PRP Records

Probable Primes Top 10000

(300935 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 ?
35012^515863-1867237155291Enzo Doria03/2016
35022^515786-461861155268Enzo Doria07/2015
35032^515644-113247155225Enzo Doria07/2014
3504(7*10^155203+107)/3155204Robert Price02/2018
350510^155163+206871155164Patrick De Geest05/2021
350610^155163-40001155163Robert Price01/2021
3507(17*10^155133-89)/9155134Robert Price07/2018
350826024^35131-35131^26024155117Frank Doornink03/2024
35092^515249+214457155106Enzo Doria10/2023
35102^515227-114997155099Enzo Doria06/2015
351126510^35061-35061^26510155090Frank Doornink03/2024
3513EPrime(155025)155025Eric W. Weisstein10/2010
3512(14*10^155024-221)/9155025Robert Price04/2018
3514(4*10^155022+173)/3155023Robert Price02/2018
35152^514652+6561154926Henri Lifchitz11/2024
3516(266*10^154897+1)/3154899Robert Price04/2020
3517(115*10^154869-1)/3154871Serge Batalov12/2014
3518(86*10^154853-221)/9154854Robert Price09/2019
35192^514361+78167154839Enzo Doria05/2016
35202^514281-115033154815Enzo Doria06/2015
352125701^35104-35104^25701154807Frank Doornink02/2024
35222^514194-3311154788Yves Minet12/2014
352325930^35067-35067^25930154779Frank Doornink03/2024
3524(14*10^154773+37)/3154774Robert Price12/2018
3525(16*10^154748+131)/3154749Robert Price03/2022
35266*10^154742-31154743Robert Price07/2020
3527(14*10^154645+139)/9154646Robert Price11/2021
35282^513690+216949154637Enzo Doria12/2023
35295*10^154618-79154619Robert Price03/2021
3530(167*10^154595+1)/3154597Robert Price04/2021
35312^513437+1879337154560Enzo Doria09/2016
35322^513306-113201154521Enzo Doria07/2014
353326415^34942-34942^26415154509Frank Doornink03/2024
353418^120818+19^120818-2154497Harsh Aggarwal05/2024
3535(10^154494-13)/3154494Robert Price12/2017
353623462^35343+35343^23462154462Norbert Schneider04/2023
35372^513042-113787154442Enzo Doria09/2014
3538(151*10^154434-7)/9154436Robert Price01/2020
3539(118*10^154428+11)/3154430Robert Price03/2022
35402^512987+29153154425Enzo Doria02/2024
3541(14*10^154413+139)/9154414Robert Price11/2021
3542(77*10^154389-149)/9154390Robert Price03/2022
354332184^34247-34247^32184154374Frank Doornink02/2024
354410^154359+49154360Robert Price02/2023
35452^512628-114053154317Enzo Doria11/2014
35462^512529-49783154287Enzo Doria10/2015
3547(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
35482^512315-115297154223Enzo Doria06/2015
3549(47*10^154221+241)/9154222Robert Price06/2022
3550(7*10^154211+173)/9154211Robert Price01/2022
35512^512243+22703154201Enzo Doria09/2023
35522^512168+79561154178Enzo Doria06/2016
3553(77*10^154175+67)/9154176Robert Price12/2021
3554(59*19^120562-5)/18154170Anonymous12/2023
3555(5*10^154158-311)/9154158Robert Price12/2021
355627169^34758-34758^27169154120Frank Doornink01/2024
3557(89*10^154103-737)/9154104Robert Price01/2022
35582^511857+23327154085Enzo Doria10/2023
35594*10^154078-57154079Robert Price10/2018
356026242^34863-34863^26242154060Frank Doornink03/2024
3561(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
35627*10^154038-57154039Robert Price06/2020
35632^511658-114371154025Enzo Doria02/2015
3564(57^87719+1)/58154022Paul Bourdelais11/2017
35652^511580-1846679154001Enzo Doria07/2015
3566(259*10^153998-1)/3154000Robert Price12/2020
35672^511541-113713153990Enzo Doria09/2014
356849958^32768+49957^32768153965Kellen Shenton11/2020
356910^153935+970801153936Patrick De Geest05/2021
357010^153935-1000001153935Robert Price08/2020
3571(16*10^153868-73)/3153869Robert Price07/2020
35729*10^153851-67153852Robert Price11/2020
35732^511077-112723153850Enzo Doria06/2014
357469^83653-68^83653153826Robert Price12/2013
35752^510963-113707153816Enzo Doria09/2014
3576(154*10^153810-1)/9153812Serge Batalov12/2014
3577(181*25^109991-75077)/8153763Curtis Bright05/2015
35782*10^153746-3153747Robert Price07/2015
35792^510626+1179379153714Enzo Doria05/2016
3580(7*10^153664+113)/3153665Robert Price02/2018
35812^510448+24991153661Enzo Doria11/2023
35822^510420+81121153652Enzo Doria07/2016
3583(197*7^181761-1)/2153608Karsten Bonath05/2017
35842^509894-459161153494Enzo Doria05/2015
3585(74*10^153489+673)/9153490Robert Price02/2022
3586(49*10^153484-211)/9153485Robert Price06/2022
35872^509841+71657153478Enzo Doria04/2016
35889*10^153446+41153447Robert Price08/2020
35892^509533-1846723153385Enzo Doria07/2015
35902^509468-39989153366Enzo Doria09/2015
359170^83117-69^83117153360Robert Price01/2014
3592(209246*34^99997-81)/11153148Eric Chen08/2023
3593(7*10^153116-1)/3153117Robert Price08/2022
3594(112*10^153025-1)/3153027Serge Batalov12/2014
359531912^33975-33975^31912153022Frank Doornink01/2024
3596(19*10^153010+131)/3153011Robert Price06/2020
35972^508174-1855151152976Enzo Doria09/2015
3598181^67757-2152974Lelio R Paula12/2017
35992^508160-1864829152972Enzo Doria01/2016
360010^152960+412563152961Patrick De Geest05/2021
360110^152960-50000000001152960Robert Price12/2020
360210^152960-423749152960Patrick De Geest05/2021
3603(71*10^152933-143)/9152934Robert Price10/2021
360432109^33932-33932^32109152919Frank Doornink02/2024
36052^507857-1848199152881Enzo Doria07/2015
36062^507638-115361152815Enzo Doria07/2015
36072^507551-114025152789Enzo Doria11/2014
3608(6^196337+1)/7152780Paul Bourdelais02/2010
3609(22*10^152670-13)/9152671Robert Price06/2018
36102^507085+28517152648Enzo Doria01/2024
36112^506917+28847152598Enzo Doria02/2024
36122^506451-22339152457Enzo Doria07/2013
361326463^34460-34460^26463152405Frank Doornink03/2024
361431898^33837-33837^31898152394Frank Doornink01/2024
36152^505995-113185152320Enzo Doria07/2014
3616(8*10^152260-17)/9152260Serge Batalov11/2022
3617(4*10^152253+149)/9152253Robert Price04/2018
361833530^33643-33643^33530152250Norbert Schneider04/2024
3619578^55117-577^55117152230Jean-Louis Charton08/2012
36202^505431-505431152150Henri Lifchitz04/2005
3621(203*10^152143+1)/3152145Robert Price03/2020
362231730^33787-33787^31730152092Frank Doornink01/2024
36232^505089+217787152047Enzo Doria01/2024
362433565^33594-33594^33565152043Norbert Schneider04/2024
36252^505053+73097152037Enzo Doria04/2016
362622*10^151998+3152000Robert Price01/2020
3627(238*10^151979-1)/3151981Robert Price04/2020
3628(2^504793-7)/46765151954Lelio R Paula12/2017
36293^318465+4151947Aurel Gibier09/2024
3630350377#+797581151937Nicolas PALAU08/2017
3631(79*10^151906-529)/9151907Robert Price01/2022
36322^504618-343991151906Enzo Doria07/2015
36332^504259+211193151798Enzo Doria08/2023
36342^504212-461939151783Enzo Doria07/2015
36357*10^151772-41151773Robert Price08/2021
36362^504054-2231151736Yves Minet10/2011
363725237^34458-34458^25237151686Frank Doornink11/2023
3638(28*10^151682+191)/3151683Robert Price02/2020
36392^503817+23961151665Enzo Doria10/2023
36402^503475-933075151562Paul Bourdelais06/2021
36412^503371+26289151530Enzo Doria12/2023
36422^503361-39883151527Enzo Doria09/2015
36432^503225+382667151486Enzo Doria10/2016
3644(206*10^151483-11)/3151485Robert Price02/2022
3645(844*10^151396-7)/9151398Robert Price05/2021
3646(26*10^151391-503)/9151392Robert Price07/2018
36472^502769+1877567151349Enzo Doria08/2016
36482^502576-4019151291Yves Minet10/2011
36495*10^151257+41151258Robert Price03/2019
36502^502290-2792501151205Enzo Doria02/2016
36512^502181+1868417151172Enzo Doria04/2016
36522^502055+22583151134Enzo Doria09/2023
3653(3*23^110967+41)/22151106Anonymous12/2023
36546*10^151063-77151064Robert Price09/2021
36552^501781-1850503151052Enzo Doria08/2015
3656(5*10^151007+37)/3151008Robert Price03/2018
36573^316494+5*2^316494151007Jon Grantham08/2023
36582^501627-991151005Yves Minet02/2014
36592^501577-115333150990Enzo Doria07/2015
366025239^34298-34298^25239150983Frank Doornink12/2023
3661(19*10^150977-7)/3150978Robert Price12/2023
36628*10^150975+3150976Robert Price08/2015
36632^501512-113669150971Enzo Doria09/2014
366434180^26101+26101^34180150962Norman Luhn04/2024
3665U(1083477)/2166953150949Serge Batalov07/2024
3666(83*10^150908+493)/9150909Robert Price12/2021
366736267^14482+14482^36267150901Norman Luhn04/2024
36682*10^150818+83150819Robert Price12/2021
366948753^1240+1240^48753150814Norman Luhn04/2024
3670(12^139739+1)/13150803Paul Bourdelais09/2011
3671(31^101111-1)/30150792Alexander Zhirkov11/2010
36722^500899-500899150786Henri Lifchitz04/2005
36732^500832+1876801150766Enzo Doria07/2016
3674(23*10^150763-59)/9150764Robert Price05/2018
367546002^1891+1891^46002150735Norman Luhn04/2024
367632001^33458-33458^32001150734Frank Doornink01/2024
36772^500699+1884953150726Enzo Doria02/2017
3678(13*10^150675-37)/3150676Robert Price01/2019
3679(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
368035365^18204+18204^35365150661Norman Luhn05/2024
36822^500337-71101150617Enzo Doria04/2016
3681(74*10^150616+133)/9150617Robert Price06/2019
3683(2*10^150612-17)/3150612Serge Batalov11/2022
36844*10^150577+91150578Robert Price08/2018
36855649^40132+40132^5649150575Norbert Schneider04/2024
36862^500160+80071150564Enzo Doria06/2016
3687(2^500120+5)/9150551Lelio R Paula12/2017
3689(43*10^150515-421)/9150516Robert Price01/2019
36884695^40994+40994^4695150516Norbert Schneider11/2023
36902^499999+15981150515Norman Luhn08/2023
3691(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
3692(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
369326614^34005-34005^26614150476Frank Doornink03/2024
36942^499861-29503150474Enzo Doria08/2015
36952^499653-113533150411Enzo Doria08/2014
3696(14*10^150391-191)/3150392Robert Price10/2020
369729033^33696+33696^29033150382Norbert Schneider10/2023
36982^499534-221150375Yves Minet06/2012
369930110^33567+33567^30110150337Norbert Schneider10/2023
370026212^34023-34023^26212150331Frank Doornink03/2024
3701(28*10^150294+41)/3150295Robert Price07/2021
37022^499225+49727150282Enzo Doria09/2016
3703(695*10^150274+7)/9150276Robert Price12/2021
37042^499054-29261150231Enzo Doria07/2015
370518580^35187+35187^18580150215Norbert Schneider10/2023
3706(844*10^150196-7)/9150198Robert Price05/2021
37072^498907-933075150186Paul Bourdelais06/2021
3708(2^498898-7)/9150183Lelio R Paula10/2015
37093*10^150182+17150183Robert Price07/2018
37105*10^150175+63150176Robert Price09/2020
371129273^33618-33618^29273150154Frank Doornink06/2024
371232363^33292+33292^32363150149Norbert Schneider07/2022
371332^99753-99753^32150144Henri Lifchitz08/2024
3714(77*10^150128+67)/9150129Robert Price12/2021
3715(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
37162^498623+1866983150101Enzo Doria03/2016
371733194^33194-213^213150073Serge Batalov04/2024
371827868^33759-33759^27868150063Frank Doornink06/2024
3719(25*10^150050-403)/9150051Robert Price12/2020
3720numbpart(18140942830)150033Serge Batalov04/2017
372110^150029+4381150030Patrick De Geest05/2016
372210^150029-41150029Serge Batalov12/2014
372333185^33185+618^618150028Serge Batalov04/2024
37249*34^97952+529150013Eric Chen08/2023
372510^150000+1158603150001Patrick De Geest09/2018
372610^150000-245703150000Patrick De Geest09/2018
3727(38*10^149999+691)/9150000Robert Price10/2018
37282043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
3729(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
37302^498238-53149985Lelio R Paula12/2017
373145728^1905+1905^45728149984Hans Havermann10/2020
3732(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
37335*10^149907+23149908Robert Price03/2019
373432^99585-829149891Eric Chen11/2023
373539347^6442+6442^39347149874Hans Havermann09/2020
37362^497850+81049149868Enzo Doria07/2016
3737V(1075416)149830Serge Batalov07/2024
373837228^10575+10575^37228149816Hans Havermann10/2020
3739(5*2^497673+1)/2743149812Lelio R Paula10/2015
3740(5*2^497671+1)/373703149810Lelio R Paula10/2015
3741(2*10^149803-143)/3149803Robert Price03/2018
374233845^26604+26604^33845149763Hans Havermann09/2020
37432^497434-2784191149743Enzo Doria10/2015
3744(865*10^149737-1)/9149739Robert Price04/2020
374510^149695-7000001149695Robert Price06/2021
374638237^8214+8214^38237149681Hans Havermann09/2020
3747(23*10^149655+19)/3149656Robert Price07/2019
37482^497068-113579149633Enzo Doria08/2014
37492^497037+73727149624Enzo Doria04/2016
375011*10^149618+3149620Robert Price07/2021


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