PRP Records

Probable Primes Top 10000

(294613 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 ?
15012^753263+217133226755Enzo Doria12/2023
15027*10^226479-9226480Robert Price02/2023
15032^751426-764321226202Enzo Doria12/2013
1504(18^180181-1)/17226176Andy Steward04/2007
15052^750740-3225996Paul Bourdelais03/2012
15062^750725+60227225991Enzo Doria02/2016
15072^750525-113743225931Enzo Doria09/2014
1508(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
15092^749444-1861889225606Enzo Doria12/2015
1510tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
15112^749096+1876861225501Enzo Doria07/2016
15122^748895+26213225440Enzo Doria12/2023
1513(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
15142^748657+79607225369Enzo Doria06/2016
1515(2^746920-11)/5224845Stefano Morozzi08/2022
15162^746653-291583224765Enzo Doria07/2015
15172^746461-114043224708Enzo Doria11/2014
15182^746302+25224660Stefano Morozzi05/2021
1519(202*10^224545-1)/3224547Robert Price06/2023
1520(19*10^224533-37)/9224534Alfred Reich12/2023
15212^745674+213949224471Enzo Doria10/2023
15222^745098-350471224297Enzo Doria06/2015
15232^745039-4897224280Yves Minet03/2021
152423*10^224232-7224234Robert Price10/2022
1525(154*10^224061-1)/9224063Serge Batalov12/2014
15262^744211-1845787224030Enzo Doria07/2015
15272^743592-134579223844Hans Havermann10/2018
15282^742452+3223501Paul Bourdelais06/2019
1529234178^9+9^234178223463Anatoly F. Selevich07/2011
15302^741651-461197223260Enzo Doria07/2015
153110^223236-1001223236Robert Price10/2022
15322^741362-1845251223173Enzo Doria07/2015
15333^467546-5*2^467546223077Jon Grantham08/2023
15342^740455-1863877222900Enzo Doria12/2015
15352^740274+217519222845Enzo Doria01/2024
1536(14*10^222718-41)/9222719Serge Batalov01/2023
15372^739636-2792219222653Enzo Doria02/2016
153811^213654-180222498Enzo Doria01/2013
15392^738957-1859743222449Enzo Doria11/2015
15404*10^222253-21222254Robert Price12/2022
15412^737825+57222108Stefano Morozzi05/2021
1542(54^128189+1)/55222073Paul Bourdelais11/2018
1543(10^221654+179)/9221654Serge Batalov12/2014
15442^736281+79817221643Enzo Doria06/2016
154510^221631+247617221632Patrick De Geest10/2013
154610^221631-9221631Alexander Gramolin02/2011
154710^221628+7221629Alfred Reich04/2021
15482^735970-1839821221550Enzo Doria06/2015
15492^735367+60293221368Enzo Doria03/2016
155077*10^221343+3221345Robert Price11/2023
1551(202*10^221092-1)/3221094Robert Price06/2023
1552(29^151153+1)/30221045Paul Bourdelais09/2017
15532^734228+24751221025Enzo Doria10/2023
15542^733264-2784089220735Enzo Doria10/2015
15552^733114-24555220690Enzo Doria09/2013
15562^731891-636259220322Enzo Doria12/2013
155798*10^220185-9220187Robert Price05/2023
1558418319^39164+418318220161Alfred Reich11/2023
15592^731124-25539220091Enzo Doria09/2013
15602^730972-462029220045Enzo Doria07/2015
15612^730833+1868627220003Enzo Doria04/2016
15622^730645-2787133219947Enzo Doria11/2015
15632^730547-25581219917Enzo Doria09/2013
1564(113*13^197420-5)/12219916Anonymous11/2022
1565(13^197420*113-5)/12219916Eric Chen10/2023
15662^730460+82291219891Enzo Doria09/2016
1567(5*10^219847-101)/3219848Robert Price08/2023
1568(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
1569L(1051849)219824Renaud Lifchitz03/2009
15703*2^730149+5219798Jon Grantham07/2023
15718*10^219740-3219741Serge Batalov01/2023
157211^210961-240219694Enzo Doria01/2013
1573(26*10^219639-77)/3219640Robert Price03/2023
15742^729611-113437219635Enzo Doria08/2014
15757^259710-2219481Paul Bourdelais01/2021
1576F(1049897)219416Henri Lifchitz10/2008
1577(1488^69151-1)/1487219386Alexander Zhirkov02/2023
15782^728604+1879321219332Enzo Doria10/2016
157933^144412+2219292Robert Price04/2015
15802^728277-183313219234Hans Havermann10/2018
15812^727998-1862711219150Enzo Doria12/2015
1582(29*10^219124+91)/3219125Robert Price12/2022
15832^727729-114073219069Enzo Doria12/2014
15842^727496-1851809218999Enzo Doria08/2015
15852^727025+25907218857Enzo Doria12/2023
15862^726591+2793143218726Enzo Doria02/2016
1587(7*10^218644+17)/3218645Robert Price06/2023
15882^725534-2791931218408Enzo Doria02/2016
1589Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
15902^722184+1877821217400Enzo Doria08/2016
1591(109*10^217360-1)/9217362Serge Batalov12/2014
15922^721721-4453217260Yves Minet03/2021
159310^216950+49216951Robert Price02/2023
1594281*499979#/46410-2702372216849Robert Smith08/2016
1595281*499979#/46410+2400766216849Robert Smith08/2016
1596tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
15972^718756-114107216368Enzo Doria12/2014
15982^717672+121216041Stefano Morozzi05/2021
15992^717305+80327215931Enzo Doria07/2016
16002^717069-59773215860Enzo Doria10/2015
160110^215802+33215803Robert Price08/2023
160230^146021-29^146021215691Jean-Louis Charton09/2018
1603277^88301-276^88301215674Jean-Louis Charton06/2012
16042^716428+215011215667Enzo Doria11/2023
1605(13*10^215592-43)/3215593Robert Price08/2023
1606227^91413-40215372Enzo Doria04/2015
1607(2^715008-21)/5215239Stefano Morozzi08/2022
16082^714717+782897215152Enzo Doria11/2016
1609tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
16102^713241+1879157214707Enzo Doria08/2016
1611(23*10^214633+91)/3214634Robert Price03/2023
161211^206081-10^206081214612Jean-Louis Charton10/2011
16132^712801-69553214575Enzo Doria01/2016
16142^712603-25357214515Enzo Doria09/2013
16152^711721-1846723214250Enzo Doria07/2015
16162^710730-396765213952Enzo Doria09/2013
1617(19*10^213934-37)/9213935Alfred Reich12/2023
1618(19*10^213730-37)/9213731Alfred Reich12/2023
1619(713^74897-1)/712213685Jinyuan Wang08/2023
16202^709773+25907213663Enzo Doria12/2023
16212^708468-114329213271Enzo Doria02/2015
16222^708293+27557213218Enzo Doria01/2024
16232^707277+28997212912Enzo Doria02/2024
1624(163*10^212779-1)/9212781Serge Batalov12/2014
16252^706838-69041212780Enzo Doria11/2015
16262^705653+25907212423Enzo Doria12/2023
162722*10^212339+7212341Robert Price10/2022
16282^704577-113871212099Enzo Doria10/2014
1629(2^704548-19)/3212090Stefano Morozzi08/2022
16302^704110-2792441211959Enzo Doria02/2016
16312^704084+28531211951Enzo Doria02/2024
16322^703943-1862947211908Enzo Doria12/2015
1633(60^119083+1)/61211746Paul Bourdelais10/2018
1634(184*10^211682-1)/3211684Robert Price12/2022
1635(10^211610-91)/9211610Serge Batalov12/2014
1636227^89797+2211565Lelio R Paula08/2012
16372^702194-3211382Paul Bourdelais03/2012
16382^702064+1874911211343Enzo Doria07/2016
16392^701968-113873211314Enzo Doria10/2014
1640(14*10^211262-41)/9211263Serge Batalov01/2023
16412^701713-113779211237Enzo Doria09/2014
16422^701616-216803211208Enzo Doria01/2024
16432^701449-25201211158Enzo Doria09/2013
16442^701403-2786977211144Enzo Doria11/2015
16452^701189-25423211079Enzo Doria09/2013
16462^701162-459161211071Enzo Doria05/2015
16472^700793+219407210960Enzo Doria03/2024
1648(24^152783-1)/23210872Paul Bourdelais04/2018
16492^700400+9385210842Lelio R Paula01/2014
16502^700304-17210813Stefano Morozzi07/2022
16512^700131+1874693210761Enzo Doria06/2016
1652(2^700095+225414)/2210750Stefano Morozzi04/2020
1653(2^700090+278254)/2210748Stefano Morozzi04/2020
1654(2^700075+303666)/2210744Stefano Morozzi04/2020
1655(2^700073+75882)/2210743Stefano Morozzi04/2020
1656(2^700074+328890)/2210743Stefano Morozzi04/2020
1657(2^700052+79162)/2210737Stefano Morozzi04/2020
1658(2^700052+304458)/2210737Stefano Morozzi04/2020
1659(2^700048+376578)/2210736Stefano Morozzi04/2020
166011^202357-1140210734Enzo Doria12/2012
1661(2^700021+25874)/2210728Stefano Morozzi04/2020
1662(2^700018+377518)/2210727Stefano Morozzi04/2020
16632^699999+300729210721Norman Luhn09/2023
1664(238*10^210712-1)/3210714Robert Price09/2023
16652^699740+25210643Stefano Morozzi05/2021
1666(23*10^210525-143)/3210526Robert Price12/2023
16672^698929-2788423210399Enzo Doria11/2015
1668(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
16692^698316+1878601210215Enzo Doria08/2016
167034*10^210097-9210099Robert Price05/2023
1671(19*10^210011-49)/3210012Robert Price06/2023
16726*10^209846-91209847Robert Price05/2023
16732^697036+1878751209829Enzo Doria08/2016
16742^696813+28607209762Enzo Doria02/2024
1675(238*10^209715-1)/3209717Robert Price09/2023
16766^269407+5209640Paul Bourdelais02/2021
1677(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
16782^696254-115151209594Enzo Doria06/2015
1679(35^135623+1)/36209410Paul Bourdelais07/2018
16807*10^209161+39209162Robert Price01/2023
16812^694633+1887257209106Enzo Doria05/2017
1682fibonacci(999790)-4208944Jon Grantham08/2023
16832^693959+180923208903Enzo Doria07/2016
1684(2^693747-11)/3208839Stefano Morozzi08/2022
16852^693462-1847561208753Enzo Doria07/2015
16862^690890-59981207979Enzo Doria11/2015
1687(38^131591+1)/39207884Paul Bourdelais07/2018
16883*2^690484+5207857Jon Grantham07/2023
16892^690163+1877063207760Enzo Doria07/2016
16907^245608-2207563Paul Bourdelais01/2021
1691(67*10^207556+23)/9207557Serge Batalov01/2023
16922^689286-29381207496Enzo Doria08/2015
16932^689122-114521207447Enzo Doria04/2015
16949*10^207254-89207255Robert Price02/2023
16952^688373+6077207221Enzo Doria02/2016
16962^688201+1875527207170Enzo Doria07/2016
1697(42^127609+1)/43207140Paul Bourdelais07/2018
16982^687938+213589207090Enzo Doria10/2023
16992^687619+81563206994Enzo Doria08/2016
17003*10^206927+37206928Robert Price08/2023
17012^687383+21803206923Enzo Doria09/2023
17022^686572-1845299206679Enzo Doria07/2015
1703(21^156217-1)/20206552Paul Bourdelais04/2010
1704(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
17052^685578+3206380Paul Bourdelais04/2012
17062^685078+218599206230Enzo Doria01/2024
17072^684836-49349206157Enzo Doria10/2015
1708(73^110603-1)/72206088Paul Bourdelais06/2018
17092^684163-2790967205954Enzo Doria12/2015
1710326^81943-325^81943205941Jean-Louis Charton07/2012
1711(2^684127-1)/23765203727205933Jens K. Andersen04/2009
1712(68*10^205510+13)/9205511Serge Batalov01/2023
17134^341233-3^341233205443Jean-Louis Charton01/2006
17142^682414+215029205428Enzo Doria11/2023
1715(963^68821-1)/962205334Jinyuan Wang01/2024
1716(43*10^205183-421)/9205184Robert Price10/2023
17172^681545+467205166Lelio R Paula11/2013
17182^681306+81049205094Enzo Doria07/2016
17192^680697+1877057204911Enzo Doria07/2016
17202^680415+71783204826Enzo Doria04/2016
172110^204764-8001204764Robert Price03/2023
1722(26*10^204730-77)/3204731Robert Price03/2023
17232^679860-459995204659Enzo Doria06/2015
17242^679593+1879547204578Enzo Doria09/2016
17252^678753+21677204326Enzo Doria08/2023
17262^678651+1875023204295Enzo Doria07/2016
17272^678561+678561204268Henri Lifchitz05/2006
17285*3^427884+2^427884204154Jon Grantham08/2023
17292^678101-114043204129Enzo Doria11/2014
17302^678028+1875631204107Enzo Doria06/2016
17312^677721+28607204015Enzo Doria01/2024
1732(19*10^203798-7)/3203799Robert Price12/2023
17332^676992-59783203795Enzo Doria10/2015
17342^676972+1866871203789Enzo Doria03/2016
17352^676815+22583203742Enzo Doria09/2023
17362^676761-9203726Robert Price01/2017
17372^676592-23203675Stefano Morozzi07/2022
17382^676563-2792407203666Enzo Doria02/2016
17392^676306-114713203589Enzo Doria04/2015
1740(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
17416*10^203365+53203366Robert Price09/2023
174210247^50678-50678^10247203250Norbert Schneider03/2022
17432^674627-25161203083Enzo Doria09/2013
17442^674603-69337203076Enzo Doria12/2015
1745(182*10^203048+1)/3203050Robert Price09/2023
17462^674459+74213203033Enzo Doria04/2016
17472^674116-458879202930Enzo Doria04/2015
17482^674076-114755202918Enzo Doria04/2015
17495^289937-4^289937202658Jean-Louis Charton03/2013
1750(2^673184-7)/3202649Stefano Morozzi08/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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