PRP Records

Probable Primes Top 10000

(295503 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 ?
45012^436300+1866871131340Enzo Doria03/2016
450214^114592-3131338Paul Bourdelais12/2020
450336197^4236+4236^36197131285Hans Havermann04/2021
4504(37*10^131270+341)/9131271Robert Price08/2018
450529863^24790+24790^29863131227Hans Havermann03/2021
4506(5*10^131223-29)/3131224Robert Price03/2018
450729524^27825+27825^29524131218Hans Havermann03/2021
4508(23*2^435891-1)/699131215Lelio R Paula07/2015
4509(11*2^435879+1)/3337131211Lelio R Paula06/2015
451030639^19136+19136^30639131192Hans Havermann04/2021
4511(2^435808+1)/641/6700417131182Lelio R Paula02/2012
4512(2^435808+1)/4294967297131182Serge Batalov12/2016
45132^435773+1875557131181Enzo Doria06/2016
4514(16*10^131180+167)/3131181Robert Price06/2019
4515(26*10^131180-77)/3131181Robert Price11/2019
4516(25*10^131144-7)/9131145Robert Price05/2018
451729299^29358-29358^29299131138Norbert Schneider03/2022
45182^435612-2789939131133Enzo Doria12/2015
451933976^7231+7231^33976131121Hans Havermann03/2021
452033715^7746+7746^33715131121Hans Havermann03/2021
452166^72047-65^72047131093Robert Price09/2013
4522(5*10^131090+37)/3131091Robert Price03/2018
45232^435468+75631131089Enzo Doria04/2016
452437^83588-2131083Lelio R Paula08/2015
4525(4^217720+11)/3131081Robert Price02/2017
452630407^20448+20448^30407131074Hans Havermann04/2021
4527(22*10^131070+179)/3131071Robert Price02/2022
452828831^29388-29388^28831131067Frank Doornink05/2024
452929487^27836+27836^29487131059Hans Havermann04/2021
453029962^23615+23615^29962131030Hans Havermann03/2021
45312^435202-113193131009Enzo Doria07/2014
453241705^1384+1384^41705131002Hans Havermann04/2021
45339*10^130998-19130999Robert Price07/2019
453436243^4108+4108^36243130969Hans Havermann04/2021
4535(445^49433+1)/446130914Jinyuan Wang05/2024
4536floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
45372^434835-111937130899Enzo Doria05/2014
4538(62*10^130895-629)/9130896Robert Price07/2021
45392^434685+72257130854Enzo Doria04/2016
4540(7*10^130825+113)/3130826Robert Price02/2018
45412^434539-29317130810Enzo Doria07/2015
4542(74*10^130791+637)/9130792Robert Price01/2022
45432^434469-114259130789Enzo Doria01/2015
4544(5*10^130763+103)/9130763Robert Price04/2022
45452^434246+33130722Robert Price11/2015
454630156^21599+21599^30156130710Hans Havermann04/2021
4547(17*10^130695-161)/9130696Robert Price02/2021
454830513^19148+19148^30513130661Hans Havermann03/2021
454929736^24761+24761^29736130654Hans Havermann04/2021
45509*10^130638+41130639Robert Price08/2020
45512^433911-91130621Lelio R Paula06/2017
455230786^17449+17449^30786130588Hans Havermann03/2021
45532^433744-114419130570Enzo Doria02/2015
45552^433708+1869451130560Enzo Doria05/2016
45542^433710+93130560Lelio R Paula06/2017
45567*10^130535-27130536Robert Price11/2022
4557(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
4558804*34^85220+713130516Eric Chen08/2023
4559(29*2^433547-1)/27130511Lelio R Paula06/2015
45603^273521+10130503Tyler NeSmith01/2021
456141659^1356+1356^41659130487Hans Havermann03/2021
45624*10^130480+9130481Robert Price05/2015
4563(23*2^433449-1)/75130481Lelio R Paula06/2015
45643*2^433422+5130474Jon Grantham07/2023
4565(23*2^433334-1)/3731130445Lelio R Paula06/2015
4566(31*10^130414-49)/9130415Robert Price11/2021
456726462^29485-29485^26462130402Frank Doornink03/2024
456833481^7848+7848^33481130401Hans Havermann03/2021
4569(17*10^130393+7)/3130394Robert Price06/2023
4570(22*10^130392+203)/9130393Robert Price10/2021
457129773^23950+23950^29773130386Hans Havermann04/2021
45722^433023-113497130353Enzo Doria08/2014
457331175^15178+15178^31175130350Hans Havermann04/2021
45742^433002+1179379130347Enzo Doria06/2016
45752^432974+19130339Robert Price08/2015
457631903^12168+12168^31903130331Hans Havermann04/2021
45772^432917+22217130322Enzo Doria09/2023
457829387^27112+27112^29387130278Hans Havermann04/2021
45792^432768+213181130277Enzo Doria09/2023
458029577^25370+25370^29577130267Hans Havermann04/2021
458131738^12685+12685^31738130231Hans Havermann03/2021
458244235^878+878^44235130206Hans Havermann04/2021
458332160^11171+11171^32160130187Hans Havermann04/2021
458429489^25956+25956^29489130172Hans Havermann04/2021
4585(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
458633005^8766+8766^33005130133Hans Havermann04/2021
4587(35*10^130132-611)/9130133Robert Price02/2022
4588(444^49408+1)/(444^256+1)130125Martin Hopf12/2023
45892^432217+41130111Lelio R Paula06/2017
4590(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
4591((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
459297^65480-2130094Lelio R Paula05/2017
459336007^4102+4102^36007130094Hans Havermann04/2021
45944*10^130088-89130089Robert Price11/2018
45952^432117-113215130081Enzo Doria07/2014
4596(4*10^130080+41)/9130080Serge Batalov11/2022
45972^431804+72511129986Enzo Doria04/2016
459827902^29237-29237^27902129978Frank Doornink03/2024
4599(2313^38809-1)/(2313^197-1)129898Ryan Propper11/2023
4600(13*10^129896+137)/3129897Robert Price06/2021
4601(13*10^129890+71)/3129891Robert Price06/2021
460229048^29101-29101^29048129882Norbert Schneider03/2022
460337832^2709+2709^37832129871Hans Havermann04/2021
460431055^15184+15184^31055129853Hans Havermann04/2021
4605(3^272141-3^136071+1)/7129844Serge Batalov03/2014
460631385^13702+13702^31385129833Hans Havermann04/2021
4607(13*10^129826+41)/9129827Tyler Busby02/2023
460828901^29102-29102^28901129822Norbert Schneider03/2022
4609(47*10^129789-119)/9129790Robert Price05/2019
4610(9*2^431141+1)/17129787Lelio R Paula06/2015
461125999^29384-29384^25999129730Frank Doornink03/2024
461225771^29408-29408^25771129723Frank Doornink02/2024
4613(166*10^129712+17)/3129714Robert Price07/2022
4614(29*2^430881-1)/21129709Lelio R Paula06/2015
46152^430807+1869563129686Enzo Doria05/2016
46162^430721-21429129660Enzo Doria07/2013
4617(4*10^129618+89)/3129619Robert Price08/2021
4618(142^60223-1)/141129616Anonymous06/2024
4619(10^129587-7^129587)/3129587Jon Grantham07/2023
46202^430415-276271129568Enzo Doria07/2015
462132282^10311+10311^32282129558Hans Havermann04/2021
462229486^24741+24741^29486129545Hans Havermann04/2021
4623(29*10^129543+313)/9129544Robert Price04/2021
462437095^3104+3104^37095129533Hans Havermann04/2021
462531132^14459+14459^31132129514Hans Havermann04/2021
462632582^9435+9435^32582129506Hans Havermann03/2021
462730442^17953+17953^30442129505Hans Havermann03/2021
4628(199*10^129487-7)/3129489Robert Price05/2020
46292^430142-2791721129486Enzo Doria03/2016
4630(7*10^129472-13)/3129473Robert Price07/2018
4631(8*10^129469+79)/3129470Robert Price10/2020
463231678^12213+12213^31678129463Hans Havermann04/2021
463310620^32143-10619^32143129412Norbert Schneider08/2023
4634(772*10^129406-7)/9129408Robert Price06/2022
463531100^14439+14439^31100129362Hans Havermann04/2021
463633009^8288+8288^33009129345Hans Havermann04/2021
463725895^29306-29306^25895129334Frank Doornink03/2024
4638(44^78697+43^78697)/87129333Aurel Gibier11/2023
463929675^22804+22804^29675129324Hans Havermann04/2021
464029068^28099+28099^29068129315Hans Havermann04/2021
46412^429568-21017129313Enzo Doria07/2013
4642(10^129295+83)/3129295Robert Price08/2021
4643(853*10^129274-7)/9129276Robert Price07/2021
464430958^14961+14961^30958129249Hans Havermann04/2021
4645(11*10^129239-179)/3129240Robert Price09/2018
464628659^28988+28988^28659129208Norbert Schneider02/2021
464729423^24616+24616^29423129203Hans Havermann03/2021
46482^429194-112685129201Enzo Doria06/2014
46492^429145-2780449129186Enzo Doria04/2016
465032500^9427+9427^32500129168Hans Havermann04/2021
465133577^7014+7014^33577129136Hans Havermann03/2021
46522^428892-113453129110Enzo Doria07/2014
4653(11*2^428881-7)/15129106Renaud Lifchitz03/2011
46542^428727-113959129060Enzo Doria10/2014
4655(7*2^428725-1)/13129059Lelio R Paula05/2014
4656(10^129051-31)/3129051Serge Batalov12/2014
4657(134*10^129038+7)/3129040Robert Price02/2020
46582^428564+71161129011Enzo Doria04/2016
465928781^28930+28930^28781129002Norbert Schneider02/2021
466029065^27424+27424^29065128995Hans Havermann04/2021
46612^428502-113285128992Enzo Doria07/2014
46622^428421-21373128968Enzo Doria06/2013
4663L(616787)128901Henri Lifchitz09/2008
466420^99055-3128874Paul Bourdelais12/2020
466591^65772-2128851Lelio R Paula05/2017
46662^428022+43128848Lelio R Paula05/2017
46672^427999-459397128841Enzo Doria05/2015
46682^427993+76847128839Enzo Doria05/2016
466931059^14060+14060^31059128833Hans Havermann03/2021
467010^128805+152871128806Patrick De Geest05/2021
467110^128805-10001128805Robert Price02/2021
46722^427824-1851507128788Enzo Doria08/2015
46732^427807-21469128783Enzo Doria07/2013
467429082^26783+26783^29082128772Hans Havermann04/2021
467540055^1638+1638^40055128750Hans Havermann04/2021
467611^123594-240128710Enzo Doria09/2012
46772^427504-21503128692Enzo Doria07/2013
467837727^2574+2574^37727128673Hans Havermann04/2021
467929686^21591+21591^29686128668Hans Havermann04/2021
468010^128668-70000000001128668Robert Price08/2021
46812^427420+91128667Lelio R Paula05/2017
46828*10^128651-37128652Robert Price03/2022
4683(68*10^128645-257)/9128646Robert Price07/2019
46842^427269-113635128621Enzo Doria08/2014
46852^427130+1877569128579Enzo Doria08/2016
46862^427068+20011128561Enzo Doria06/2023
46872^427016-115349128545Enzo Doria07/2015
4688(4*10^128510+137)/3128511Robert Price03/2018
46892^426889-112879128507Enzo Doria06/2014
46902^426804+1869931128481Enzo Doria05/2016
46912^426750+77635128465Enzo Doria05/2016
469227708^28913-28913^27708128450Frank Doornink03/2024
469336988^2969+2969^36988128445Hans Havermann03/2021
469436664^3185+3185^36664128439Hans Havermann03/2021
469532618^8649+8649^32618128416Hans Havermann04/2021
469628883^27874+27874^28883128391Hans Havermann04/2021
46972^426425-91128367Lelio R Paula05/2017
4698(15*2^426398-1)/11128359Lelio R Paula05/2014
46992^426352+74971128345Enzo Doria04/2016
4700(199*10^128343-7)/3128345Robert Price05/2020
47014*10^128343-21128344Robert Price09/2018
4702(65*10^128338+493)/9128339Robert Price08/2021
470335632^3997+3997^35632128337Hans Havermann04/2021
47042^426300-1863689128330Enzo Doria03/2016
47052^426293+1881017128327Enzo Doria11/2016
4706(88*10^128324-637)/9128325Robert Price11/2020
4707(491*10^128285+31)/9128287Robert Price04/2022
470839103^1908+1908^39103128281Hans Havermann04/2021
47092^426043+35128252Robert Price11/2015
4710(4*10^128244-19)/3128245Robert Price03/2018
471126220^29021-29021^26220128234Frank Doornink03/2024
471235489^4102+4102^35489128222Hans Havermann04/2021
471334721^4926+4926^34721128208Hans Havermann04/2021
4714(305*10^128198+1)/9128200Robert Price02/2020
47152^425808-459959128181Enzo Doria06/2015
471630632^15291+15291^30632128178Hans Havermann04/2021
471735981^3648+3648^35981128167Hans Havermann04/2021
47182^425627-113605128127Enzo Doria08/2014
4719(4*10^128109+119)/3128110Robert Price12/2021
4720(22*10^128094+53)/3128095Robert Price07/2019
4721(86*10^128086-221)/9128087Robert Price09/2019
472218565^30002-30002^18565128070Norbert Schneider01/2015
4723(2^425287-9)/2737128021Lelio R Paula05/2015
4724(3*2^425233-1)/25128007Lelio R Paula05/2014
4725Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
47262^425205+4911128000Marek Hubal02/2017
472729241^23836+23836^29241127995Hans Havermann04/2021
47282^425118-113663127974Enzo Doria08/2014
4729(86*10^127967-329)/9127968Robert Price01/2020
47302^425061+1869761127957Enzo Doria05/2016
4731746^44541+44541^746127955Norbert Schneider07/2019
473230236^17043+17043^30236127946Hans Havermann03/2021
47332^424938+212419127920Enzo Doria08/2023
47342^424918-21141127914Enzo Doria07/2013
4735(62*10^127903+91)/9127904Robert Price07/2021
47362^424864-29489127897Enzo Doria08/2015
473730438^15893+15893^30438127877Hans Havermann02/2021
4738(97*10^127858-1)/3127860Serge Batalov12/2014
473928929^26258+26258^28929127845Hans Havermann03/2021
474030563^15220+15220^30563127828Hans Havermann03/2021
47412^424632-2786639127827Enzo Doria03/2016
474210^127821-700001127821Robert Price08/2021
47432^424577-113755127811Enzo Doria09/2014
4744(7*2^424512-1)/3127792Lelio R Paula05/2014
4745(56*10^127752+691)/9127753Robert Price05/2019
474611^122629-720127705Enzo Doria11/2012
474722*10^127645+3127647Robert Price01/2020
474828715^27844+27844^28715127631Hans Havermann03/2021
4749(56*10^127612+187)/9127613Robert Price10/2021
4750(5*36^81995+821)/7127609Eric Chen01/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 22 2024 13:34 (Time in France)

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