PRP Records

Probable Primes Top 10000

(291192 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 ?
10012^737825+57222108Stefano Morozzi05/2021
1002(54^128189+1)/55222073Paul Bourdelais11/2018
1003(10^221654+179)/9221654Serge Batalov12/2014
10042^736281+79817221643Enzo Doria06/2016
100510^221631+247617221632Patrick De Geest10/2013
100610^221631-9221631Alexander Gramolin02/2011
100710^221628+7221629Alfred Reich04/2021
10082^735970-1839821221550Enzo Doria06/2015
10092^735367+60293221368Enzo Doria03/2016
1010(29^151153+1)/30221045Paul Bourdelais09/2017
10112^733264-2784089220735Enzo Doria10/2015
10122^733114-24555220690Enzo Doria09/2013
10132^731891-636259220322Enzo Doria12/2013
10142^731124-25539220091Enzo Doria09/2013
10152^730972-462029220045Enzo Doria07/2015
10162^730833+1868627220003Enzo Doria04/2016
10172^730645-2787133219947Enzo Doria11/2015
10182^730547-25581219917Enzo Doria09/2013
10192^730460+82291219891Enzo Doria09/2016
1020(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
1021L(1051849)219824Renaud Lifchitz03/2009
102211^210961-240219694Enzo Doria01/2013
10232^729611-113437219635Enzo Doria08/2014
10247^259710-2219481Paul Bourdelais01/2021
1025F(1049897)219416Henri Lifchitz10/2008
10262^728604+1879321219332Enzo Doria10/2016
102733^144412+2219292Robert Price04/2015
10282^728277-183313219234Hans Havermann10/2018
10292^727998-1862711219150Enzo Doria12/2015
10302^727729-114073219069Enzo Doria12/2014
10312^727496-1851809218999Enzo Doria08/2015
10322^726591+2793143218726Enzo Doria02/2016
10332^725534-2791931218408Enzo Doria02/2016
1034Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
10352^722184+1877821217400Enzo Doria08/2016
1036(109*10^217360-1)/9217362Serge Batalov12/2014
10372^721721-4453217260Yves Minet03/2021
1038281*499979#/46410-2702372216849Robert Smith08/2016
1039281*499979#/46410+2400766216849Robert Smith08/2016
1040tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
10412^718756-114107216368Enzo Doria12/2014
10422^717672+121216041Stefano Morozzi05/2021
10432^717305+80327215931Enzo Doria07/2016
10442^717069-59773215860Enzo Doria10/2015
104530^146021-29^146021215691Jean-Louis Charton09/2018
1046277^88301-276^88301215674Jean-Louis Charton06/2012
1047227^91413-40215372Enzo Doria04/2015
1048(2^715008-21)/5215239Stefano Morozzi08/2022
10492^714717+782897215152Enzo Doria11/2016
1050tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
10512^713241+1879157214707Enzo Doria08/2016
105211^206081-10^206081214612Jean-Louis Charton10/2011
10532^712801-69553214575Enzo Doria01/2016
10542^712603-25357214515Enzo Doria09/2013
10552^711721-1846723214250Enzo Doria07/2015
10562^710730-396765213952Enzo Doria09/2013
10572^708468-114329213271Enzo Doria02/2015
1058(163*10^212779-1)/9212781Serge Batalov12/2014
10592^706838-69041212780Enzo Doria11/2015
10602^704577-113871212099Enzo Doria10/2014
1061(2^704548-19)/3212090Stefano Morozzi08/2022
10622^704110-2792441211959Enzo Doria02/2016
10632^703943-1862947211908Enzo Doria12/2015
1064(60^119083+1)/61211746Paul Bourdelais10/2018
1065(10^211610-91)/9211610Serge Batalov12/2014
1066227^89797+2211565Lelio R Paula08/2012
10672^702194-3211382Paul Bourdelais03/2012
10682^702064+1874911211343Enzo Doria07/2016
10692^701968-113873211314Enzo Doria10/2014
10702^701713-113779211237Enzo Doria09/2014
10712^701449-25201211158Enzo Doria09/2013
10722^701403-2786977211144Enzo Doria11/2015
10732^701189-25423211079Enzo Doria09/2013
10742^701162-459161211071Enzo Doria05/2015
1075(24^152783-1)/23210872Paul Bourdelais04/2018
10762^700400+9385210842Lelio R Paula01/2014
10772^700304-17210813Stefano Morozzi07/2022
10782^700131+1874693210761Enzo Doria06/2016
1079(2^700095+225414)/2210750Stefano Morozzi04/2020
1080(2^700090+278254)/2210748Stefano Morozzi04/2020
1081(2^700075+303666)/2210744Stefano Morozzi04/2020
1082(2^700073+75882)/2210743Stefano Morozzi04/2020
1083(2^700074+328890)/2210743Stefano Morozzi04/2020
1084(2^700052+79162)/2210737Stefano Morozzi04/2020
1085(2^700052+304458)/2210737Stefano Morozzi04/2020
1086(2^700048+376578)/2210736Stefano Morozzi04/2020
108711^202357-1140210734Enzo Doria12/2012
1088(2^700021+25874)/2210728Stefano Morozzi04/2020
1089(2^700018+377518)/2210727Stefano Morozzi04/2020
10902^699740+25210643Stefano Morozzi05/2021
10912^698929-2788423210399Enzo Doria11/2015
1092(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
10932^698316+1878601210215Enzo Doria08/2016
10942^697036+1878751209829Enzo Doria08/2016
10956^269407+5209640Paul Bourdelais02/2021
1096(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
10972^696254-115151209594Enzo Doria06/2015
1098(35^135623+1)/36209410Paul Bourdelais07/2018
10992^694633+1887257209106Enzo Doria05/2017
11002^693959+180923208903Enzo Doria07/2016
1101(2^693747-11)/3208839Stefano Morozzi08/2022
11022^693462-1847561208753Enzo Doria07/2015
11032^690890-59981207979Enzo Doria11/2015
1104(38^131591+1)/39207884Paul Bourdelais07/2018
11052^690163+1877063207760Enzo Doria07/2016
11067^245608-2207563Paul Bourdelais01/2021
11072^689286-29381207496Enzo Doria08/2015
11082^689122-114521207447Enzo Doria04/2015
11092^688373+6077207221Enzo Doria02/2016
11102^688201+1875527207170Enzo Doria07/2016
1111(42^127609+1)/43207140Paul Bourdelais07/2018
11122^687619+81563206994Enzo Doria08/2016
11132^686572-1845299206679Enzo Doria07/2015
1114(21^156217-1)/20206552Paul Bourdelais04/2010
1115(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
11162^685578+3206380Paul Bourdelais04/2012
11172^684836-49349206157Enzo Doria10/2015
1118(73^110603-1)/72206088Paul Bourdelais06/2018
11192^684163-2790967205954Enzo Doria12/2015
1120326^81943-325^81943205941Jean-Louis Charton07/2012
1121(2^684127-1)/23765203727205933Jens K. Andersen04/2009
11224^341233-3^341233205443Jean-Louis Charton01/2006
11232^681545+467205166Lelio R Paula11/2013
11242^681306+81049205094Enzo Doria07/2016
11252^680697+1877057204911Enzo Doria07/2016
11262^680415+71783204826Enzo Doria04/2016
11272^679860-459995204659Enzo Doria06/2015
11282^679593+1879547204578Enzo Doria09/2016
11292^678651+1875023204295Enzo Doria07/2016
11302^678561+678561204268Henri Lifchitz05/2006
11312^678101-114043204129Enzo Doria11/2014
11322^678028+1875631204107Enzo Doria06/2016
11332^676992-59783203795Enzo Doria10/2015
11342^676972+1866871203789Enzo Doria03/2016
11352^676761-9203726Robert Price01/2017
11362^676592-23203675Stefano Morozzi07/2022
11372^676563-2792407203666Enzo Doria02/2016
11382^676306-114713203589Enzo Doria04/2015
1139(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
114010247^50678-50678^10247203250Norbert Schneider03/2022
11412^674627-25161203083Enzo Doria09/2013
11422^674603-69337203076Enzo Doria12/2015
11432^674459+74213203033Enzo Doria04/2016
11442^674116-458879202930Enzo Doria04/2015
11452^674076-114755202918Enzo Doria04/2015
11465^289937-4^289937202658Jean-Louis Charton03/2013
1147(2^673184-7)/3202649Stefano Morozzi08/2022
1148(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
11492^672556-1835519202460Enzo Doria04/2015
11502^671446-351401202126Enzo Doria07/2015
11512^671373+77747202104Enzo Doria05/2016
11522^670726-114845201909Enzo Doria05/2015
11532^670539-25045201853Enzo Doria09/2013
115443284^43519-43519^43284201769Norbert Schneider08/2018
11552^670213+282317201755Enzo Doria09/2016
11562^670133+89201731Stefano Morozzi05/2021
11572^669854-113501201647Enzo Doria08/2014
11582^669718+81619201606Enzo Doria08/2016
1159(145*10^201504-1)/9201506Serge Batalov12/2014
11602^668938-1839821201371Enzo Doria06/2015
11612^668492+1879303201237Enzo Doria08/2016
11626^258413-5^258413201085Jean-Louis Charton03/2013
116310194^50161-50161^10194201063Norbert Schneider09/2020
11642^667894+1875589201057Enzo Doria06/2016
11652^667569-1836559200959Enzo Doria05/2015
1166(172*10^200746-1)/9200748Serge Batalov12/2014
11672^666430+782569200616Enzo Doria10/2016
1168(86^103471+1)/87200163Paul Bourdelais05/2018
1169103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
1170103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
1171numbpart(32235776596)200002Serge Batalov04/2017
1172(10^200001+149)/3200001Serge Batalov12/2014
117310^200000+571791200001Patrick De Geest08/2019
1174(3^419180-621444)/3200000Stefano Morozzi06/2019
1175(3^419180-1941384)/3200000Stefano Morozzi08/2019
117610^200000-45557200000Patrick De Geest08/2019
1177(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
117892*10^199980-9199982Robert Price12/2021
1179(85*10^199951-139)/9199952Robert Price08/2021
1180(10^199926+7)/29/373/2339199919Alfred Reich08/2021
118123*10^199833-9199835Robert Price10/2021
1182(299*10^199801-17)/3199803Robert Price04/2020
11836*10^199788+77199789Robert Price06/2020
1184(23*10^199615+37)/3199616Robert Price02/2022
1185(17*10^199607-167)/3199608Robert Price05/2022
11862^663020-933075199589Paul Bourdelais06/2021
1187(14*10^199447+73)/3199448Robert Price12/2018
1188(2^662424-15)/7199409Stefano Morozzi08/2022
11892^662103-29287199313Enzo Doria08/2015
1190(2*10^199283+457)/9199283Robert Price01/2018
1191(10^199248-19)/9199248Robert Price01/2018
1192(83*10^199213+529)/9199214Robert Price12/2021
1193(194*10^199146-17)/3199148Robert Price09/2020
1194(151*10^199003-1)/3199005Robert Price03/2020
11959*10^198946-73198947Robert Price01/2021
119645*10^198931-7198933Robert Price07/2020
11972^660482-2891198825Yves Minet05/2016
11982^659589-21198557Stefano Morozzi07/2022
11992^659583+1879223198555Enzo Doria08/2016
1200(53*10^198529+1)/9198530Serge Batalov07/2010
1201(49*10^198403+311)/9198404Robert Price06/2019
120296*10^198376-7198378Robert Price03/2021
1203(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
12042^658828-29819198327Enzo Doria08/2015
12052^658776-2791229198312Enzo Doria01/2016
1206(35*10^198294-377)/9198295Robert Price07/2018
1207(4*10^198268+137)/3198269Robert Price03/2018
12082^658544-1854029198242Enzo Doria09/2015
1209(62*10^198229-233)/9198230Robert Price02/2022
1210(26*10^198200-41)/3198201Robert Price02/2022
1211(157^90239-1)/156198154Alexander Zhirkov06/2016
12122*10^197959-37197960Robert Price11/2021
1213(232*10^197897+17)/3197899Robert Price04/2021
1214(4*10^197778+173)/3197779Robert Price02/2018
121578*10^197702-7197704Robert Price10/2020
1216(17*10^197640-23)/3197641Robert Price03/2021
1217(29*10^197629-77)/3197630Robert Price02/2020
12182^656462+1874419197615Enzo Doria06/2016
1219(89^101363+1)/90197595Paul Bourdelais11/2017
12202^655893-344563197444Enzo Doria07/2015
12212^655875+71333197439Enzo Doria04/2016
12222^655845-9197430Robert Price01/2017
1223(299*10^197426+1)/3197428Robert Price04/2020
12242^655682-1849121197380Enzo Doria08/2015
12254*10^197268-89197269Robert Price11/2018
1226(11*10^197198-89)/3197199Robert Price05/2021
12272^655045-49603197189Enzo Doria10/2015
12282^655000-2784089197175Enzo Doria10/2015
1229(18^157051-1)/17197141Paul Bourdelais03/2010
1230(154*10^197005+17)/9197007Robert Price06/2022
12312^654400-39719196995Enzo Doria09/2015
1232(14*10^196965-221)/9196966Robert Price04/2018
12332^654216-459995196939Enzo Doria06/2015
1234(17*10^196921+31)/3196922Robert Price01/2019
1235(14*10^196885-89)/3196886Robert Price05/2020
12363*10^196881-59196882Robert Price09/2018
12372^653851+82295196829Enzo Doria09/2016
1238(38*10^196792+691)/9196793Robert Price10/2018
1239(65*10^196768+493)/9196769Robert Price08/2021
12412^653636-29429196765Enzo Doria08/2015
12402^653638-11196765Stefano Morozzi07/2022
12422^653601-69673196754Enzo Doria02/2016
1243(44*10^196684+1)/9196685Serge Batalov07/2010
12442^652786-1852571196509Enzo Doria08/2015
12452^652752-1325196498Yves Minet07/2015
12462^652470-1859141196414Enzo Doria10/2015
12472^652307+1877483196364Enzo Doria08/2016
12482^652293-115273196360Enzo Doria06/2015
1249(47*10^196281+403)/9196282Robert Price03/2019
1250(7*10^196125-31)/3196126Robert Price12/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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