PRP Records

Probable Primes Top 10000

(291910 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 ?
325140387^2260+2260^40387135463Hans Havermann12/2020
32522^449944-113247135447Enzo Doria07/2014
32532^449770-113247135395Enzo Doria07/2014
32542^449637-21471135355Enzo Doria07/2013
32552^449571-75135335Lelio R Paula08/2017
3256(14*10^135301-53)/3135302Robert Price12/2018
3257(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
3258(13*10^135279+437)/9135280Robert Price04/2018
32592^449330-35135262Lelio R Paula08/2017
3260(19*2^449325+1)/9135261Lelio R Paula07/2015
3261(13*10^135184-43)/3135185Robert Price11/2018
32622^449049-115309135178Enzo Doria07/2015
3263(10^135174+191)/3135174Robert Price02/2018
32642^449030-15135172Lelio R Paula08/2017
3265(157*10^135151-1)/3135153Robert Price01/2022
3266(2^448966+100280245065)135153Paul Bourdelais05/2022
3267(27*2^448936-1)/11135144Lelio R Paula07/2015
3268(37*10^135099+251)/9135100Robert Price09/2021
326932221^15586+15586^32221135095Hans Havermann12/2020
32702^448762-351401135091Enzo Doria07/2015
32712*10^135083-43135084Robert Price04/2018
327231357^20278+20278^31357135056Hans Havermann12/2020
327332242^15445+15445^32242135055Hans Havermann12/2020
3274k(198476)135054Robert Price07/2020
327532461^14470+14470^32461135053Hans Havermann12/2020
327631353^20288+20288^31353135045Hans Havermann12/2020
32775*10^135019+77135020Robert Price12/2018
3278(10^135011+719)/9135011Serge Batalov12/2014
3279(197*10^134978+7)/3134980Robert Price12/2020
32802^448386-2786261134978Enzo Doria03/2016
3281(73*10^134939+143)/9134940Robert Price07/2019
328233957^9392+9392^33957134903Hans Havermann12/2020
32832^448113-113949134896Enzo Doria11/2014
328430958^22755+22755^30958134887Hans Havermann12/2020
32852^447888-2786639134828Enzo Doria03/2016
32862^447870-396765134823Enzo Doria07/2013
32872^447766-21791134791Enzo Doria07/2013
3288(19*10^134786-49)/3134787Robert Price05/2019
3289Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
3290(23*2^447647+1)/155134755Lelio R Paula07/2015
32912^447552-1019134727Yves Minet02/2014
3292(2*10^134720-41)/3134720Robert Price02/2018
3293(25*10^134695-97)/9134696Robert Price01/2022
32942^447437-113569134692Enzo Doria08/2014
32952^447426-65134689Lelio R Paula08/2017
32962^447357-2797573134668Enzo Doria04/2016
32972^447278+93134645Lelio R Paula08/2017
329833193^11370+11370^33193134623Hans Havermann12/2020
329930736^23979+23979^30736134619Hans Havermann11/2020
33002^447094-113193134589Enzo Doria07/2014
33013^282041-9934134568Enzo Doria05/2014
33022^447019-109039134567Enzo Doria04/2014
330331376^19437+19437^31376134561Hans Havermann12/2020
33042^446990-22041134558Enzo Doria07/2013
3305123^64370+122134528Karsten Bonath04/2018
330630100^29461+29461^30100134525Hans Havermann11/2020
330731251^20158+20158^31251134519Hans Havermann11/2020
33082^446782-39701134495Enzo Doria09/2015
330931817^16858+16858^31817134485Hans Havermann12/2020
331032448^13937+13937^32448134471Hans Havermann12/2020
33112^446494-16485134409Enzo Doria04/2013
331230042^29785+29785^30042134408Hans Havermann12/2020
331329504^30069-30069^29504134405Norbert Schneider12/2014
33142^446441+65134393Lelio R Paula08/2017
3315(10^134385+719)/9134385Serge Batalov12/2014
331630043^29688+29688^30043134370Hans Havermann12/2020
3317(2*10^134364+529)/9134364Robert Price01/2018
331834657^7512+7512^34657134323Hans Havermann11/2020
3319(13*2^446187-1)/661134314Lelio R Paula07/2015
33205^192103+3^192103+2^192103+1134275Matthias Baur12/2019
332142035^1564+1564^42035134270Hans Havermann12/2020
3323(2^446022-7)/339134264Lelio R Paula07/2015
332230621^24248+24248^30621134264Hans Havermann12/2020
332430341^26562+26562^30341134237Hans Havermann11/2020
332510^134209+99867134210Patrick De Geest05/2021
332610^134209-80000001134209Robert Price04/2021
332710^134209-323283134209Patrick De Geest05/2021
332829976^29953+29953^29976134186Hans Havermann12/2020
332935038^6755+6755^35038134183Hans Havermann12/2020
333063^74568+2134174Lelio R Paula06/2017
33312^445671-22071134161Enzo Doria07/2013
3332532^49205+49205^532134129Norbert Schneider02/2019
333336453^4780+4780^36453134127Hans Havermann04/2021
3334(28*10^134122-1)/9134123Serge Batalov10/2014
33352^445515-113859134114Enzo Doria10/2014
3337(22*10^134111-37)/3134112Robert Price04/2019
333631083^20636+20636^31083134112Hans Havermann04/2021
333831622^17379+17379^31622134079Hans Havermann04/2021
3339(277*10^134059-7)/9134061Robert Price02/2022
33402^445328-216917134058Enzo Doria05/2014
33412^445202+1874899134020Enzo Doria06/2016
3342(35*10^134003-89)/9134004Robert Price02/2022
3343(13*2^445102+1)/17133989Lelio R Paula07/2015
3344(35*10^133979-593)/9133980Robert Price07/2018
33452*10^133955+51133956Robert Price05/2018
3346(49*10^133952+437)/9133953Robert Price09/2021
33472^444964-113639133948Enzo Doria08/2014
334831811^16240+16240^31811133943Hans Havermann04/2021
334910^133902+167841133903Patrick De Geest05/2021
335128118^30097-30097^28118133902Norbert Schneider01/2015
335010^133902-100001133902Robert Price07/2020
33522^444784-113859133894Enzo Doria10/2014
335332303^13914+13914^32303133846Hans Havermann04/2021
3354(2276213*2^444444+1)/3133797Alex_soldier11/2022
3355(1403559*2^444444+1)/5133797Alex_soldier11/2022
3356(1209887*2^444444+1)/9133797Alex_soldier11/2022
3357(608239*2^444444+1)/25133796Alex_soldier11/2022
3358(1824587*2^444444+1)/27133796Alex_soldier11/2022
3359(40795*2^444444+1)/7133795Alex_soldier11/2022
336030739^22458+22458^30739133757Hans Havermann04/2021
336134942^6721+6721^34942133739Hans Havermann04/2021
3362(2^444046+100280245065)133672Paul Bourdelais05/2022
336334792^6935+6935^34792133638Hans Havermann04/2021
3364(266*10^133603+1)/3133605Robert Price04/2020
336532261^13842+13842^32261133600Hans Havermann04/2021
3366(89*10^133580+1)/9133581Serge Batalov05/2010
3367(134*10^133573-11)/3133575Robert Price01/2022
336862^74521-61^74521133571Robert Price05/2013
3369(182*10^133543+1)/3133545Robert Price02/2020
3370(103*10^133535+11)/3133537Robert Price01/2021
337132589^12520+12520^32589133537Hans Havermann03/2021
337234516^7373+7373^34516133496Hans Havermann04/2021
33738*10^133487-37133488Robert Price03/2022
337430135^26882+26882^30135133482Hans Havermann04/2021
33752^443198-1867301133416Enzo Doria03/2016
3376(19*10^133390+101)/3133391Robert Price09/2019
3377(71^72043-1)/70133369Paul Bourdelais09/2017
337836117^4910+4910^36117133311Hans Havermann04/2021
33792^442799+1874633133296Enzo Doria06/2016
3380L(637751)133283Henri Lifchitz09/2008
3381109^65410-2133269Lelio R Paula10/2017
33822^442688-113489133263Enzo Doria08/2014
3383(7*2^442640-1)/783133246Lelio R Paula07/2015
3384(9*2^442463+1)/17441133192Lelio R Paula07/2015
33852^442437-1849993133187Enzo Doria08/2015
33862^442430-2791721133185Enzo Doria03/2016
3387(13*2^442428-1)/309133183Lelio R Paula07/2015
338829959^27870+27870^29959133172Hans Havermann03/2021
3389(25*2^442379-1)/71133169Lelio R Paula07/2015
339034240^7737+7737^34240133145Hans Havermann03/2021
3391452^50145+50145^452133142Norbert Schneider09/2020
339230659^21796+21796^30659133011Hans Havermann04/2021
339333276^9935+9935^33276133010Hans Havermann04/2021
339430111^26122+26122^30111133001Hans Havermann04/2021
339530790^20869+20869^30790132998Hans Havermann04/2021
3397(2^441799+78557)/5132995Lelio R Paula07/2015
33968*10^132994-27132995Robert Price10/2021
3398(109*10^132992+11)/3132994Robert Price06/2022
33992^441781-2787883132990Enzo Doria03/2016
3400(3*2^441685+1)/749132959Lelio R Paula07/2015
34012^441618+37132941Lelio R Paula08/2017
340234857^6514+6514^34857132940Hans Havermann04/2021
340334065^7988+7988^34065132937Hans Havermann04/2021
340435571^5452+5452^35571132914Hans Havermann04/2021
34052^441521-113575132912Enzo Doria08/2014
34067*10^132884-99132885Robert Price06/2019
3407(103*10^132879+17)/3132881Robert Price08/2020
34082^441396-65132874Lelio R Paula08/2017
340933350^9633+9633^33350132859Hans Havermann04/2021
34102^441330+1871959132854Enzo Doria05/2016
34112^441063+383132774Lelio R Paula06/2012
3412(10^132753+7)/17/19132751Alfred Reich06/2021
3413(22*10^132746+53)/3132747Robert Price07/2019
3414(77*10^132744-149)/9132745Robert Price03/2022
3415(22*10^132732+119)/3132733Robert Price04/2021
34162^440846+1870909132708Enzo Doria05/2016
34172^440656-113489132651Enzo Doria08/2014
3418numbpart(14180123587)132646Serge Batalov04/2017
341932950^10591+10591^32950132622Hans Havermann04/2021
342033302^9597+9597^33302132614Hans Havermann04/2021
3421(19*10^132550+191)/3132551Robert Price05/2019
3422(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
3423(38^83891+1)/39132529Robert Price09/2013
34242*10^132493-43132494Robert Price04/2018
342531352^16809+16809^31352132480Hans Havermann04/2021
3426(418*10^132441+23)/9132443Robert Price02/2020
34272^439931-21132433Lelio R Paula08/2017
342847^79201-46^79201132432Robert Price10/2012
34292^439897-113653132423Enzo Doria08/2014
343035505^5362+5362^35505132410Hans Havermann03/2021
343130079^25222+25222^30079132402Hans Havermann04/2021
3432(5*2^439822+1)/9132400Lelio R Paula06/2015
3433(695*10^132356+7)/9132358Robert Price12/2021
3434(112*10^132337-1)/3132339Serge Batalov12/2014
34352^439576-113247132326Enzo Doria07/2014
343630059^25230+25230^30059132318Hans Havermann04/2021
34372^439497-29143132302Enzo Doria07/2015
34382^439409-114193132276Enzo Doria12/2014
3439(44*10^132233-233)/9132234Robert Price01/2019
34409*10^132148-7132149Robert Price09/2015
3441(47*10^132125-119)/9132126Robert Price05/2019
34422^438845+1870217132106Enzo Doria05/2016
34432^438789+87855132089Lelio R Paula01/2016
34442^438774-2786411132085Enzo Doria03/2016
34452^438755-1848205132079Enzo Doria07/2015
344630502^21381+21381^30502132075Hans Havermann04/2021
34472^438739-112087132074Enzo Doria06/2014
3448(2^438438+100280245065)131983Paul Bourdelais05/2022
344935872^4777+4777^35872131979Hans Havermann04/2021
345031198^16945+16945^31198131938Hans Havermann03/2021
345113907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
3452L(631181)131910Henri Lifchitz09/2008
3453(47*10^131886-119)/9131887Robert Price05/2019
3454(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
34552^438079-1863877131875Enzo Doria03/2016
3456(16*10^131872-37)/3131873Robert Price05/2021
3457(2^438067+5)/329131869Lelio R Paula06/2015
34582^437908-113855131824Enzo Doria09/2014
34592^437884-286349131817Enzo Doria07/2015
34605^188558+4131797Tyler NeSmith05/2021
3461(11*10^131784-17)/3131785Robert Price06/2018
34634*10^131719-93131720Robert Price07/2020
346231629^14606+14606^31629131720Hans Havermann04/2021
34643^276062-112292131716Enzo Doria07/2014
3465(7*10^131682+89)/3131683Robert Price08/2020
346629512^28969+28969^29512131681Hans Havermann03/2021
34672^437343+75953131654Enzo Doria04/2016
346835^85243-34^85243131621Robert Price05/2012
3469(28*10^131586+59)/3131587Robert Price05/2021
3470(59*10^131575+391)/9131576Robert Price03/2021
347139984^1945+1945^39984131505Hans Havermann03/2021
3472(203*10^131457+1)/3131459Robert Price03/2020
34737*10^131421-41131422Robert Price08/2021
347487309^32+32^87309131414Hans Havermann03/2021
3475(68^71713+1)/69131413Paul Bourdelais09/2017
3476(650*10^131391+43)/9131393Tyler Busby01/2023
34772^436451+1884713131385Enzo Doria03/2017
34782^436365+35131359Robert Price11/2015
34792^436300+1866871131340Enzo Doria03/2016
3480(7*10^131339+179)/3131340Robert Price09/2018
348114^114592-3131338Paul Bourdelais12/2020
348236197^4236+4236^36197131285Hans Havermann04/2021
3483(37*10^131270+341)/9131271Robert Price08/2018
348429863^24790+24790^29863131227Hans Havermann03/2021
3485(5*10^131223-29)/3131224Robert Price03/2018
348629524^27825+27825^29524131218Hans Havermann03/2021
3487(23*2^435891-1)/699131215Lelio R Paula07/2015
3488(11*2^435879+1)/3337131211Lelio R Paula06/2015
348930639^19136+19136^30639131192Hans Havermann04/2021
3490(2^435808+1)/641/6700417131182Lelio R Paula02/2012
3491(2^435808+1)/4294967297131182Serge Batalov12/2016
34922^435773+1875557131181Enzo Doria06/2016
3494(16*10^131180+167)/3131181Robert Price06/2019
3493(26*10^131180-77)/3131181Robert Price11/2019
3495(25*10^131144-7)/9131145Robert Price05/2018
349629299^29358-29358^29299131138Norbert Schneider03/2022
34972^435612-2789939131133Enzo Doria12/2015
349833976^7231+7231^33976131121Hans Havermann03/2021
349933715^7746+7746^33715131121Hans Havermann03/2021
350066^72047-65^72047131093Robert Price09/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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