PRP Records

Probable Primes Top 10000

(301678 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
3752(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
3751(2^519925-5)/3156513Stefano Morozzi08/2022
3753(4*10^156501+119)/3156502Robert Price12/2021
3754(83*10^156476-101)/9156477Robert Price08/2021
37553*10^156435-97156436Robert Price07/2018
375610^156428+111156429Boyan Hu10/2024
3757(8*10^156371-77)/3156372Robert Price07/2018
375853^90679-52^90679156356Robert Price01/2013
375931267^34782-34782^31267156349Frank Doornink01/2024
3760(418*10^156309-31)/9156311Robert Price05/2022
37612^519106-59141156267Enzo Doria10/2015
376225929^35404-35404^25929156266Frank Doornink03/2024
37632^519053+6077156251Enzo Doria02/2016
376431199^34764-34764^31199156235Frank Doornink01/2024
37652^518968-1860989156225Enzo Doria11/2015
3766(25*10^156221-7)/9156222Robert Price05/2018
37672^518931-2782297156214Enzo Doria09/2015
37682^518608-2939156117Yves Minet09/2014
376910*27^109005+697156027Curtis Bright05/2015
3770(49*10^155933-319)/9155934Robert Price10/2021
37712^517967-113485155924Enzo Doria08/2014
3772(103*10^155904+17)/3155906Robert Price08/2020
3773(8*10^155887-719)/9155887Robert Price03/2021
37742^517789+29231155871Enzo Doria02/2024
37754*10^155853-39155854Robert Price09/2020
37762^517698+4429155843Lelio R Paula01/2013
377732015^34584-34584^32015155814Frank Doornink01/2024
37782^517543-113257155796Enzo Doria07/2014
3779(14*10^155740-143)/3155741Robert Price11/2018
378031959^34564-34564^31959155697Frank Doornink01/2024
378131^104309-30^104309155563Henri Lifchitz08/2013
37822^516742-39851155555Enzo Doria09/2015
3783(22*10^155543+47)/3155544Robert Price06/2021
3784(19*10^155504+131)/3155505Robert Price06/2020
37857*10^155496+61155497Robert Price08/2019
37862^516440+1878421155464Enzo Doria08/2016
378726012^35173-35173^26012155295Frank Doornink03/2024
37882^515863-1867237155291Enzo Doria03/2016
37892^515786-461861155268Enzo Doria07/2015
37902^515644-113247155225Enzo Doria07/2014
3791(7*10^155203+107)/3155204Robert Price02/2018
379210^155163+206871155164Patrick De Geest05/2021
379310^155163-40001155163Robert Price01/2021
3794(17*10^155133-89)/9155134Robert Price07/2018
379526024^35131-35131^26024155117Frank Doornink03/2024
37962^515249+214457155106Enzo Doria10/2023
37972^515227-114997155099Enzo Doria06/2015
379826510^35061-35061^26510155090Frank Doornink03/2024
3800EPrime(155025)155025Eric W. Weisstein10/2010
3799(14*10^155024-221)/9155025Robert Price04/2018
3801(4*10^155022+173)/3155023Robert Price02/2018
38022^514652+6561154926Henri Lifchitz11/2024
3803(266*10^154897+1)/3154899Robert Price04/2020
3804(115*10^154869-1)/3154871Serge Batalov12/2014
3805(86*10^154853-221)/9154854Robert Price09/2019
38062^514361+78167154839Enzo Doria05/2016
38072^514281-115033154815Enzo Doria06/2015
380825701^35104-35104^25701154807Frank Doornink02/2024
38092^514194-3311154788Yves Minet12/2014
381025930^35067-35067^25930154779Frank Doornink03/2024
3811(14*10^154773+37)/3154774Robert Price12/2018
3812(16*10^154748+131)/3154749Robert Price03/2022
38136*10^154742-31154743Robert Price07/2020
3814(14*10^154645+139)/9154646Robert Price11/2021
38152^513690+216949154637Enzo Doria12/2023
38165*10^154618-79154619Robert Price03/2021
3817(167*10^154595+1)/3154597Robert Price04/2021
38182^513437+1879337154560Enzo Doria09/2016
38192^513306-113201154521Enzo Doria07/2014
382026415^34942-34942^26415154509Frank Doornink03/2024
382118^120818+19^120818-2154497Harsh Aggarwal05/2024
3822(10^154494-13)/3154494Robert Price12/2017
382323462^35343+35343^23462154462Norbert Schneider04/2023
38242^513042-113787154442Enzo Doria09/2014
3825(151*10^154434-7)/9154436Robert Price01/2020
3826(118*10^154428+11)/3154430Robert Price03/2022
38272^512987+29153154425Enzo Doria02/2024
3828(14*10^154413+139)/9154414Robert Price11/2021
3829(77*10^154389-149)/9154390Robert Price03/2022
383032184^34247-34247^32184154374Frank Doornink02/2024
3831(27393*35^99972-499)/34154367Eric Chen05/2025
383210^154359+49154360Robert Price02/2023
38332^512628-114053154317Enzo Doria11/2014
38342^512529-49783154287Enzo Doria10/2015
3835(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
38362^512315-115297154223Enzo Doria06/2015
3837(47*10^154221+241)/9154222Robert Price06/2022
3838(7*10^154211+173)/9154211Robert Price01/2022
38392^512243+22703154201Enzo Doria09/2023
38402^512168+79561154178Enzo Doria06/2016
3841(77*10^154175+67)/9154176Robert Price12/2021
3842(59*19^120562-5)/18154170Anonymous12/2023
3843(5*10^154158-311)/9154158Robert Price12/2021
384427169^34758-34758^27169154120Frank Doornink01/2024
3845(89*10^154103-737)/9154104Robert Price01/2022
38462^511857+23327154085Enzo Doria10/2023
38474*10^154078-57154079Robert Price10/2018
384826242^34863-34863^26242154060Frank Doornink03/2024
3849(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
38507*10^154038-57154039Robert Price06/2020
38512^511658-114371154025Enzo Doria02/2015
3852(57^87719+1)/58154022Paul Bourdelais11/2017
38532^511580-1846679154001Enzo Doria07/2015
3854(259*10^153998-1)/3154000Robert Price12/2020
38552^511541-113713153990Enzo Doria09/2014
385649958^32768+49957^32768153965Kellen Shenton11/2020
385710^153935+970801153936Patrick De Geest05/2021
385810^153935-1000001153935Robert Price08/2020
3859(16*10^153868-73)/3153869Robert Price07/2020
38609*10^153851-67153852Robert Price11/2020
38612^511077-112723153850Enzo Doria06/2014
386269^83653-68^83653153826Robert Price12/2013
38632^510963-113707153816Enzo Doria09/2014
3864(154*10^153810-1)/9153812Serge Batalov12/2014
3865(181*25^109991-75077)/8153763Curtis Bright05/2015
38662*10^153746-3153747Robert Price07/2015
38672^510626+1179379153714Enzo Doria05/2016
3868(7*10^153664+113)/3153665Robert Price02/2018
38692^510448+24991153661Enzo Doria11/2023
38702^510420+81121153652Enzo Doria07/2016
3871(197*7^181761-1)/2153608Karsten Bonath05/2017
38722^509894-459161153494Enzo Doria05/2015
3873(74*10^153489+673)/9153490Robert Price02/2022
3874(49*10^153484-211)/9153485Robert Price06/2022
38752^509841+71657153478Enzo Doria04/2016
38769*10^153446+41153447Robert Price08/2020
38772^509533-1846723153385Enzo Doria07/2015
38782^509468-39989153366Enzo Doria09/2015
387970^83117-69^83117153360Robert Price01/2014
3880(209246*34^99997-81)/11153148Eric Chen08/2023
3881(7*10^153116-1)/3153117Robert Price08/2022
3882(112*10^153025-1)/3153027Serge Batalov12/2014
388331912^33975-33975^31912153022Frank Doornink01/2024
3884(19*10^153010+131)/3153011Robert Price06/2020
38852^508174-1855151152976Enzo Doria09/2015
3886181^67757-2152974Lelio R Paula12/2017
38872^508160-1864829152972Enzo Doria01/2016
388810^152960+412563152961Patrick De Geest05/2021
388910^152960-50000000001152960Robert Price12/2020
389010^152960-423749152960Patrick De Geest05/2021
3891(71*10^152933-143)/9152934Robert Price10/2021
389232109^33932-33932^32109152919Frank Doornink02/2024
38932^507857-1848199152881Enzo Doria07/2015
38942^507638-115361152815Enzo Doria07/2015
38952^507551-114025152789Enzo Doria11/2014
3896(6^196337+1)/7152780Paul Bourdelais02/2010
3897(22*10^152670-13)/9152671Robert Price06/2018
38982^507085+28517152648Enzo Doria01/2024
38992^506917+28847152598Enzo Doria02/2024
39002^506451-22339152457Enzo Doria07/2013
390126463^34460-34460^26463152405Frank Doornink03/2024
390231898^33837-33837^31898152394Frank Doornink01/2024
39032^505995-113185152320Enzo Doria07/2014
3904(8*10^152260-17)/9152260Serge Batalov11/2022
3905(4*10^152253+149)/9152253Robert Price04/2018
390633530^33643-33643^33530152250Norbert Schneider04/2024
3907578^55117-577^55117152230Jean-Louis Charton08/2012
39082^505431-505431152150Henri Lifchitz04/2005
3909(203*10^152143+1)/3152145Robert Price03/2020
391031730^33787-33787^31730152092Frank Doornink01/2024
39112^505089+217787152047Enzo Doria01/2024
391233565^33594-33594^33565152043Norbert Schneider04/2024
39132^505053+73097152037Enzo Doria04/2016
391422*10^151998+3152000Robert Price01/2020
3915(238*10^151979-1)/3151981Robert Price04/2020
3916(2^504793-7)/46765151954Lelio R Paula12/2017
39173^318465+4151947Aurel Gibier09/2024
3918350377#+797581151937Nicolas PALAU08/2017
3919(79*10^151906-529)/9151907Robert Price01/2022
39202^504618-343991151906Enzo Doria07/2015
39212^504259+211193151798Enzo Doria08/2023
39222^504212-461939151783Enzo Doria07/2015
39237*10^151772-41151773Robert Price08/2021
39242^504054-2231151736Yves Minet10/2011
392525237^34458-34458^25237151686Frank Doornink11/2023
3926(28*10^151682+191)/3151683Robert Price02/2020
39272^503817+23961151665Enzo Doria10/2023
39282^503475-933075151562Paul Bourdelais06/2021
39292^503371+26289151530Enzo Doria12/2023
39302^503361-39883151527Enzo Doria09/2015
39312^503225+382667151486Enzo Doria10/2016
3932(206*10^151483-11)/3151485Robert Price02/2022
3933(844*10^151396-7)/9151398Robert Price05/2021
3934(26*10^151391-503)/9151392Robert Price07/2018
39352^502769+1877567151349Enzo Doria08/2016
39362^502576-4019151291Yves Minet10/2011
39375*10^151257+41151258Robert Price03/2019
39382^502290-2792501151205Enzo Doria02/2016
39392^502181+1868417151172Enzo Doria04/2016
39402^502055+22583151134Enzo Doria09/2023
3941(3*23^110967+41)/22151106Anonymous12/2023
39426*10^151063-77151064Robert Price09/2021
39432^501781-1850503151052Enzo Doria08/2015
3944(2^82589933-1)%(10^151020)151020Anonymous05/2025
3945(5*10^151007+37)/3151008Robert Price03/2018
39463^316494+5*2^316494151007Jon Grantham08/2023
39472^501627-991151005Yves Minet02/2014
39482^501577-115333150990Enzo Doria07/2015
394925239^34298-34298^25239150983Frank Doornink12/2023
3950(19*10^150977-7)/3150978Robert Price12/2023
39518*10^150975+3150976Robert Price08/2015
39522^501512-113669150971Enzo Doria09/2014
395334180^26101+26101^34180150962Norman Luhn04/2024
3954U(1083477)/2166953150949Serge Batalov07/2024
3955(83*10^150908+493)/9150909Robert Price12/2021
395636267^14482+14482^36267150901Norman Luhn04/2024
39572*10^150818+83150819Robert Price12/2021
395848753^1240+1240^48753150814Norman Luhn04/2024
3959(12^139739+1)/13150803Paul Bourdelais09/2011
3960(31^101111-1)/30150792Alexander Zhirkov11/2010
39612^500899-500899150786Henri Lifchitz04/2005
39622^500832+1876801150766Enzo Doria07/2016
3963(23*10^150763-59)/9150764Robert Price05/2018
396446002^1891+1891^46002150735Norman Luhn04/2024
396532001^33458-33458^32001150734Frank Doornink01/2024
39662^500699+1884953150726Enzo Doria02/2017
3967(13*10^150675-37)/3150676Robert Price01/2019
3968(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
396935365^18204+18204^35365150661Norman Luhn05/2024
39712^500337-71101150617Enzo Doria04/2016
3970(74*10^150616+133)/9150617Robert Price06/2019
3972(2*10^150612-17)/3150612Serge Batalov11/2022
39734*10^150577+91150578Robert Price08/2018
39745649^40132+40132^5649150575Norbert Schneider04/2024
39752^500160+80071150564Enzo Doria06/2016
3976(2^500120+5)/9150551Lelio R Paula12/2017
3978(43*10^150515-421)/9150516Robert Price01/2019
39774695^40994+40994^4695150516Norbert Schneider11/2023
39792^499999+15981150515Norman Luhn08/2023
3980(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
3981(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
398226614^34005-34005^26614150476Frank Doornink03/2024
39832^499861-29503150474Enzo Doria08/2015
39842^499653-113533150411Enzo Doria08/2014
3985(14*10^150391-191)/3150392Robert Price10/2020
398629033^33696+33696^29033150382Norbert Schneider10/2023
39872^499534-221150375Yves Minet06/2012
398830110^33567+33567^30110150337Norbert Schneider10/2023
398926212^34023-34023^26212150331Frank Doornink03/2024
3990(28*10^150294+41)/3150295Robert Price07/2021
39912^499225+49727150282Enzo Doria09/2016
3992(695*10^150274+7)/9150276Robert Price12/2021
39932^499054-29261150231Enzo Doria07/2015
399418580^35187+35187^18580150215Norbert Schneider10/2023
3995(844*10^150196-7)/9150198Robert Price05/2021
39962^498907-933075150186Paul Bourdelais06/2021
3997(2^498898-7)/9150183Lelio R Paula10/2015
39983*10^150182+17150183Robert Price07/2018
39995*10^150175+63150176Robert Price09/2020
400029273^33618-33618^29273150154Frank Doornink06/2024


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 28 2025 10:26 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!