PRP Records

Probable Primes Top 10000

(301429 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 ?
47512*10^135663+69135664Robert Price06/2020
475233962^9867+9867^33962135651Hans Havermann11/2020
475334474^8605+8605^34474135647Hans Havermann11/2020
475434501^8508+8508^34501135583Hans Havermann12/2020
475535487^6614+6614^35487135577Hans Havermann12/2020
4756(13725^32768+1)/131074135573Lelio R Paula03/2012
4757(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
4758(5^193939+1)/6135557Paul Bourdelais12/2008
4759(76*10^135553-49)/9135554Robert Price07/2022
47605*3^284077+2^284077135540Jon Grantham08/2023
4761(844*10^135527-7)/9135529Robert Price05/2021
476227191^30560-30560^27191135517Frank Doornink01/2024
476340387^2260+2260^40387135463Hans Havermann12/2020
47642^449944-113247135447Enzo Doria07/2014
47652^449770-113247135395Enzo Doria07/2014
47662^449637-21471135355Enzo Doria07/2013
476726061^30650-30650^26061135351Frank Doornink03/2024
47682^449571-75135335Lelio R Paula08/2017
4769(14*10^135301-53)/3135302Robert Price12/2018
4770(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
4771(13*10^135279+437)/9135280Robert Price04/2018
47722^449330-35135262Lelio R Paula08/2017
4773(19*2^449325+1)/9135261Lelio R Paula07/2015
4774(2709^39601+1)/(2709^199+1)135260Martin Hopf12/2023
4775(13*10^135184-43)/3135185Robert Price11/2018
47762^449049-115309135178Enzo Doria07/2015
4777(10^135174+191)/3135174Robert Price02/2018
47782^449030-15135172Lelio R Paula08/2017
4779(157*10^135151-1)/3135153Robert Price01/2022
4780(2^448966+100280245065)135153Paul Bourdelais05/2022
4781(27*2^448936-1)/11135144Lelio R Paula07/2015
4782(37*10^135099+251)/9135100Robert Price09/2021
478332221^15586+15586^32221135095Hans Havermann12/2020
47842^448762-351401135091Enzo Doria07/2015
47852*10^135083-43135084Robert Price04/2018
478631357^20278+20278^31357135056Hans Havermann12/2020
478732242^15445+15445^32242135055Hans Havermann12/2020
4788k(198476)135054Robert Price07/2020
478932461^14470+14470^32461135053Hans Havermann12/2020
479031353^20288+20288^31353135045Hans Havermann12/2020
47915*10^135019+77135020Robert Price12/2018
4792(10^135011+719)/9135011Serge Batalov12/2014
4793(197*10^134978+7)/3134980Robert Price12/2020
47942^448386-2786261134978Enzo Doria03/2016
479526480^30517-30517^26480134975Frank Doornink03/2024
4796(73*10^134939+143)/9134940Robert Price07/2019
479733957^9392+9392^33957134903Hans Havermann12/2020
47982^448122+20809134899Enzo Doria08/2023
47992^448113-113949134896Enzo Doria11/2014
480030958^22755+22755^30958134887Hans Havermann12/2020
48012^447888-2786639134828Enzo Doria03/2016
48022^447870-396765134823Enzo Doria07/2013
480310^(2*67404+1)-10^67404-1134809Robert Price07/2023
48042^447766-21791134791Enzo Doria07/2013
4805(19*10^134786-49)/3134787Robert Price05/2019
4806Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
4807(23*2^447647+1)/155134755Lelio R Paula07/2015
48082^447552-1019134727Yves Minet02/2014
4809(2*10^134720-41)/3134720Robert Price02/2018
4810(25*10^134695-97)/9134696Robert Price01/2022
48112^447437-113569134692Enzo Doria08/2014
48122^447426-65134689Lelio R Paula08/2017
48132^447357-2797573134668Enzo Doria04/2016
48142^447278+93134645Lelio R Paula08/2017
481533193^11370+11370^33193134623Hans Havermann12/2020
481630736^23979+23979^30736134619Hans Havermann11/2020
48172^447094-113193134589Enzo Doria07/2014
48183^282041-9934134568Enzo Doria05/2014
48192^447019-109039134567Enzo Doria04/2014
482031376^19437+19437^31376134561Hans Havermann12/2020
48212^446990-22041134558Enzo Doria07/2013
4822123^64370+122134528Karsten Bonath04/2018
482330100^29461+29461^30100134525Hans Havermann11/2020
482431251^20158+20158^31251134519Hans Havermann11/2020
48252^446782-39701134495Enzo Doria09/2015
482631817^16858+16858^31817134485Hans Havermann12/2020
482732448^13937+13937^32448134471Hans Havermann12/2020
48285^192321+3^192321-1134427Jon Grantham08/2023
48292^446494-16485134409Enzo Doria04/2013
483030042^29785+29785^30042134408Hans Havermann12/2020
483129504^30069-30069^29504134405Norbert Schneider12/2014
48322^446441+65134393Lelio R Paula08/2017
4833(10^134385+719)/9134385Serge Batalov12/2014
483430043^29688+29688^30043134370Hans Havermann12/2020
4835(2*10^134364+529)/9134364Robert Price01/2018
483634657^7512+7512^34657134323Hans Havermann11/2020
4837(13*2^446187-1)/661134314Lelio R Paula07/2015
48385^192103+3^192103+2^192103+1134275Matthias Baur12/2019
483942035^1564+1564^42035134270Hans Havermann12/2020
4841(2^446022-7)/339134264Lelio R Paula07/2015
484030621^24248+24248^30621134264Hans Havermann12/2020
484230341^26562+26562^30341134237Hans Havermann11/2020
4843(189^58967-1)/188134234Anonymous06/2024
484410^134209+99867134210Patrick De Geest05/2021
484510^134209-80000001134209Robert Price04/2021
484610^134209-323283134209Patrick De Geest05/2021
484729976^29953+29953^29976134186Hans Havermann12/2020
484835038^6755+6755^35038134183Hans Havermann12/2020
484963^74568+2134174Lelio R Paula06/2017
48502^445671-22071134161Enzo Doria07/2013
4851532^49205+49205^532134129Norbert Schneider02/2019
485236453^4780+4780^36453134127Hans Havermann04/2021
4853(28*10^134122-1)/9134123Serge Batalov10/2014
48542^445515-113859134114Enzo Doria10/2014
4856(22*10^134111-37)/3134112Robert Price04/2019
485531083^20636+20636^31083134112Hans Havermann04/2021
48573*2^445478+5134103Jon Grantham07/2023
485831622^17379+17379^31622134079Hans Havermann04/2021
48595*2^445380-3134074Jon Grantham07/2023
4860(6*32^89076+4241)/31134073Eric Chen11/2023
4861(277*10^134059-7)/9134061Robert Price02/2022
48622^445328-216917134058Enzo Doria05/2014
48632^445202+1874899134020Enzo Doria06/2016
48645^191739-3^191739-1134020Jon Grantham08/2023
4865(35*10^134003-89)/9134004Robert Price02/2022
4866(13*2^445102+1)/17133989Lelio R Paula07/2015
4867(35*10^133979-593)/9133980Robert Price07/2018
48682*10^133955+51133956Robert Price05/2018
4869(49*10^133952+437)/9133953Robert Price09/2021
48702^444964-113639133948Enzo Doria08/2014
487131811^16240+16240^31811133943Hans Havermann04/2021
487210^133902+167841133903Patrick De Geest05/2021
487428118^30097-30097^28118133902Norbert Schneider01/2015
487310^133902-100001133902Robert Price07/2020
48752^444784-113859133894Enzo Doria10/2014
4876(132^63127-1)/131133864Anonymous06/2024
487732303^13914+13914^32303133846Hans Havermann04/2021
4878(2276213*2^444444+1)/3133797Alex_soldier11/2022
4879(1403559*2^444444+1)/5133797Alex_soldier11/2022
4880(1209887*2^444444+1)/9133797Alex_soldier11/2022
4881(608239*2^444444+1)/25133796Alex_soldier11/2022
4882(1824587*2^444444+1)/27133796Alex_soldier11/2022
4883(40795*2^444444+1)/7133795Alex_soldier11/2022
488430739^22458+22458^30739133757Hans Havermann04/2021
488534942^6721+6721^34942133739Hans Havermann04/2021
4886(3^280229-1)/1120918133698Aurel Gibier03/2025
4887(2^444046+100280245065)133672Paul Bourdelais05/2022
488834792^6935+6935^34792133638Hans Havermann04/2021
4889(266*10^133603+1)/3133605Robert Price04/2020
489032261^13842+13842^32261133600Hans Havermann04/2021
4891(89*10^133580+1)/9133581Serge Batalov05/2010
4892(134*10^133573-11)/3133575Robert Price01/2022
489326726^30173-30173^26726133574Frank Doornink03/2024
48942^443721+39527133574Enzo Doria11/2024
489562^74521-61^74521133571Robert Price05/2013
4896(182*10^133543+1)/3133545Robert Price02/2020
4897(103*10^133535+11)/3133537Robert Price01/2021
489832589^12520+12520^32589133537Hans Havermann03/2021
4899L(638839)/274700771133502Serge Batalov07/2024
490034516^7373+7373^34516133496Hans Havermann04/2021
49018*10^133487-37133488Robert Price03/2022
490230135^26882+26882^30135133482Hans Havermann04/2021
49032^443198-1867301133416Enzo Doria03/2016
490427^93192+26133392Anonymous09/2024
4905(19*10^133390+101)/3133391Robert Price09/2019
4906(71^72043-1)/70133369Paul Bourdelais09/2017
490736117^4910+4910^36117133311Hans Havermann04/2021
49082^442799+1874633133296Enzo Doria06/2016
4909L(637751)133283Henri Lifchitz09/2008
4910109^65410-2133269Lelio R Paula10/2017
49112^442688-113489133263Enzo Doria08/2014
4912(7*2^442640-1)/783133246Lelio R Paula07/2015
4913(9*2^442463+1)/17441133192Lelio R Paula07/2015
49142^442437-1849993133187Enzo Doria08/2015
49152^442430-2791721133185Enzo Doria03/2016
4916(13*2^442428-1)/309133183Lelio R Paula07/2015
491729959^27870+27870^29959133172Hans Havermann03/2021
4918(25*2^442379-1)/71133169Lelio R Paula07/2015
49192^442368+213691133167Enzo Doria09/2023
492034240^7737+7737^34240133145Hans Havermann03/2021
4921452^50145+50145^452133142Norbert Schneider09/2020
4922(355^52201-1)/354133122Tom Wu08/2024
4923(3^278981-1)/14507014133101Paul Vanderveen05/2025
492430659^21796+21796^30659133011Hans Havermann04/2021
492533276^9935+9935^33276133010Hans Havermann04/2021
492630111^26122+26122^30111133001Hans Havermann04/2021
492730790^20869+20869^30790132998Hans Havermann04/2021
4929(2^441799+78557)/5132995Lelio R Paula07/2015
49288*10^132994-27132995Robert Price10/2021
4930(109*10^132992+11)/3132994Robert Price06/2022
49312^441781-2787883132990Enzo Doria03/2016
4932fibonacci(636232)+4132965Jon Grantham08/2023
4933(3*2^441685+1)/749132959Lelio R Paula07/2015
49342^441618+37132941Lelio R Paula08/2017
493534857^6514+6514^34857132940Hans Havermann04/2021
493634065^7988+7988^34065132937Hans Havermann04/2021
493735571^5452+5452^35571132914Hans Havermann04/2021
49382^441521-113575132912Enzo Doria08/2014
49397*10^132884-99132885Robert Price06/2019
494026987^29988-29988^26987132882Frank Doornink03/2024
4941(103*10^132879+17)/3132881Robert Price08/2020
49422^441396-65132874Lelio R Paula08/2017
494333350^9633+9633^33350132859Hans Havermann04/2021
49442^441330+1871959132854Enzo Doria05/2016
494525772^30111-30111^25772132825Frank Doornink02/2024
49462^441063+383132774Lelio R Paula06/2012
4947(10^132753+7)/17/19132751Alfred Reich06/2021
4948(22*10^132746+53)/3132747Robert Price07/2019
4949(77*10^132744-149)/9132745Robert Price03/2022
4950(22*10^132732+119)/3132733Robert Price04/2021
49512^440846+1870909132708Enzo Doria05/2016
4952(948^44579-1)/947132701Jinyuan Wang04/2023
49532^440656-113489132651Enzo Doria08/2014
4954numbpart(14180123587)132646Serge Batalov04/2017
495532950^10591+10591^32950132622Hans Havermann04/2021
495633302^9597+9597^33302132614Hans Havermann04/2021
4957(19*10^132550+191)/3132551Robert Price05/2019
4958(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
4959(38^83891+1)/39132529Robert Price09/2013
49602*10^132493-43132494Robert Price04/2018
496131352^16809+16809^31352132480Hans Havermann04/2021
4962(418*10^132441+23)/9132443Robert Price02/2020
49632^439931-21132433Lelio R Paula08/2017
496447^79201-46^79201132432Robert Price10/2012
49652^439897-113653132423Enzo Doria08/2014
496635505^5362+5362^35505132410Hans Havermann03/2021
496730079^25222+25222^30079132402Hans Havermann04/2021
4968(5*2^439822+1)/9132400Lelio R Paula06/2015
4969(695*10^132356+7)/9132358Robert Price12/2021
4970(112*10^132337-1)/3132339Serge Batalov12/2014
49712^439576-113247132326Enzo Doria07/2014
4972(7^156589-1)/65346468774132323Paul Vanderveen05/2025
497330059^25230+25230^30059132318Hans Havermann04/2021
49742^439497-29143132302Enzo Doria07/2015
49752^439409-114193132276Enzo Doria12/2014
4976(39^83137+2^83137)/41132275Robert Price12/2024
4977(44*10^132233-233)/9132234Robert Price01/2019
497825507^30000-30000^25507132200Frank Doornink02/2024
49799*10^132148-7132149Robert Price09/2015
4980V(790390)132144Serge Batalov07/2024
4981(47*10^132125-119)/9132126Robert Price05/2019
49822^438900+214051132123Enzo Doria10/2023
49832^438845+1870217132106Enzo Doria05/2016
49842^438789+87855132089Lelio R Paula01/2016
49852^438774-2786411132085Enzo Doria03/2016
49862^438755-1848205132079Enzo Doria07/2015
498730502^21381+21381^30502132075Hans Havermann04/2021
49882^438739-112087132074Enzo Doria06/2014
4989(2^438438+100280245065)131983Paul Bourdelais05/2022
499035872^4777+4777^35872131979Hans Havermann04/2021
499131198^16945+16945^31198131938Hans Havermann03/2021
499213907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
4993L(631181)131910Henri Lifchitz09/2008
4994(47*10^131886-119)/9131887Robert Price05/2019
49955*2^438096-3131881Jon Grantham07/2023
4996(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
49972^438079-1863877131875Enzo Doria03/2016
4998(16*10^131872-37)/3131873Robert Price05/2021
4999(2^438067+5)/329131869Lelio R Paula06/2015
50002^437908-113855131824Enzo Doria09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 21 2025 13:33 (Time in France)

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