PRP Records

Probable Primes Top 10000

(301429 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
50012^437884-286349131817Enzo Doria07/2015
500215^112072+14131807Alfred Reich10/2023
50035^188558+4131797Tyler NeSmith05/2021
5004(11*10^131784-17)/3131785Robert Price06/2018
5005(166^59357-1)/165131777Anonymous06/2024
50074*10^131719-93131720Robert Price07/2020
500631629^14606+14606^31629131720Hans Havermann04/2021
50083^276062-112292131716Enzo Doria07/2014
50092^437539+2025131713Henri Lifchitz01/2025
501011*31^88313+322688131708Eric Chen05/2024
5011(7*10^131682+89)/3131683Robert Price08/2020
501229512^28969+28969^29512131681Hans Havermann03/2021
50132^437343+75953131654Enzo Doria04/2016
501435^85243-34^85243131621Robert Price05/2012
5015(28*10^131586+59)/3131587Robert Price05/2021
5016(59*10^131575+391)/9131576Robert Price03/2021
501739984^1945+1945^39984131505Hans Havermann03/2021
501825842^29801-29801^25842131492Frank Doornink03/2024
501928592^29505-29505^28592131482Frank Doornink05/2024
502025647^29818-29818^25647131469Frank Doornink02/2024
5021(203*10^131457+1)/3131459Robert Price03/2020
50227*10^131421-41131422Robert Price08/2021
502387309^32+32^87309131414Hans Havermann03/2021
5024(68^71713+1)/69131413Paul Bourdelais09/2017
50252^436521+224885131406Enzo Doria07/2024
5026(650*10^131391+43)/9131393Tyler Busby01/2023
50272^436451+1884713131385Enzo Doria03/2017
50282^436365+35131359Robert Price11/2015
50302^436300+1866871131340Enzo Doria03/2016
5029(7*10^131339+179)/3131340Robert Price09/2018
503114^114592-3131338Paul Bourdelais12/2020
503236197^4236+4236^36197131285Hans Havermann04/2021
5033(37*10^131270+341)/9131271Robert Price08/2018
503429863^24790+24790^29863131227Hans Havermann03/2021
5035(5*10^131223-29)/3131224Robert Price03/2018
503629524^27825+27825^29524131218Hans Havermann03/2021
5037(23*2^435891-1)/699131215Lelio R Paula07/2015
5038(11*2^435879+1)/3337131211Lelio R Paula06/2015
503930639^19136+19136^30639131192Hans Havermann04/2021
5040(2^435808+1)/641/6700417131182Lelio R Paula02/2012
5041(2^435808+1)/4294967297131182Serge Batalov12/2016
50422^435773+1875557131181Enzo Doria06/2016
5044(16*10^131180+167)/3131181Robert Price06/2019
5043(26*10^131180-77)/3131181Robert Price11/2019
5045(25*10^131144-7)/9131145Robert Price05/2018
504629299^29358-29358^29299131138Norbert Schneider03/2022
50472^435612-2789939131133Enzo Doria12/2015
504833976^7231+7231^33976131121Hans Havermann03/2021
504933715^7746+7746^33715131121Hans Havermann03/2021
505066^72047-65^72047131093Robert Price09/2013
5051(5*10^131090+37)/3131091Robert Price03/2018
50522^435468+75631131089Enzo Doria04/2016
505337^83588-2131083Lelio R Paula08/2015
5054(4^217720+11)/3131081Robert Price02/2017
505530407^20448+20448^30407131074Hans Havermann04/2021
5056(22*10^131070+179)/3131071Robert Price02/2022
505728831^29388-29388^28831131067Frank Doornink05/2024
505829487^27836+27836^29487131059Hans Havermann04/2021
505929962^23615+23615^29962131030Hans Havermann03/2021
50602^435202-113193131009Enzo Doria07/2014
506141705^1384+1384^41705131002Hans Havermann04/2021
50629*10^130998-19130999Robert Price07/2019
506336243^4108+4108^36243130969Hans Havermann04/2021
5064(445^49433+1)/446130914Jinyuan Wang05/2024
5065floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
50662^434835-111937130899Enzo Doria05/2014
5067(62*10^130895-629)/9130896Robert Price07/2021
50682^434807+225130890Henri Lifchitz11/2024
50692^434685+72257130854Enzo Doria04/2016
5070(7*10^130825+113)/3130826Robert Price02/2018
50712^434539-29317130810Enzo Doria07/2015
5072(74*10^130791+637)/9130792Robert Price01/2022
50732^434469-114259130789Enzo Doria01/2015
5074(5*10^130763+103)/9130763Robert Price04/2022
50752^434246+33130722Robert Price11/2015
507630156^21599+21599^30156130710Hans Havermann04/2021
5077(17*10^130695-161)/9130696Robert Price02/2021
507830513^19148+19148^30513130661Hans Havermann03/2021
507929736^24761+24761^29736130654Hans Havermann04/2021
50809*10^130638+41130639Robert Price08/2020
50812^433911-91130621Lelio R Paula06/2017
508230786^17449+17449^30786130588Hans Havermann03/2021
50832^433744-114419130570Enzo Doria02/2015
50852^433708+1869451130560Enzo Doria05/2016
50842^433710+93130560Lelio R Paula06/2017
50867*10^130535-27130536Robert Price11/2022
5087(17^130533)%(10^130533)130533Henri Lifchitz05/2025
5088(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
5089804*34^85220+713130516Eric Chen08/2023
5090(29*2^433547-1)/27130511Lelio R Paula06/2015
50913^273521+10130503Tyler NeSmith01/2021
509241659^1356+1356^41659130487Hans Havermann03/2021
50934*10^130480+9130481Robert Price05/2015
5094(23*2^433449-1)/75130481Lelio R Paula06/2015
50953*2^433422+5130474Jon Grantham07/2023
5096(23*2^433334-1)/3731130445Lelio R Paula06/2015
5097(31*10^130414-49)/9130415Robert Price11/2021
509826462^29485-29485^26462130402Frank Doornink03/2024
509933481^7848+7848^33481130401Hans Havermann03/2021
5100(17*10^130393+7)/3130394Robert Price06/2023
5101(22*10^130392+203)/9130393Robert Price10/2021
510229773^23950+23950^29773130386Hans Havermann04/2021
51032^433023-113497130353Enzo Doria08/2014
510431175^15178+15178^31175130350Hans Havermann04/2021
51052^433002+1179379130347Enzo Doria06/2016
51062^432974+19130339Robert Price08/2015
510731903^12168+12168^31903130331Hans Havermann04/2021
51082^432917+22217130322Enzo Doria09/2023
510929387^27112+27112^29387130278Hans Havermann04/2021
51102^432768+213181130277Enzo Doria09/2023
511129577^25370+25370^29577130267Hans Havermann04/2021
511231738^12685+12685^31738130231Hans Havermann03/2021
511344235^878+878^44235130206Hans Havermann04/2021
511432160^11171+11171^32160130187Hans Havermann04/2021
511529489^25956+25956^29489130172Hans Havermann04/2021
5116(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
511733005^8766+8766^33005130133Hans Havermann04/2021
5118(35*10^130132-611)/9130133Robert Price02/2022
5119(444^49408+1)/(444^256+1)130125Martin Hopf12/2023
51202^432217+41130111Lelio R Paula06/2017
5121(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
5122((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
512397^65480-2130094Lelio R Paula05/2017
512436007^4102+4102^36007130094Hans Havermann04/2021
51254*10^130088-89130089Robert Price11/2018
51262^432117-113215130081Enzo Doria07/2014
5127(4*10^130080+41)/9130080Serge Batalov11/2022
51282^431804+72511129986Enzo Doria04/2016
512927902^29237-29237^27902129978Frank Doornink03/2024
5130(2313^38809-1)/(2313^197-1)129898Ryan Propper11/2023
5131(13*10^129896+137)/3129897Robert Price06/2021
5132(13*10^129890+71)/3129891Robert Price06/2021
513329048^29101-29101^29048129882Norbert Schneider03/2022
513437832^2709+2709^37832129871Hans Havermann04/2021
513531055^15184+15184^31055129853Hans Havermann04/2021
5137(3^272141-3^136071+1)/7129844Serge Batalov03/2014
5136Phi(1632846L,3)129844Anonymous03/2025
513831385^13702+13702^31385129833Hans Havermann04/2021
5139(13*10^129826+41)/9129827Tyler Busby02/2023
514028901^29102-29102^28901129822Norbert Schneider03/2022
5141(47*10^129789-119)/9129790Robert Price05/2019
5142(9*2^431141+1)/17129787Lelio R Paula06/2015
514325999^29384-29384^25999129730Frank Doornink03/2024
514425771^29408-29408^25771129723Frank Doornink02/2024
5145(166*10^129712+17)/3129714Robert Price07/2022
5146(29*2^430881-1)/21129709Lelio R Paula06/2015
51472^430807+1869563129686Enzo Doria05/2016
51482^430721-21429129660Enzo Doria07/2013
5149(4*10^129618+89)/3129619Robert Price08/2021
5150(142^60223-1)/141129616Anonymous06/2024
5151(10^129587-7^129587)/3129587Jon Grantham07/2023
51522^430415-276271129568Enzo Doria07/2015
515332282^10311+10311^32282129558Hans Havermann04/2021
515429486^24741+24741^29486129545Hans Havermann04/2021
5155(29*10^129543+313)/9129544Robert Price04/2021
515637095^3104+3104^37095129533Hans Havermann04/2021
515731132^14459+14459^31132129514Hans Havermann04/2021
515832582^9435+9435^32582129506Hans Havermann03/2021
515930442^17953+17953^30442129505Hans Havermann03/2021
5160(199*10^129487-7)/3129489Robert Price05/2020
51612^430142-2791721129486Enzo Doria03/2016
5162(7*10^129472-13)/3129473Robert Price07/2018
5163(8*10^129469+79)/3129470Robert Price10/2020
516431678^12213+12213^31678129463Hans Havermann04/2021
516510620^32143-10619^32143129412Norbert Schneider08/2023
5166(772*10^129406-7)/9129408Robert Price06/2022
5167(535^47431-1)/534129406Tom Wu09/2024
5168((3*20425-8193)*F(618977)-(20425-8193)*L(618977))/2129363Yaroslav Berezhko03/2025
516931100^14439+14439^31100129362Hans Havermann04/2021
517033009^8288+8288^33009129345Hans Havermann04/2021
517125895^29306-29306^25895129334Frank Doornink03/2024
5172(44^78697+43^78697)/87129333Aurel Gibier11/2023
517329675^22804+22804^29675129324Hans Havermann04/2021
517429068^28099+28099^29068129315Hans Havermann04/2021
51752^429568-21017129313Enzo Doria07/2013
5176(10^129295+83)/3129295Robert Price08/2021
5177(853*10^129274-7)/9129276Robert Price07/2021
517830958^14961+14961^30958129249Hans Havermann04/2021
5179(11*10^129239-179)/3129240Robert Price09/2018
518028659^28988+28988^28659129208Norbert Schneider02/2021
518129423^24616+24616^29423129203Hans Havermann03/2021
51822^429194-112685129201Enzo Doria06/2014
51832^429145-2780449129186Enzo Doria04/2016
518432500^9427+9427^32500129168Hans Havermann04/2021
518533577^7014+7014^33577129136Hans Havermann03/2021
51862^428892-113453129110Enzo Doria07/2014
5187(11*2^428881-7)/15129106Renaud Lifchitz03/2011
51882^428727-113959129060Enzo Doria10/2014
5189(7*2^428725-1)/13129059Lelio R Paula05/2014
5190(10^129051-31)/3129051Serge Batalov12/2014
5191(3^732836)/(2^732836)129047Henri Lifchitz05/2025
5192(134*10^129038+7)/3129040Robert Price02/2020
51932^428564+71161129011Enzo Doria04/2016
519428781^28930+28930^28781129002Norbert Schneider02/2021
519529065^27424+27424^29065128995Hans Havermann04/2021
51962^428502-113285128992Enzo Doria07/2014
51972^428421-21373128968Enzo Doria06/2013
5198L(616787)128901Henri Lifchitz09/2008
5199(765^44701-1)/764128900Tom Wu07/2024
520020^99055-3128874Paul Bourdelais12/2020
520191^65772-2128851Lelio R Paula05/2017
52022^428022+43128848Lelio R Paula05/2017
52032^427999-459397128841Enzo Doria05/2015
52042^427993+76847128839Enzo Doria05/2016
520531059^14060+14060^31059128833Hans Havermann03/2021
520610^128805+152871128806Patrick De Geest05/2021
520710^128805-10001128805Robert Price02/2021
52082^427824-1851507128788Enzo Doria08/2015
52092^427807-21469128783Enzo Doria07/2013
521029082^26783+26783^29082128772Hans Havermann04/2021
521140055^1638+1638^40055128750Hans Havermann04/2021
5212(923^43411-1)/922128720Tom Wu07/2024
521311^123594-240128710Enzo Doria09/2012
52142^427504-21503128692Enzo Doria07/2013
521537727^2574+2574^37727128673Hans Havermann04/2021
521629686^21591+21591^29686128668Hans Havermann04/2021
521710^128668-70000000001128668Robert Price08/2021
521810^128668-350729128668Alfred Reich08/2024
52192^427420+91128667Lelio R Paula05/2017
52208*10^128651-37128652Robert Price03/2022
5221(68*10^128645-257)/9128646Robert Price07/2019
52222^427269-113635128621Enzo Doria08/2014
52232^427130+1877569128579Enzo Doria08/2016
52242^427068+20011128561Enzo Doria06/2023
52252^427016-115349128545Enzo Doria07/2015
52262^427001+1334025128541Henri Lifchitz11/2024
5227(4*10^128510+137)/3128511Robert Price03/2018
52282^426889-112879128507Enzo Doria06/2014
52292^426804+1869931128481Enzo Doria05/2016
52302^426750+77635128465Enzo Doria05/2016
523127708^28913-28913^27708128450Frank Doornink03/2024
523236988^2969+2969^36988128445Hans Havermann03/2021
523336664^3185+3185^36664128439Hans Havermann03/2021
523432618^8649+8649^32618128416Hans Havermann04/2021
523528883^27874+27874^28883128391Hans Havermann04/2021
52362^426425-91128367Lelio R Paula05/2017
5237(15*2^426398-1)/11128359Lelio R Paula05/2014
52382^426352+74971128345Enzo Doria04/2016
5239(199*10^128343-7)/3128345Robert Price05/2020
52404*10^128343-21128344Robert Price09/2018
5241(65*10^128338+493)/9128339Robert Price08/2021
524235632^3997+3997^35632128337Hans Havermann04/2021
52432^426300-1863689128330Enzo Doria03/2016
52442^426293+1881017128327Enzo Doria11/2016
5245(88*10^128324-637)/9128325Robert Price11/2020
5246(491*10^128285+31)/9128287Robert Price04/2022
524739103^1908+1908^39103128281Hans Havermann04/2021
52482^426043+35128252Robert Price11/2015
5249(4*10^128244-19)/3128245Robert Price03/2018
525026220^29021-29021^26220128234Frank Doornink03/2024


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 21 2025 13:33 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!