08/2021
367210^158755-50001158755Robert Price08/2020
3673(61*10^158748-619)/9158749Robert Price03/2022
367411^152420-210158730Enzo Doria09/2012
3675(13*10^158694+401)/9158695Robert Price01/2018
36762^527052-69059158659Enzo Doria11/2015
36772^526849-113233158598Enzo Doria07/2014
367824286^36161+36161^24286158579Norbert Schneider08/2023
3679(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
3680(299*10^158544-17)/3158546Robert Price04/2020
36812^526658-3551158540Yves Minet03/2017
36827*10^158465-11158466Robert Price06/2019
3683(7^187507-3^187507)/4158462Jon Grantham08/2023
36842^526375-23115158455Enzo Doria08/2013
3685(77*10^158407-293)/9158408Robert Price09/2019
368631209^35242-35242^31209158388Frank Doornink01/2024
368732071^35144-35144^32071158363Frank Doornink01/2024
36882^526028-112793158351Enzo Doria07/2014
3689(229*10^158339-1)/3158341Robert Price07/2020
369032042^35123-35123^32042158255Frank Doornink01/2024
36912^525690-9221158249Lelio R Paula01/2013
36922*10^158242-7158243Robert Price10/2015
36932^525667-525667^2158242Henri Lifchitz12/2017
3694(56*10^158230+187)/9158231Robert Price10/2021
369510^158209-7000000001158209Robert Price12/2021
369631050^35207-35207^31050158153Frank Doornink01/2024
36972^525186-1857431158097Enzo Doria10/2015
369831527^35108-35108^31527157940Frank Doornink01/2024
36992^524515-23245157895Enzo Doria08/2013
37002^524499-109087157890Enzo Doria04/2014
37012^524384-219533157856Enzo Doria03/2024
37032^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
37042^524288+189093157827Makoto Morimoto01/2016
37022^524288-164073157827Matthias Baur03/2020
3705(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
3706(10^157792+359)/9157792Serge Batalov12/2014
37072^524154+25157787Stefano Morozzi04/2021
37082^523924+1876591157717Enzo Doria07/2016
3709(17*10^157705+67)/3157706Robert Price01/2019
3710(46^94841+1)/47157696Robert Price01/2014
37112^523774+77839157672Enzo Doria05/2016
37122^523587+2799143157616Enzo Doria04/2016
37132^523496+220141157588Enzo Doria03/2024
37142^523371+1872113157551Enzo Doria05/2016
37158*10^157477+27157478Robert Price09/2021
3716p(30987)#-p(30987+1)157417Henri Lifchitz11/2024
371732268^34909-34909^32268157397Frank Doornink02/2024
3718(8*10^157368+49)/3157369Robert Price05/2020
3719(82*10^157319+449)/9157320Robert Price11/2019
37202^522535-351457157299Enzo Doria07/2015
372125401^35704-35704^25401157271Frank Doornink01/2024
37222^522226+2799079157206Enzo Doria04/2016
3723(134*10^157191-11)/3157193Robert Price01/2022
37242^522134-1849451157178Enzo Doria08/2015
37259*10^157152+71157153Robert Price08/2020
37264*10^157150+93157151Robert Price08/2018
372731227^34952-34952^31227157093Frank Doornink01/2024
3728(32^104347+5^104347)/37157057Anonymous12/2023
3729fibonacci(751442)-2157042Jon Grantham08/2023
37302^521401-29593156958Enzo Doria08/2015
37317*10^156956+87156957Robert Price07/2019
37322^521348-23397156942Enzo Doria08/2013
373310^156902+34509156903Patrick De Geest08/2021
373510^156902-80000001156902Robert Price04/2021
373410^156902-69789156902Patrick De Geest08/2021
3736(98^78797+1)/99156901Paul Bourdelais12/2017
373765^86522+64156857Lelio R Paula04/2016
37388^173687-7^173687156855Jean-Louis Charton09/2004
37392^520977-1858183156830Enzo Doria10/2015
3740(8*10^156718-101)/3156719Robert Price08/2018
3741(10^156640+7)/53156639Alfred Reich07/2021
37422^520314-1849481156631Enzo Doria08/2015
3743(16*10^156563-637)/9156564Robert Price09/2022
3744(13*10^156522+89)/3156523Robert Price09/2018
3746(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
3745(2^519925-5)/3156513Stefano Morozzi08/2022
3747(4*10^156501+119)/3156502Robert Price12/2021
3748(83*10^156476-101)/9156477Robert Price08/2021
37493*10^156435-97156436Robert Price07/2018
375010^156428+111156429Boyan Hu10/2024


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2025 15:18 (Time in France)

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