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 ?
3501(71*10^165663-539)/9165664Robert Price07/2019
350225682^37567-37567^25682165657Frank Doornink02/2024
35032^550270-69551165648Enzo Doria12/2015
35042^550250+29329165642Enzo Doria03/2024
3505(202*10^165569-13)/9165571Robert Price01/2020
35062^550000-23625165567Enzo Doria08/2013
350731688^36783-36783^31688165557Frank Doornink01/2024
35082^549675-1852057165469Enzo Doria08/2015
35092^549663+212543165466Enzo Doria08/2023
3510(3^549633)%(2^549633)165456Henri Lifchitz06/2025
3511(529*10^165394-7)/9165396Robert Price08/2021
351226253^37424-37424^26253165384Frank Doornink03/2024
3513-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
3514(28*10^165358-1)/9165359Serge Batalov10/2014
35152^549278+1879669165350Enzo Doria09/2016
3516(7*10^165350-439)/9165350Robert Price02/2018
35172^549252-351269165342Enzo Doria06/2015
35182^549221+335931165332Enzo Doria09/2024
351967*10^165327-9165329Robert Price03/2021
3520(14*10^165282+73)/3165283Robert Price12/2018
3521(8*10^165283-629)/9165283Robert Price01/2022
35222^549049+2797607165281Enzo Doria04/2016
3523(218*10^165258+7)/9165260Robert Price06/2022
3524(7*10^165239+107)/3165240Robert Price02/2018
35252^548880+23961165230Enzo Doria10/2023
35265*2^548778+3165200Jon Grantham07/2023
3527(44^100511-1)/43165184Paul Bourdelais11/2017
3528(7*10^165134+107)/3165135Robert Price02/2018
3529(301*10^165082+23)/9165084Robert Price06/2021
3530(23*10^165060-83)/3165061Robert Price08/2019
35317*10^165023-27165024Robert Price11/2022
3532(76*10^164984+77)/9164985Robert Price10/2019
353331058^36715-36715^31058164931Frank Doornink01/2024
3534(4*10^164929-211)/9164929Robert Price03/2022
353510^164878-500001164878Robert Price03/2022
35369*10^164791-89164792Robert Price04/2020
3537(2^788414)%F(788414)164769Henri Lifchitz05/2025
35382^547178-1856501164717Enzo Doria10/2015
353911^158160-60164707Enzo Doria07/2012
3540(26*10^164643-167)/3164644Robert Price10/2019
3541(10^164643+83)/3164643Robert Price08/2021
35422^546398-59201164483Enzo Doria10/2015
35432^546332-114893164463Enzo Doria05/2015
354436087^36087-36080^36080164462Henri Lifchitz08/2024
354532003^36504-36504^32003164458Frank Doornink01/2024
3546(65*10^164427+277)/9164428Robert Price08/2021
35472^545958+1876189164350Enzo Doria07/2016
35482^545878-49841164326Enzo Doria10/2015
3549(10^164284+77)/3164284Robert Price01/2018
35502^545668-4019164263Yves Minet04/2017
355110^164216+780639164217Patrick De Geest08/2021
355310^164216-50000000001164216Robert Price12/2020
355210^164216-891051164216Patrick De Geest08/2021
3554(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
3555(16*10^164122+197)/3164123Robert Price04/2019
35562^545185+76757164118Enzo Doria05/2016
35572^545076-114329164085Enzo Doria01/2015
3558(2*10^164043-143)/3164043Robert Price03/2018
3559(33085^36481-1)/(33085^191-1)164018Ryan Propper11/2023
3560(29^112153+1)/30164011Lelio R Paula03/2017
35612^544757+1874777163989Enzo Doria06/2016
35622^544723+211193163978Enzo Doria08/2023
35632^544444-457199163894Enzo Doria01/2015
3564(32804^36481-1)/(32804^191-1)163883Ryan Propper11/2023
35652^544264-343529163840Enzo Doria07/2015
35667*10^163780+9163781Robert Price09/2015
3567(2^783598)%L(783598)163761Henri Lifchitz05/2025
35682^543989+2793047163758Enzo Doria02/2016
3569(28*10^163709+113)/3163710Robert Price03/2020
3570(2^543398)/(543398^2)163568Henri Lifchitz05/2025
3571(2013^49729-1)/(2013^223-1)163561Ryan Propper11/2023
3572(23*10^163523+301)/9163524Robert Price06/2021
3573(68*10^163521-329)/9163522Robert Price03/2021
357435820^35899+35899^35820163489Norbert Schneider11/2021
35752^542870-69551163421Enzo Doria12/2015
35762^542502+24799163310Enzo Doria10/2023
35772^542395+72533163278Enzo Doria04/2016
35782^542258+216949163236Enzo Doria12/2023
35792^542072-3683163180Yves Minet03/2017
3580fibonacci(780566)-4163129Jon Grantham08/2023
3581(682*10^163106-7)/9163108Robert Price08/2021
35822^541779-1867357163092Enzo Doria04/2016
3583(29*10^163056+313)/9163057Robert Price04/2021
35842^541476+214743163001Enzo Doria11/2023
358513^142159+14^142159-2162933Harsh Aggarwal05/2024
35868*10^162924+9162925Robert Price12/2015
35872^540905+81557162829Enzo Doria08/2016
35882^540628-2939162746Yves Minet09/2014
3589919^54919-918^54919162743Jean-Louis Charton01/2013
3590(203*10^162689+1)/3162691Robert Price03/2020
35913*10^162620-59162621Robert Price09/2018
35922^540180+26791162611Enzo Doria12/2023
35933^340694-112960162553Enzo Doria07/2014
35942^539925+81162534Henri Lifchitz11/2024
35952^539807-114081162499Enzo Doria12/2014
3596414^62093+62093^414162498Norbert Schneider03/2022
35972^539654-114893162453Enzo Doria05/2015
35989*10^162449-71162450Robert Price11/2020
35992^539617-1851583162441Enzo Doria08/2015
3600(509*10^162422+31)/9162424Robert Price08/2022
3601(91*10^162410+11)/3162412Robert Price02/2020
36022^539346+81049162360Enzo Doria07/2016
36032^539220-115499162322Enzo Doria07/2015
36042^539217-113713162321Enzo Doria09/2014
36059^170099-8^170099162316Jean-Louis Charton05/2005
36064*10^162263-39162264Robert Price09/2020
360731243^36098-36098^31243162252Frank Doornink01/2024
360831987^36000-36000^31987162180Frank Doornink01/2024
3609(115*10^162153-1)/3162155Serge Batalov12/2014
3610(10^162138+11)/3162138Serge Batalov07/2015
3611(61*10^162100-403)/9162101Robert Price10/2021
36122^538473-112723162097Enzo Doria06/2014
36132^538157+79337162002Enzo Doria06/2016
36142^538136-114749161996Enzo Doria05/2015
36152^538104+1531161986Lelio R Paula01/2013
3616(9*29^110727-1199)/14161927Curtis Bright05/2015
3617((2^179294-1)^3+2)/11161918Serge Batalov03/2023
361831198^36027-36027^31198161910Frank Doornink01/2024
36192^537815-22737161899Enzo Doria07/2013
36202^537804-39839161896Enzo Doria09/2015
3621(754*10^161816-7)/9161818Robert Price05/2020
36222^537461+29867161792Enzo Doria03/2024
36232^537458-59201161791Enzo Doria10/2015
36242*10^161766+51161767Robert Price05/2018
3625(7*10^161760+131)/3161761Robert Price06/2020
36262^537209-49849161717Enzo Doria10/2015
3627(58*10^161691+329)/9161692Robert Price05/2019
362823*10^161668-3161670Robert Price10/2021
36292^536937+1879397161635Enzo Doria09/2016
36303*2^536868-5161614Jon Grantham07/2023
363134*10^161593-9161595Robert Price06/2020
3632(31*10^161582-1)/3161584Robert Price02/2020
363324494^36813+36813^24494161575Norbert Schneider11/2023
36342^536569-22881161524Enzo Doria07/2013
3635(46*10^161505+593)/9161506Robert Price04/2022
363610^161253+573493161254Patrick De Geest07/2018
363710^161253-8001161253Robert Price03/2018
363897*10^161247-3161249Robert Price05/2020
36397*10^161192-9161193Robert Price10/2015
36402^535415-19161176Stefano Morozzi07/2022
36412^535269-113803161133Enzo Doria09/2014
36422^535205-23295161113Enzo Doria08/2013
3643(49*10^161105+437)/9161106Robert Price09/2021
36442^534961+6561161040Henri Lifchitz11/2024
3645(89^82609+1)/90161036Paul Bourdelais10/2017
364635385^35385-17692^17692160960Henri Lifchitz10/2024
36472^534429-19160880Stefano Morozzi07/2022
36482^534359-23229160859Enzo Doria08/2013
364910^160836-1001160836Robert Price10/2022
3650457^60454+60454^457160803Norbert Schneider07/2021
36518*10^160782+53160783Robert Price08/2020
365267^88037-66^88037160763Robert Price10/2013
3653(88*10^160761-637)/9160762Robert Price11/2020
36542^533981+81160745Henri Lifchitz11/2024
36552^533948-1852559160735Enzo Doria08/2015
3656(2^769082)%F(769082)160728Henri Lifchitz05/2025
36572^533665-23335160650Enzo Doria08/2013
36582^533600+217981160630Enzo Doria01/2024
3659(19*10^160619+77)/3160620Robert Price05/2019
36602^533350-5160555Stefano Morozzi07/2022
3661(38*10^160508+151)/9160509Robert Price03/2022
36623^336353-2^336353160482Mike Oakes10/2007
366326134^36315-36315^26134160411Frank Doornink03/2024
366425821^36358-36358^25821160411Frank Doornink03/2024
36652*10^160339-63160340Robert Price01/2022
366624419^36532+36532^24419160293Norbert Schneider10/2023
3667(91*10^160249+11)/3160251Robert Price02/2020
3668(772*10^160239-7)/9160241Robert Price06/2022
3669(2*10^160226+187)/9160226Robert Price06/2022
36702^532253+1868417160225Enzo Doria04/2016
36712^532108-291989160181Enzo Doria07/2015
3672(28*10^160171-79)/3160172Robert Price02/2021
3673(26*10^160166-131)/3160167Robert Price10/2019
367455*10^160145+9160147Robert Price03/2022
3675(17*10^160143+67)/3160144Robert Price01/2019
3676(394^61637-1)/393159977Jinyuan Wang04/2023
3677(19*10^159921-49)/3159922Robert Price05/2019
36782^531110-1853771159881Enzo Doria09/2015
3679(275^65536+53^65536)/2159864Kellen Shenton11/2020
36802^530992-1845299159845Enzo Doria07/2015
36812^530810+25159790Stefano Morozzi04/2021
368225590^36241-36241^25590159753Frank Doornink02/2024
3683(136*10^159736-1)/9159738Serge Batalov12/2014
36842^530417-113833159672Enzo Doria09/2014
36852^530406-69701159669Enzo Doria02/2016
36865*10^159656+41159657Robert Price03/2019
36878*10^159614+29159615Robert Price11/2021
36887^188858-188858^7159604Norbert Schneider05/2018
368928^110278+27159590Alfred Reich02/2024
3690(45^96517-2^96517)/43159562Robert Price11/2024
36917*10^159553-27159554Robert Price11/2022
36923^334409-5*2^334409159554Jon Grantham08/2023
3693(24^115597-1)/23159547Paul Bourdelais09/2017
369425472^36209-36209^25472159540Frank Doornink01/2024
3695(17*10^159438-377)/9159439Robert Price03/2018
3696(49^94321+2^94321)/51159420Robert Price06/2025
3697(203*10^159381+1)/3159383Robert Price03/2020
369832282^35343-35343^32282159361Frank Doornink02/2024
36992^529215+219383159310Enzo Doria02/2024
370089*10^159258-9159260Robert Price05/2020
37012^528944-461315159229Enzo Doria07/2015
3702(13*10^159147+161)/3159148Robert Price11/2018
37032^528620-113879159131Enzo Doria10/2014
370432125^35306-35306^32125159119Frank Doornink02/2024
3705(47*10^159083+259)/9159084Robert Price03/2022
3706(861^54181-1)/860159019Jinyuan Wang11/2023
37072^528000-23307158944Enzo Doria08/2013
3708(29*10^158909+61)/9158910Robert Price08/2018
37092^527817+1876817158889Enzo Doria07/2016
37102^527774-49451158876Enzo Doria10/2015
37112^527745-291553158868Enzo Doria07/2015
3712(91*10^158862+11)/3158864Robert Price02/2020
37132^527644-1856999158837Enzo Doria10/2015
3714(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
3715(17*10^158819+7)/3158820Robert Price06/2023
37162^527573-1863253158816Enzo Doria12/2015
37172^527553-23401158810Enzo Doria08/2013
3718(49*10^158783+437)/9158784Robert Price09/2021
371910^158755+310207158756Patrick De Geest08/2021
372010^158755-50001158755Robert Price08/2020
3721(61*10^158748-619)/9158749Robert Price03/2022
372211^152420-210158730Enzo Doria09/2012
3723(13*10^158694+401)/9158695Robert Price01/2018
37242^527052-69059158659Enzo Doria11/2015
37252^526849-113233158598Enzo Doria07/2014
372624286^36161+36161^24286158579Norbert Schneider08/2023
3727(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
3728(299*10^158544-17)/3158546Robert Price04/2020
37292^526658-3551158540Yves Minet03/2017
37307*10^158465-11158466Robert Price06/2019
3731(7^187507-3^187507)/4158462Jon Grantham08/2023
37322^526375-23115158455Enzo Doria08/2013
3733(77*10^158407-293)/9158408Robert Price09/2019
373431209^35242-35242^31209158388Frank Doornink01/2024
373532071^35144-35144^32071158363Frank Doornink01/2024
37362^526028-112793158351Enzo Doria07/2014
3737(229*10^158339-1)/3158341Robert Price07/2020
373832042^35123-35123^32042158255Frank Doornink01/2024
37392^525690-9221158249Lelio R Paula01/2013
37402*10^158242-7158243Robert Price10/2015
37412^525667-525667^2158242Henri Lifchitz12/2017
3742(56*10^158230+187)/9158231Robert Price10/2021
374310^158209-7000000001158209Robert Price12/2021
374431050^35207-35207^31050158153Frank Doornink01/2024
37452^525186-1857431158097Enzo Doria10/2015
374631527^35108-35108^31527157940Frank Doornink01/2024
37472^524515-23245157895Enzo Doria08/2013
37482^524499-109087157890Enzo Doria04/2014
37492^524384-219533157856Enzo Doria03/2024
37502^524288-164073157827Matthias Baur03/2020


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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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