PRP Records

Probable Primes Top 10000

(294627 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 ?
40012^451560-112349135934Enzo Doria06/2014
40022^451530+45135925Lelio R Paula08/2017
400331622^19875+19875^31622135922Hans Havermann11/2020
4004(25*10^135906-73)/3135907Robert Price09/2019
40052^451450-21743135900Enzo Doria07/2013
4006(7*10^135879+11)/9135879Tyler Busby01/2023
400735218^7199+7199^35218135846Hans Havermann11/2020
400835661^6446+6446^35661135844Hans Havermann11/2020
4009(7*33^89453-4743239)/32135835Eric Chen12/2023
401031869^18248+18248^31869135801Hans Havermann12/2020
4011(77*10^135789+157)/9135790Robert Price05/2022
40122^450958+60529135752Enzo Doria08/2023
40132^450805+65135706Lelio R Paula08/2017
401430761^25728+25728^30761135669Hans Havermann12/2020
40152*10^135663+69135664Robert Price06/2020
401633962^9867+9867^33962135651Hans Havermann11/2020
401734474^8605+8605^34474135647Hans Havermann11/2020
401834501^8508+8508^34501135583Hans Havermann12/2020
401935487^6614+6614^35487135577Hans Havermann12/2020
4020(13725^32768+1)/131074135573Lelio R Paula03/2012
4021(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
4022(5^193939+1)/6135557Paul Bourdelais12/2008
4023(76*10^135553-49)/9135554Robert Price07/2022
40245*3^284077+2^284077135540Jon Grantham08/2023
4025(844*10^135527-7)/9135529Robert Price05/2021
402627191^30560-30560^27191135517Frank Doornink01/2024
402740387^2260+2260^40387135463Hans Havermann12/2020
40282^449944-113247135447Enzo Doria07/2014
40292^449770-113247135395Enzo Doria07/2014
40302^449637-21471135355Enzo Doria07/2013
40312^449571-75135335Lelio R Paula08/2017
4032(14*10^135301-53)/3135302Robert Price12/2018
4033(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
4034(13*10^135279+437)/9135280Robert Price04/2018
40352^449330-35135262Lelio R Paula08/2017
4036(19*2^449325+1)/9135261Lelio R Paula07/2015
4037(2709^39601+1)/(2709^199+1)135260Martin Hopf12/2023
4038(13*10^135184-43)/3135185Robert Price11/2018
40392^449049-115309135178Enzo Doria07/2015
4040(10^135174+191)/3135174Robert Price02/2018
40412^449030-15135172Lelio R Paula08/2017
4042(157*10^135151-1)/3135153Robert Price01/2022
4043(2^448966+100280245065)135153Paul Bourdelais05/2022
4044(27*2^448936-1)/11135144Lelio R Paula07/2015
4045(37*10^135099+251)/9135100Robert Price09/2021
404632221^15586+15586^32221135095Hans Havermann12/2020
40472^448762-351401135091Enzo Doria07/2015
40482*10^135083-43135084Robert Price04/2018
404931357^20278+20278^31357135056Hans Havermann12/2020
405032242^15445+15445^32242135055Hans Havermann12/2020
4051k(198476)135054Robert Price07/2020
405232461^14470+14470^32461135053Hans Havermann12/2020
405331353^20288+20288^31353135045Hans Havermann12/2020
40545*10^135019+77135020Robert Price12/2018
4055(10^135011+719)/9135011Serge Batalov12/2014
4056(197*10^134978+7)/3134980Robert Price12/2020
40572^448386-2786261134978Enzo Doria03/2016
4058(73*10^134939+143)/9134940Robert Price07/2019
405933957^9392+9392^33957134903Hans Havermann12/2020
40602^448122+20809134899Enzo Doria08/2023
40612^448113-113949134896Enzo Doria11/2014
406230958^22755+22755^30958134887Hans Havermann12/2020
40632^447888-2786639134828Enzo Doria03/2016
40642^447870-396765134823Enzo Doria07/2013
406510^(2*67404+1)-10^67404-1134809Robert Price07/2023
40662^447766-21791134791Enzo Doria07/2013
4067(19*10^134786-49)/3134787Robert Price05/2019
4068Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
4069(23*2^447647+1)/155134755Lelio R Paula07/2015
40702^447552-1019134727Yves Minet02/2014
4071(2*10^134720-41)/3134720Robert Price02/2018
4072(25*10^134695-97)/9134696Robert Price01/2022
40732^447437-113569134692Enzo Doria08/2014
40742^447426-65134689Lelio R Paula08/2017
40752^447357-2797573134668Enzo Doria04/2016
40762^447278+93134645Lelio R Paula08/2017
407733193^11370+11370^33193134623Hans Havermann12/2020
407830736^23979+23979^30736134619Hans Havermann11/2020
40792^447094-113193134589Enzo Doria07/2014
40803^282041-9934134568Enzo Doria05/2014
40812^447019-109039134567Enzo Doria04/2014
408231376^19437+19437^31376134561Hans Havermann12/2020
40832^446990-22041134558Enzo Doria07/2013
4084123^64370+122134528Karsten Bonath04/2018
408530100^29461+29461^30100134525Hans Havermann11/2020
408631251^20158+20158^31251134519Hans Havermann11/2020
40872^446782-39701134495Enzo Doria09/2015
408831817^16858+16858^31817134485Hans Havermann12/2020
408932448^13937+13937^32448134471Hans Havermann12/2020
40905^192321+3^192321-1134427Jon Grantham08/2023
40912^446494-16485134409Enzo Doria04/2013
409230042^29785+29785^30042134408Hans Havermann12/2020
409329504^30069-30069^29504134405Norbert Schneider12/2014
40942^446441+65134393Lelio R Paula08/2017
4095(10^134385+719)/9134385Serge Batalov12/2014
409630043^29688+29688^30043134370Hans Havermann12/2020
4097(2*10^134364+529)/9134364Robert Price01/2018
409834657^7512+7512^34657134323Hans Havermann11/2020
4099(13*2^446187-1)/661134314Lelio R Paula07/2015
41005^192103+3^192103+2^192103+1134275Matthias Baur12/2019
410142035^1564+1564^42035134270Hans Havermann12/2020
4103(2^446022-7)/339134264Lelio R Paula07/2015
410230621^24248+24248^30621134264Hans Havermann12/2020
410430341^26562+26562^30341134237Hans Havermann11/2020
410510^134209+99867134210Patrick De Geest05/2021
410610^134209-80000001134209Robert Price04/2021
410710^134209-323283134209Patrick De Geest05/2021
410829976^29953+29953^29976134186Hans Havermann12/2020
410935038^6755+6755^35038134183Hans Havermann12/2020
411063^74568+2134174Lelio R Paula06/2017
41112^445671-22071134161Enzo Doria07/2013
4112532^49205+49205^532134129Norbert Schneider02/2019
411336453^4780+4780^36453134127Hans Havermann04/2021
4114(28*10^134122-1)/9134123Serge Batalov10/2014
41152^445515-113859134114Enzo Doria10/2014
4117(22*10^134111-37)/3134112Robert Price04/2019
411631083^20636+20636^31083134112Hans Havermann04/2021
41183*2^445478+5134103Jon Grantham07/2023
411931622^17379+17379^31622134079Hans Havermann04/2021
41205*2^445380-3134074Jon Grantham07/2023
4121(6*32^89076+4241)/31134073Eric Chen11/2023
4122(277*10^134059-7)/9134061Robert Price02/2022
41232^445328-216917134058Enzo Doria05/2014
41242^445202+1874899134020Enzo Doria06/2016
41255^191739-3^191739-1134020Jon Grantham08/2023
4126(35*10^134003-89)/9134004Robert Price02/2022
4127(13*2^445102+1)/17133989Lelio R Paula07/2015
4128(35*10^133979-593)/9133980Robert Price07/2018
41292*10^133955+51133956Robert Price05/2018
4130(49*10^133952+437)/9133953Robert Price09/2021
41312^444964-113639133948Enzo Doria08/2014
413231811^16240+16240^31811133943Hans Havermann04/2021
413310^133902+167841133903Patrick De Geest05/2021
413528118^30097-30097^28118133902Norbert Schneider01/2015
413410^133902-100001133902Robert Price07/2020
41362^444784-113859133894Enzo Doria10/2014
413732303^13914+13914^32303133846Hans Havermann04/2021
4138(2276213*2^444444+1)/3133797Alex_soldier11/2022
4139(1403559*2^444444+1)/5133797Alex_soldier11/2022
4140(1209887*2^444444+1)/9133797Alex_soldier11/2022
4141(608239*2^444444+1)/25133796Alex_soldier11/2022
4142(1824587*2^444444+1)/27133796Alex_soldier11/2022
4143(40795*2^444444+1)/7133795Alex_soldier11/2022
414430739^22458+22458^30739133757Hans Havermann04/2021
414534942^6721+6721^34942133739Hans Havermann04/2021
4146(2^444046+100280245065)133672Paul Bourdelais05/2022
414734792^6935+6935^34792133638Hans Havermann04/2021
4148(266*10^133603+1)/3133605Robert Price04/2020
414932261^13842+13842^32261133600Hans Havermann04/2021
4150(89*10^133580+1)/9133581Serge Batalov05/2010
4151(134*10^133573-11)/3133575Robert Price01/2022
415262^74521-61^74521133571Robert Price05/2013
4153(182*10^133543+1)/3133545Robert Price02/2020
4154(103*10^133535+11)/3133537Robert Price01/2021
415532589^12520+12520^32589133537Hans Havermann03/2021
415634516^7373+7373^34516133496Hans Havermann04/2021
41578*10^133487-37133488Robert Price03/2022
415830135^26882+26882^30135133482Hans Havermann04/2021
41592^443198-1867301133416Enzo Doria03/2016
4160(19*10^133390+101)/3133391Robert Price09/2019
4161(71^72043-1)/70133369Paul Bourdelais09/2017
416236117^4910+4910^36117133311Hans Havermann04/2021
41632^442799+1874633133296Enzo Doria06/2016
4164L(637751)133283Henri Lifchitz09/2008
4165109^65410-2133269Lelio R Paula10/2017
41662^442688-113489133263Enzo Doria08/2014
4167(7*2^442640-1)/783133246Lelio R Paula07/2015
4168(9*2^442463+1)/17441133192Lelio R Paula07/2015
41692^442437-1849993133187Enzo Doria08/2015
41702^442430-2791721133185Enzo Doria03/2016
4171(13*2^442428-1)/309133183Lelio R Paula07/2015
417229959^27870+27870^29959133172Hans Havermann03/2021
4173(25*2^442379-1)/71133169Lelio R Paula07/2015
41742^442368+213691133167Enzo Doria09/2023
417534240^7737+7737^34240133145Hans Havermann03/2021
4176452^50145+50145^452133142Norbert Schneider09/2020
417730659^21796+21796^30659133011Hans Havermann04/2021
417833276^9935+9935^33276133010Hans Havermann04/2021
417930111^26122+26122^30111133001Hans Havermann04/2021
418030790^20869+20869^30790132998Hans Havermann04/2021
4182(2^441799+78557)/5132995Lelio R Paula07/2015
41818*10^132994-27132995Robert Price10/2021
4183(109*10^132992+11)/3132994Robert Price06/2022
41842^441781-2787883132990Enzo Doria03/2016
4185fibonacci(636232)+4132965Jon Grantham08/2023
4186(3*2^441685+1)/749132959Lelio R Paula07/2015
41872^441618+37132941Lelio R Paula08/2017
418834857^6514+6514^34857132940Hans Havermann04/2021
418934065^7988+7988^34065132937Hans Havermann04/2021
419035571^5452+5452^35571132914Hans Havermann04/2021
41912^441521-113575132912Enzo Doria08/2014
41927*10^132884-99132885Robert Price06/2019
4193(103*10^132879+17)/3132881Robert Price08/2020
41942^441396-65132874Lelio R Paula08/2017
419533350^9633+9633^33350132859Hans Havermann04/2021
41962^441330+1871959132854Enzo Doria05/2016
419725772^30111-30111^25772132825Frank Doornink02/2024
41982^441063+383132774Lelio R Paula06/2012
4199(10^132753+7)/17/19132751Alfred Reich06/2021
4200(22*10^132746+53)/3132747Robert Price07/2019
4201(77*10^132744-149)/9132745Robert Price03/2022
4202(22*10^132732+119)/3132733Robert Price04/2021
42032^440846+1870909132708Enzo Doria05/2016
4204(948^44579-1)/947132701Jinyuan Wang04/2023
42052^440656-113489132651Enzo Doria08/2014
4206numbpart(14180123587)132646Serge Batalov04/2017
420732950^10591+10591^32950132622Hans Havermann04/2021
420833302^9597+9597^33302132614Hans Havermann04/2021
4209(19*10^132550+191)/3132551Robert Price05/2019
4210(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
4211(38^83891+1)/39132529Robert Price09/2013
42122*10^132493-43132494Robert Price04/2018
421331352^16809+16809^31352132480Hans Havermann04/2021
4214(418*10^132441+23)/9132443Robert Price02/2020
42152^439931-21132433Lelio R Paula08/2017
421647^79201-46^79201132432Robert Price10/2012
42172^439897-113653132423Enzo Doria08/2014
421835505^5362+5362^35505132410Hans Havermann03/2021
421930079^25222+25222^30079132402Hans Havermann04/2021
4220(5*2^439822+1)/9132400Lelio R Paula06/2015
4221(695*10^132356+7)/9132358Robert Price12/2021
4222(112*10^132337-1)/3132339Serge Batalov12/2014
42232^439576-113247132326Enzo Doria07/2014
422430059^25230+25230^30059132318Hans Havermann04/2021
42252^439497-29143132302Enzo Doria07/2015
42262^439409-114193132276Enzo Doria12/2014
4227(44*10^132233-233)/9132234Robert Price01/2019
422825507^30000-30000^25507132200Frank Doornink02/2024
42299*10^132148-7132149Robert Price09/2015
4230(47*10^132125-119)/9132126Robert Price05/2019
42312^438900+214051132123Enzo Doria10/2023
42322^438845+1870217132106Enzo Doria05/2016
42332^438789+87855132089Lelio R Paula01/2016
42342^438774-2786411132085Enzo Doria03/2016
42352^438755-1848205132079Enzo Doria07/2015
423630502^21381+21381^30502132075Hans Havermann04/2021
42372^438739-112087132074Enzo Doria06/2014
4238(2^438438+100280245065)131983Paul Bourdelais05/2022
423935872^4777+4777^35872131979Hans Havermann04/2021
424031198^16945+16945^31198131938Hans Havermann03/2021
424113907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
4242L(631181)131910Henri Lifchitz09/2008
4243(47*10^131886-119)/9131887Robert Price05/2019
42445*2^438096-3131881Jon Grantham07/2023
4245(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
42462^438079-1863877131875Enzo Doria03/2016
4247(16*10^131872-37)/3131873Robert Price05/2021
4248(2^438067+5)/329131869Lelio R Paula06/2015
42492^437908-113855131824Enzo Doria09/2014
42502^437884-286349131817Enzo Doria07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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