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 ?
50012^446494-16485134409Enzo Doria04/2013
500230042^29785+29785^30042134408Hans Havermann12/2020
500329504^30069-30069^29504134405Norbert Schneider12/2014
50042^446441+65134393Lelio R Paula08/2017
5005(10^134385+719)/9134385Serge Batalov12/2014
500630043^29688+29688^30043134370Hans Havermann12/2020
5007(2*10^134364+529)/9134364Robert Price01/2018
500834657^7512+7512^34657134323Hans Havermann11/2020
5009(13*2^446187-1)/661134314Lelio R Paula07/2015
50105^192103+3^192103+2^192103+1134275Matthias Baur12/2019
501142035^1564+1564^42035134270Hans Havermann12/2020
5013(2^446022-7)/339134264Lelio R Paula07/2015
501230621^24248+24248^30621134264Hans Havermann12/2020
501430341^26562+26562^30341134237Hans Havermann11/2020
5015(189^58967-1)/188134234Anonymous06/2024
501610^134209+99867134210Patrick De Geest05/2021
501710^134209-80000001134209Robert Price04/2021
501810^134209-323283134209Patrick De Geest05/2021
501929976^29953+29953^29976134186Hans Havermann12/2020
502035038^6755+6755^35038134183Hans Havermann12/2020
502163^74568+2134174Lelio R Paula06/2017
50222^445671-22071134161Enzo Doria07/2013
5023532^49205+49205^532134129Norbert Schneider02/2019
502436453^4780+4780^36453134127Hans Havermann04/2021
5025(28*10^134122-1)/9134123Serge Batalov10/2014
50262^445515-113859134114Enzo Doria10/2014
5028(22*10^134111-37)/3134112Robert Price04/2019
502731083^20636+20636^31083134112Hans Havermann04/2021
50293*2^445478+5134103Jon Grantham07/2023
503031622^17379+17379^31622134079Hans Havermann04/2021
50315*2^445380-3134074Jon Grantham07/2023
5032(6*32^89076+4241)/31134073Eric Chen11/2023
5033(277*10^134059-7)/9134061Robert Price02/2022
50342^445328-216917134058Enzo Doria05/2014
50352^445202+1874899134020Enzo Doria06/2016
50365^191739-3^191739-1134020Jon Grantham08/2023
5037(35*10^134003-89)/9134004Robert Price02/2022
5038(13*2^445102+1)/17133989Lelio R Paula07/2015
5039(35*10^133979-593)/9133980Robert Price07/2018
50402*10^133955+51133956Robert Price05/2018
5041(49*10^133952+437)/9133953Robert Price09/2021
50422^444964-113639133948Enzo Doria08/2014
504331811^16240+16240^31811133943Hans Havermann04/2021
504410^133902+167841133903Patrick De Geest05/2021
504628118^30097-30097^28118133902Norbert Schneider01/2015
504510^133902-100001133902Robert Price07/2020
50472^444784-113859133894Enzo Doria10/2014
5048(132^63127-1)/131133864Anonymous06/2024
504932303^13914+13914^32303133846Hans Havermann04/2021
5050(29^91493-3^91493)/26133798Robert Price06/2025
5051(2276213*2^444444+1)/3133797Alex_soldier11/2022
5052(1403559*2^444444+1)/5133797Alex_soldier11/2022
5053(1209887*2^444444+1)/9133797Alex_soldier11/2022
5054(608239*2^444444+1)/25133796Alex_soldier11/2022
5055(1824587*2^444444+1)/27133796Alex_soldier11/2022
5056(40795*2^444444+1)/7133795Alex_soldier11/2022
505730739^22458+22458^30739133757Hans Havermann04/2021
505834942^6721+6721^34942133739Hans Havermann04/2021
5059(3^280229-1)/1120918133698Aurel Gibier03/2025
5060(2^444046+100280245065)133672Paul Bourdelais05/2022
506134792^6935+6935^34792133638Hans Havermann04/2021
5062(266*10^133603+1)/3133605Robert Price04/2020
506332261^13842+13842^32261133600Hans Havermann04/2021
5064(89*10^133580+1)/9133581Serge Batalov05/2010
5065(134*10^133573-11)/3133575Robert Price01/2022
506626726^30173-30173^26726133574Frank Doornink03/2024
50672^443721+39527133574Enzo Doria11/2024
506862^74521-61^74521133571Robert Price05/2013
5069(182*10^133543+1)/3133545Robert Price02/2020
5070(103*10^133535+11)/3133537Robert Price01/2021
507132589^12520+12520^32589133537Hans Havermann03/2021
5072L(638839)/274700771133502Serge Batalov07/2024
507334516^7373+7373^34516133496Hans Havermann04/2021
50748*10^133487-37133488Robert Price03/2022
507530135^26882+26882^30135133482Hans Havermann04/2021
50762^443198-1867301133416Enzo Doria03/2016
507727^93192+26133392Anonymous09/2024
5078(19*10^133390+101)/3133391Robert Price09/2019
5079(71^72043-1)/70133369Paul Bourdelais09/2017
508036117^4910+4910^36117133311Hans Havermann04/2021
50812^442799+1874633133296Enzo Doria06/2016
5082L(637751)133283Henri Lifchitz09/2008
5083109^65410-2133269Lelio R Paula10/2017
50842^442688-113489133263Enzo Doria08/2014
5085(7*2^442640-1)/783133246Lelio R Paula07/2015
5086(9*2^442463+1)/17441133192Lelio R Paula07/2015
50872^442437-1849993133187Enzo Doria08/2015
50882^442430-2791721133185Enzo Doria03/2016
5089(13*2^442428-1)/309133183Lelio R Paula07/2015
509029959^27870+27870^29959133172Hans Havermann03/2021
5091(25*2^442379-1)/71133169Lelio R Paula07/2015
50922^442368+213691133167Enzo Doria09/2023
509334240^7737+7737^34240133145Hans Havermann03/2021
5094452^50145+50145^452133142Norbert Schneider09/2020
5095(355^52201-1)/354133122Tom Wu08/2024
5096(3^278981-1)/14507014133101Paul Vanderveen05/2025
509730659^21796+21796^30659133011Hans Havermann04/2021
509833276^9935+9935^33276133010Hans Havermann04/2021
509930111^26122+26122^30111133001Hans Havermann04/2021
510030790^20869+20869^30790132998Hans Havermann04/2021
5102(2^441799+78557)/5132995Lelio R Paula07/2015
51018*10^132994-27132995Robert Price10/2021
5103(109*10^132992+11)/3132994Robert Price06/2022
51042^441781-2787883132990Enzo Doria03/2016
5105fibonacci(636232)+4132965Jon Grantham08/2023
5106(3*2^441685+1)/749132959Lelio R Paula07/2015
51072^441618+37132941Lelio R Paula08/2017
510834857^6514+6514^34857132940Hans Havermann04/2021
510934065^7988+7988^34065132937Hans Havermann04/2021
511035571^5452+5452^35571132914Hans Havermann04/2021
51112^441521-113575132912Enzo Doria08/2014
51127*10^132884-99132885Robert Price06/2019
511326987^29988-29988^26987132882Frank Doornink03/2024
5114(103*10^132879+17)/3132881Robert Price08/2020
51152^441396-65132874Lelio R Paula08/2017
511633350^9633+9633^33350132859Hans Havermann04/2021
51172^441330+1871959132854Enzo Doria05/2016
511825772^30111-30111^25772132825Frank Doornink02/2024
51192^441063+383132774Lelio R Paula06/2012
5120(10^132753+7)/17/19132751Alfred Reich06/2021
5121(22*10^132746+53)/3132747Robert Price07/2019
5122(77*10^132744-149)/9132745Robert Price03/2022
5123(22*10^132732+119)/3132733Robert Price04/2021
51242^440846+1870909132708Enzo Doria05/2016
5125(948^44579-1)/947132701Jinyuan Wang04/2023
51262^440656-113489132651Enzo Doria08/2014
5127numbpart(14180123587)132646Serge Batalov04/2017
512832950^10591+10591^32950132622Hans Havermann04/2021
512933302^9597+9597^33302132614Hans Havermann04/2021
5130(19*10^132550+191)/3132551Robert Price05/2019
5131(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
5132(38^83891+1)/39132529Robert Price09/2013
51332*10^132493-43132494Robert Price04/2018
513431352^16809+16809^31352132480Hans Havermann04/2021
5135(418*10^132441+23)/9132443Robert Price02/2020
51362^439931-21132433Lelio R Paula08/2017
513747^79201-46^79201132432Robert Price10/2012
51382^439897-113653132423Enzo Doria08/2014
513935505^5362+5362^35505132410Hans Havermann03/2021
514030079^25222+25222^30079132402Hans Havermann04/2021
5141(5*2^439822+1)/9132400Lelio R Paula06/2015
5142(695*10^132356+7)/9132358Robert Price12/2021
5143(112*10^132337-1)/3132339Serge Batalov12/2014
51442^439576-113247132326Enzo Doria07/2014
5145(7^156589-1)/65346468774132323Paul Vanderveen05/2025
514630059^25230+25230^30059132318Hans Havermann04/2021
51472^439497-29143132302Enzo Doria07/2015
51482^439409-114193132276Enzo Doria12/2014
5149(39^83137+2^83137)/41132275Robert Price12/2024
5150(44*10^132233-233)/9132234Robert Price01/2019
515125507^30000-30000^25507132200Frank Doornink02/2024
51529*10^132148-7132149Robert Price09/2015
5153V(790390)132144Serge Batalov07/2024
5154(47*10^132125-119)/9132126Robert Price05/2019
51552^438900+214051132123Enzo Doria10/2023
51562^438845+1870217132106Enzo Doria05/2016
51572^438789+87855132089Lelio R Paula01/2016
51582^438774-2786411132085Enzo Doria03/2016
51592^438755-1848205132079Enzo Doria07/2015
516030502^21381+21381^30502132075Hans Havermann04/2021
51612^438739-112087132074Enzo Doria06/2014
5162(588859*29^90289-19)/28132043Eric Chen06/2025
5163(2^438438+100280245065)131983Paul Bourdelais05/2022
516435872^4777+4777^35872131979Hans Havermann04/2021
516531198^16945+16945^31198131938Hans Havermann03/2021
516613907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
5167L(631181)131910Henri Lifchitz09/2008
5168(47*10^131886-119)/9131887Robert Price05/2019
51695*2^438096-3131881Jon Grantham07/2023
5170(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
51712^438079-1863877131875Enzo Doria03/2016
5172(16*10^131872-37)/3131873Robert Price05/2021
5173(2^438067+5)/329131869Lelio R Paula06/2015
51742^437908-113855131824Enzo Doria09/2014
51752^437884-286349131817Enzo Doria07/2015
517615^112072+14131807Alfred Reich10/2023
51775^188558+4131797Tyler NeSmith05/2021
5178(11*10^131784-17)/3131785Robert Price06/2018
5179(166^59357-1)/165131777Anonymous06/2024
51814*10^131719-93131720Robert Price07/2020
518031629^14606+14606^31629131720Hans Havermann04/2021
51823^276062-112292131716Enzo Doria07/2014
51832^437539+2025131713Henri Lifchitz01/2025
518411*31^88313+322688131708Eric Chen05/2024
5185(7*10^131682+89)/3131683Robert Price08/2020
518629512^28969+28969^29512131681Hans Havermann03/2021
51872^437343+75953131654Enzo Doria04/2016
518835^85243-34^85243131621Robert Price05/2012
5189(28*10^131586+59)/3131587Robert Price05/2021
5190(59*10^131575+391)/9131576Robert Price03/2021
519139984^1945+1945^39984131505Hans Havermann03/2021
519225842^29801-29801^25842131492Frank Doornink03/2024
519328592^29505-29505^28592131482Frank Doornink05/2024
519425647^29818-29818^25647131469Frank Doornink02/2024
5195(203*10^131457+1)/3131459Robert Price03/2020
51967*10^131421-41131422Robert Price08/2021
519787309^32+32^87309131414Hans Havermann03/2021
5198(68^71713+1)/69131413Paul Bourdelais09/2017
51992^436521+224885131406Enzo Doria07/2024
5200(650*10^131391+43)/9131393Tyler Busby01/2023
52012^436451+1884713131385Enzo Doria03/2017
52022^436365+35131359Robert Price11/2015
52042^436300+1866871131340Enzo Doria03/2016
5203(7*10^131339+179)/3131340Robert Price09/2018
520514^114592-3131338Paul Bourdelais12/2020
520636197^4236+4236^36197131285Hans Havermann04/2021
5207(37*10^131270+341)/9131271Robert Price08/2018
520829863^24790+24790^29863131227Hans Havermann03/2021
5209(5*10^131223-29)/3131224Robert Price03/2018
521029524^27825+27825^29524131218Hans Havermann03/2021
5211(23*2^435891-1)/699131215Lelio R Paula07/2015
5212(11*2^435879+1)/3337131211Lelio R Paula06/2015
521330639^19136+19136^30639131192Hans Havermann04/2021
5214(2^435808+1)/641/6700417131182Lelio R Paula02/2012
5215(2^435808+1)/4294967297131182Serge Batalov12/2016
52162^435773+1875557131181Enzo Doria06/2016
5218(16*10^131180+167)/3131181Robert Price06/2019
5217(26*10^131180-77)/3131181Robert Price11/2019
5219(25*10^131144-7)/9131145Robert Price05/2018
522029299^29358-29358^29299131138Norbert Schneider03/2022
52212^435612-2789939131133Enzo Doria12/2015
522233976^7231+7231^33976131121Hans Havermann03/2021
522333715^7746+7746^33715131121Hans Havermann03/2021
522466^72047-65^72047131093Robert Price09/2013
5225(5*10^131090+37)/3131091Robert Price03/2018
52262^435468+75631131089Enzo Doria04/2016
522737^83588-2131083Lelio R Paula08/2015
5228(4^217720+11)/3131081Robert Price02/2017
522930407^20448+20448^30407131074Hans Havermann04/2021
5230(22*10^131070+179)/3131071Robert Price02/2022
523128831^29388-29388^28831131067Frank Doornink05/2024
523229487^27836+27836^29487131059Hans Havermann04/2021
523329962^23615+23615^29962131030Hans Havermann03/2021
52342^435202-113193131009Enzo Doria07/2014
523541705^1384+1384^41705131002Hans Havermann04/2021
52369*10^130998-19130999Robert Price07/2019
523736243^4108+4108^36243130969Hans Havermann04/2021
5238(445^49433+1)/446130914Jinyuan Wang05/2024
5239floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
52402^434835-111937130899Enzo Doria05/2014
5241(62*10^130895-629)/9130896Robert Price07/2021
52422^434807+225130890Henri Lifchitz11/2024
52432^434685+72257130854Enzo Doria04/2016
5244(7*10^130825+113)/3130826Robert Price02/2018
52452^434539-29317130810Enzo Doria07/2015
5246(74*10^130791+637)/9130792Robert Price01/2022
52472^434469-114259130789Enzo Doria01/2015
5248(5*10^130763+103)/9130763Robert Price04/2022
52492^434246+33130722Robert Price11/2015
525030156^21599+21599^30156130710Hans Havermann04/2021


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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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