PRP Records

Probable Primes Top 10000

(292102 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 ?
35012^437884-286349131817Enzo Doria07/2015
35025^188558+4131797Tyler NeSmith05/2021
3503(11*10^131784-17)/3131785Robert Price06/2018
35054*10^131719-93131720Robert Price07/2020
350431629^14606+14606^31629131720Hans Havermann04/2021
35063^276062-112292131716Enzo Doria07/2014
3507(7*10^131682+89)/3131683Robert Price08/2020
350829512^28969+28969^29512131681Hans Havermann03/2021
35092^437343+75953131654Enzo Doria04/2016
351035^85243-34^85243131621Robert Price05/2012
3511(28*10^131586+59)/3131587Robert Price05/2021
3512(59*10^131575+391)/9131576Robert Price03/2021
351339984^1945+1945^39984131505Hans Havermann03/2021
3514(203*10^131457+1)/3131459Robert Price03/2020
35157*10^131421-41131422Robert Price08/2021
351687309^32+32^87309131414Hans Havermann03/2021
3517(68^71713+1)/69131413Paul Bourdelais09/2017
3518(650*10^131391+43)/9131393Tyler Busby01/2023
35192^436451+1884713131385Enzo Doria03/2017
35202^436365+35131359Robert Price11/2015
35212^436300+1866871131340Enzo Doria03/2016
3522(7*10^131339+179)/3131340Robert Price09/2018
352314^114592-3131338Paul Bourdelais12/2020
352436197^4236+4236^36197131285Hans Havermann04/2021
3525(37*10^131270+341)/9131271Robert Price08/2018
352629863^24790+24790^29863131227Hans Havermann03/2021
3527(5*10^131223-29)/3131224Robert Price03/2018
352829524^27825+27825^29524131218Hans Havermann03/2021
3529(23*2^435891-1)/699131215Lelio R Paula07/2015
3530(11*2^435879+1)/3337131211Lelio R Paula06/2015
353130639^19136+19136^30639131192Hans Havermann04/2021
3532(2^435808+1)/641/6700417131182Lelio R Paula02/2012
3533(2^435808+1)/4294967297131182Serge Batalov12/2016
35342^435773+1875557131181Enzo Doria06/2016
3535(16*10^131180+167)/3131181Robert Price06/2019
3536(26*10^131180-77)/3131181Robert Price11/2019
3537(25*10^131144-7)/9131145Robert Price05/2018
353829299^29358-29358^29299131138Norbert Schneider03/2022
35392^435612-2789939131133Enzo Doria12/2015
354033976^7231+7231^33976131121Hans Havermann03/2021
354133715^7746+7746^33715131121Hans Havermann03/2021
354266^72047-65^72047131093Robert Price09/2013
3543(5*10^131090+37)/3131091Robert Price03/2018
35442^435468+75631131089Enzo Doria04/2016
354537^83588-2131083Lelio R Paula08/2015
3546(4^217720+11)/3131081Robert Price02/2017
354730407^20448+20448^30407131074Hans Havermann04/2021
3548(22*10^131070+179)/3131071Robert Price02/2022
354929487^27836+27836^29487131059Hans Havermann04/2021
355029962^23615+23615^29962131030Hans Havermann03/2021
35512^435202-113193131009Enzo Doria07/2014
355241705^1384+1384^41705131002Hans Havermann04/2021
35539*10^130998-19130999Robert Price07/2019
355436243^4108+4108^36243130969Hans Havermann04/2021
3555floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
35562^434835-111937130899Enzo Doria05/2014
3557(62*10^130895-629)/9130896Robert Price07/2021
35582^434685+72257130854Enzo Doria04/2016
3559(7*10^130825+113)/3130826Robert Price02/2018
35602^434539-29317130810Enzo Doria07/2015
3561(74*10^130791+637)/9130792Robert Price01/2022
35622^434469-114259130789Enzo Doria01/2015
3563(5*10^130763+103)/9130763Robert Price04/2022
35642^434246+33130722Robert Price11/2015
356530156^21599+21599^30156130710Hans Havermann04/2021
3566(17*10^130695-161)/9130695Robert Price02/2021
356730513^19148+19148^30513130661Hans Havermann03/2021
356829736^24761+24761^29736130654Hans Havermann04/2021
35699*10^130638+41130639Robert Price08/2020
35702^433911-91130621Lelio R Paula06/2017
357130786^17449+17449^30786130588Hans Havermann03/2021
35722^433744-114419130570Enzo Doria02/2015
35742^433708+1869451130560Enzo Doria05/2016
35732^433710+93130560Lelio R Paula06/2017
35757*10^130535-27130536Robert Price11/2022
3576(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
3577(29*2^433547-1)/27130511Lelio R Paula06/2015
35783^273521+10130503Tyler NeSmith01/2021
357941659^1356+1356^41659130487Hans Havermann03/2021
35804*10^130480+9130481Robert Price05/2015
3581(23*2^433449-1)/75130481Lelio R Paula06/2015
3582(23*2^433334-1)/3731130445Lelio R Paula06/2015
3583(31*10^130414-49)/9130415Robert Price11/2021
358433481^7848+7848^33481130401Hans Havermann03/2021
3585(22*10^130392+203)/9130393Robert Price10/2021
358629773^23950+23950^29773130386Hans Havermann04/2021
35872^433023-113497130353Enzo Doria08/2014
358831175^15178+15178^31175130350Hans Havermann04/2021
35892^433002+1179379130347Enzo Doria06/2016
35902^432974+19130339Robert Price08/2015
359131903^12168+12168^31903130331Hans Havermann04/2021
359229387^27112+27112^29387130278Hans Havermann04/2021
359329577^25370+25370^29577130267Hans Havermann04/2021
359431738^12685+12685^31738130231Hans Havermann03/2021
359544235^878+878^44235130206Hans Havermann04/2021
359632160^11171+11171^32160130187Hans Havermann04/2021
359729489^25956+25956^29489130172Hans Havermann04/2021
3598(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
359933005^8766+8766^33005130133Hans Havermann04/2021
3600(35*10^130132-611)/9130133Robert Price02/2022
36012^432217+41130111Lelio R Paula06/2017
3602(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
3603((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
360497^65480-2130094Lelio R Paula05/2017
360536007^4102+4102^36007130094Hans Havermann04/2021
36064*10^130088-89130089Robert Price11/2018
36072^432117-113215130081Enzo Doria07/2014
3608(4*10^130080+41)/9130080Serge Batalov11/2022
36092^431804+72511129986Enzo Doria04/2016
3610(13*10^129896+137)/3129897Robert Price06/2021
3611(13*10^129890+71)/3129891Robert Price06/2021
361229048^29101-29101^29048129882Norbert Schneider03/2022
361337832^2709+2709^37832129871Hans Havermann04/2021
361431055^15184+15184^31055129853Hans Havermann04/2021
3615(3^272141-3^136071+1)/7129844Serge Batalov03/2014
361631385^13702+13702^31385129833Hans Havermann04/2021
3617(13*10^129826+41)/9129827Tyler Busby02/2023
361828901^29102-29102^28901129822Norbert Schneider03/2022
3619(47*10^129789-119)/9129790Robert Price05/2019
3620(9*2^431141+1)/17129787Lelio R Paula06/2015
3621(166*10^129712+17)/3129714Robert Price07/2022
3622(29*2^430881-1)/21129709Lelio R Paula06/2015
36232^430807+1869563129686Enzo Doria05/2016
36242^430721-21429129660Enzo Doria07/2013
3625(4*10^129618+89)/3129619Robert Price08/2021
36262^430415-276271129568Enzo Doria07/2015
362732282^10311+10311^32282129558Hans Havermann04/2021
362829486^24741+24741^29486129545Hans Havermann04/2021
3629(29*10^129543+313)/9129544Robert Price04/2021
363037095^3104+3104^37095129533Hans Havermann04/2021
363131132^14459+14459^31132129514Hans Havermann04/2021
363232582^9435+9435^32582129506Hans Havermann03/2021
363330442^17953+17953^30442129505Hans Havermann03/2021
3634(199*10^129487-7)/3129489Robert Price05/2020
36352^430142-2791721129486Enzo Doria03/2016
3636(7*10^129472-13)/3129473Robert Price07/2018
3637(8*10^129469+79)/3129470Robert Price10/2020
363831678^12213+12213^31678129463Hans Havermann04/2021
3639(772*10^129406-7)/9129408Robert Price06/2022
364031100^14439+14439^31100129362Hans Havermann04/2021
364133009^8288+8288^33009129345Hans Havermann04/2021
364229675^22804+22804^29675129324Hans Havermann04/2021
364329068^28099+28099^29068129315Hans Havermann04/2021
36442^429568-21017129313Enzo Doria07/2013
3645(10^129295+83)/3129295Robert Price08/2021
3646(853*10^129274-7)/9129276Robert Price07/2021
364730958^14961+14961^30958129249Hans Havermann04/2021
3648(11*10^129239-179)/3129240Robert Price09/2018
364928659^28988+28988^28659129208Norbert Schneider02/2021
365029423^24616+24616^29423129203Hans Havermann03/2021
36512^429194-112685129201Enzo Doria06/2014
36522^429145-2780449129186Enzo Doria04/2016
365332500^9427+9427^32500129168Hans Havermann04/2021
365433577^7014+7014^33577129136Hans Havermann03/2021
36552^428892-113453129110Enzo Doria07/2014
3656(11*2^428881-7)/15129106Renaud Lifchitz03/2011
36572^428727-113959129060Enzo Doria10/2014
3658(7*2^428725-1)/13129059Lelio R Paula05/2014
3659(10^129051-31)/3129051Serge Batalov12/2014
3660(134*10^129038+7)/3129040Robert Price02/2020
36612^428564+71161129011Enzo Doria04/2016
366228781^28930+28930^28781129002Norbert Schneider02/2021
366329065^27424+27424^29065128995Hans Havermann04/2021
36642^428502-113285128992Enzo Doria07/2014
36652^428421-21373128968Enzo Doria06/2013
3666L(616787)128901Henri Lifchitz09/2008
366720^99055-3128874Paul Bourdelais12/2020
366891^65772-2128851Lelio R Paula05/2017
36692^428022+43128848Lelio R Paula05/2017
36702^427999-459397128841Enzo Doria05/2015
36712^427993+76847128839Enzo Doria05/2016
367231059^14060+14060^31059128833Hans Havermann03/2021
367310^128805+152871128806Patrick De Geest05/2021
367410^128805-10001128805Robert Price02/2021
36752^427824-1851507128788Enzo Doria08/2015
36762^427807-21469128783Enzo Doria07/2013
367729082^26783+26783^29082128772Hans Havermann04/2021
367840055^1638+1638^40055128750Hans Havermann04/2021
367911^123594-240128710Enzo Doria09/2012
36802^427504-21503128692Enzo Doria07/2013
368137727^2574+2574^37727128673Hans Havermann04/2021
368229686^21591+21591^29686128668Hans Havermann04/2021
368310^128668-70000000001128668Robert Price08/2021
36842^427420+91128667Lelio R Paula05/2017
36858*10^128651-37128652Robert Price03/2022
3686(68*10^128645-257)/9128646Robert Price07/2019
36872^427269-113635128621Enzo Doria08/2014
36882^427130+1877569128579Enzo Doria08/2016
36892^427016-115349128545Enzo Doria07/2015
3690(4*10^128510+137)/3128511Robert Price03/2018
36912^426889-112879128507Enzo Doria06/2014
36922^426804+1869931128481Enzo Doria05/2016
36932^426750+77635128465Enzo Doria05/2016
369436988^2969+2969^36988128445Hans Havermann03/2021
369536664^3185+3185^36664128439Hans Havermann03/2021
369632618^8649+8649^32618128416Hans Havermann04/2021
369728883^27874+27874^28883128391Hans Havermann04/2021
36982^426425-91128367Lelio R Paula05/2017
3699(15*2^426398-1)/11128359Lelio R Paula05/2014
37002^426352+74971128345Enzo Doria04/2016
3701(199*10^128343-7)/3128345Robert Price05/2020
37024*10^128343-21128344Robert Price09/2018
3703(65*10^128338+493)/9128339Robert Price08/2021
370435632^3997+3997^35632128337Hans Havermann04/2021
37052^426300-1863689128330Enzo Doria03/2016
37062^426293+1881017128327Enzo Doria11/2016
3707(88*10^128324-637)/9128325Robert Price11/2020
3708(491*10^128285+31)/9128287Robert Price04/2022
370939103^1908+1908^39103128281Hans Havermann04/2021
37102^426043+35128252Robert Price11/2015
3711(4*10^128244-19)/3128245Robert Price03/2018
371235489^4102+4102^35489128222Hans Havermann04/2021
371334721^4926+4926^34721128208Hans Havermann04/2021
3714(305*10^128198+1)/9128200Robert Price02/2020
37152^425808-459959128181Enzo Doria06/2015
371630632^15291+15291^30632128178Hans Havermann04/2021
371735981^3648+3648^35981128167Hans Havermann04/2021
37182^425627-113605128127Enzo Doria08/2014
3719(4*10^128109+119)/3128110Robert Price12/2021
3720(22*10^128094+53)/3128095Robert Price07/2019
3721(86*10^128086-221)/9128087Robert Price09/2019
372218565^30002-30002^18565128070Norbert Schneider01/2015
3723(2^425287-9)/2737128021Lelio R Paula05/2015
3724(3*2^425233-1)/25128007Lelio R Paula05/2014
3725Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
37262^425205+4911128000Marek Hubal02/2017
372729241^23836+23836^29241127995Hans Havermann04/2021
37282^425118-113663127974Enzo Doria08/2014
3729(86*10^127967-329)/9127968Robert Price01/2020
37302^425061+1869761127957Enzo Doria05/2016
3731746^44541+44541^746127955Norbert Schneider07/2019
373230236^17043+17043^30236127946Hans Havermann03/2021
37332^424918-21141127914Enzo Doria07/2013
3734(62*10^127903+91)/9127904Robert Price07/2021
37352^424864-29489127897Enzo Doria08/2015
373630438^15893+15893^30438127877Hans Havermann02/2021
3737(97*10^127858-1)/3127860Serge Batalov12/2014
373828929^26258+26258^28929127845Hans Havermann03/2021
373930563^15220+15220^30563127828Hans Havermann03/2021
37402^424632-2786639127827Enzo Doria03/2016
374110^127821-700001127821Robert Price08/2021
37422^424577-113755127811Enzo Doria09/2014
3743(7*2^424512-1)/3127792Lelio R Paula05/2014
3744(56*10^127752+691)/9127753Robert Price05/2019
374511^122629-720127705Enzo Doria11/2012
374622*10^127645+3127647Robert Price01/2020
374728715^27844+27844^28715127631Hans Havermann03/2021
3748(56*10^127612+187)/9127613Robert Price10/2021
3749(5*36^81995+821)/7127609Eric Chen01/2021
37504*10^127562-39127563Robert Price09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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