PRP Records

Probable Primes Top 10000

(291910 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 ?
10012^780408-113453234927Enzo Doria08/2014
10022^780368-1864829234915Enzo Doria01/2016
10032^779593-1836559234681Enzo Doria05/2015
1004(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
1005(5^335429+1)/6234455Paul Bourdelais08/2010
10062^778395-113617234321Enzo Doria08/2014
100723*10^234025-7234027Robert Price10/2022
1008Phi(78125,5517)233857Anonymous09/2022
10092^776245-2792353233674Enzo Doria02/2016
10102^776060-114029233618Enzo Doria11/2014
10112^775987-2789557233596Enzo Doria12/2015
10122^775672+1866721233501Enzo Doria03/2016
10132^775238+57233370Stefano Morozzi05/2021
1014(11^223999+1)/12233270Paul Bourdelais02/2010
10152^774118+1885789233033Enzo Doria04/2017
101621^176191-20^176191232964Jean-Louis Charton01/2015
10172^773679-113425232901Enzo Doria08/2014
101810^232599+192489232600Patrick De Geest12/2013
101910^232599-3232599Markus Tervooren10/2010
10202^772552-458879232562Enzo Doria04/2015
10212^772214+1874899232460Enzo Doria06/2016
10222^771994-1862771232394Enzo Doria12/2015
10232^771889+1876037232362Enzo Doria07/2016
10242^771660+1866511232293Enzo Doria02/2016
10255^332150-18188232163Enzo Doria06/2014
10263^485977-2^485977231870Mike Oakes09/2009
10272^770082-114161231818Enzo Doria01/2015
1028(20^177967+1)/21231540Paul Bourdelais05/2013
1029(4*10^231254+23)/9231254Serge Batalov11/2022
10302^767622-9221231078Lelio R Paula01/2016
10312^767344+1880311230994Enzo Doria09/2016
1032(3^483611-1)/2230741Paul Bourdelais02/2010
1033(10^230706+179)/9230706Serge Batalov12/2014
10342^766309+1875257230682Enzo Doria06/2016
10352^765635+1879883230480Enzo Doria09/2016
10362^764348-113697230092Enzo Doria09/2014
10372^764131+78863230027Enzo Doria05/2016
10382^763701+60197229897Enzo Doria03/2016
10394*10^229836+21229837Robert Price12/2022
10402^762841-25905229639Enzo Doria10/2013
10412^761117-113569229120Enzo Doria08/2014
1042(98^114859+1)/99228709Paul Bourdelais12/2018
1043(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
10442^757985-2790013228177Enzo Doria12/2015
10452^757038-1862081227892Enzo Doria12/2015
10462^756839+95849227832Makoto Morimoto10/2013
1047(2^756839+6989)/756091227826Makoto Morimoto09/2016
1048(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
10492^756773-112723227812Enzo Doria07/2014
1050524309#+616367227431Makoto Morimoto02/2016
10512^755097-114193227307Enzo Doria12/2014
10527*10^227178+39227179Robert Price01/2023
10532^754473-2791513227120Enzo Doria01/2016
10542^754376+25227090Stefano Morozzi05/2021
10552^754038+25226989Stefano Morozzi05/2021
10562^751426-764321226202Enzo Doria12/2013
1057(18^180181-1)/17226176Andy Steward04/2007
10582^750740-3225996Paul Bourdelais03/2012
10592^750725+60227225991Enzo Doria02/2016
10602^750525-113743225931Enzo Doria09/2014
1061(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
10622^749444-1861889225606Enzo Doria12/2015
1063tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
10642^749096+1876861225501Enzo Doria07/2016
1065(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
10662^748657+79607225369Enzo Doria06/2016
1067(2^746920-11)/5224845Stefano Morozzi08/2022
10682^746653-291583224765Enzo Doria07/2015
10692^746461-114043224708Enzo Doria11/2014
10702^746302+25224660Stefano Morozzi05/2021
10712^745098-350471224297Enzo Doria06/2015
10722^745039-4897224280Yves Minet03/2021
107323*10^224232-7224234Robert Price10/2022
1074(154*10^224061-1)/9224063Serge Batalov12/2014
10752^744211-1845787224030Enzo Doria07/2015
10762^743592-134579223844Hans Havermann10/2018
10772^742452+3223501Paul Bourdelais06/2019
1078234178^9+9^234178223463Anatoly F. Selevich07/2011
10792^741651-461197223260Enzo Doria07/2015
108010^223236-1001223236Robert Price10/2022
10812^741362-1845251223173Enzo Doria07/2015
10822^740455-1863877222900Enzo Doria12/2015
1083(14*10^222718-41)/9222719Serge Batalov01/2023
10842^739636-2792219222653Enzo Doria02/2016
108511^213654-180222498Enzo Doria01/2013
10862^738957-1859743222449Enzo Doria11/2015
10874*10^222253-21222254Robert Price12/2022
10882^737825+57222108Stefano Morozzi05/2021
1089(54^128189+1)/55222073Paul Bourdelais11/2018
1090(10^221654+179)/9221654Serge Batalov12/2014
10912^736281+79817221643Enzo Doria06/2016
109210^221631+247617221632Patrick De Geest10/2013
109310^221631-9221631Alexander Gramolin02/2011
109410^221628+7221629Alfred Reich04/2021
10952^735970-1839821221550Enzo Doria06/2015
10962^735367+60293221368Enzo Doria03/2016
1097(29^151153+1)/30221045Paul Bourdelais09/2017
10982^733264-2784089220735Enzo Doria10/2015
10992^733114-24555220690Enzo Doria09/2013
11002^731891-636259220322Enzo Doria12/2013
11012^731124-25539220091Enzo Doria09/2013
11022^730972-462029220045Enzo Doria07/2015
11032^730833+1868627220003Enzo Doria04/2016
11042^730645-2787133219947Enzo Doria11/2015
11052^730547-25581219917Enzo Doria09/2013
1106(113*13^197420-5)/12219916Anonymous11/2022
11072^730460+82291219891Enzo Doria09/2016
1108(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
1109L(1051849)219824Renaud Lifchitz03/2009
11108*10^219740-3219741Serge Batalov01/2023
111111^210961-240219694Enzo Doria01/2013
11122^729611-113437219635Enzo Doria08/2014
11137^259710-2219481Paul Bourdelais01/2021
1114F(1049897)219416Henri Lifchitz10/2008
11152^728604+1879321219332Enzo Doria10/2016
111633^144412+2219292Robert Price04/2015
11172^728277-183313219234Hans Havermann10/2018
11182^727998-1862711219150Enzo Doria12/2015
1119(29*10^219124+91)/3219125Robert Price12/2022
11202^727729-114073219069Enzo Doria12/2014
11212^727496-1851809218999Enzo Doria08/2015
11222^726591+2793143218726Enzo Doria02/2016
11232^725534-2791931218408Enzo Doria02/2016
1124Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
11252^722184+1877821217400Enzo Doria08/2016
1126(109*10^217360-1)/9217362Serge Batalov12/2014
11272^721721-4453217260Yves Minet03/2021
1128281*499979#/46410-2702372216849Robert Smith08/2016
1129281*499979#/46410+2400766216849Robert Smith08/2016
1130tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
11312^718756-114107216368Enzo Doria12/2014
11322^717672+121216041Stefano Morozzi05/2021
11332^717305+80327215931Enzo Doria07/2016
11342^717069-59773215860Enzo Doria10/2015
113530^146021-29^146021215691Jean-Louis Charton09/2018
1136277^88301-276^88301215674Jean-Louis Charton06/2012
1137227^91413-40215372Enzo Doria04/2015
1138(2^715008-21)/5215239Stefano Morozzi08/2022
11392^714717+782897215152Enzo Doria11/2016
1140tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
11412^713241+1879157214707Enzo Doria08/2016
114211^206081-10^206081214612Jean-Louis Charton10/2011
11432^712801-69553214575Enzo Doria01/2016
11442^712603-25357214515Enzo Doria09/2013
11452^711721-1846723214250Enzo Doria07/2015
11462^710730-396765213952Enzo Doria09/2013
11472^708468-114329213271Enzo Doria02/2015
1148(163*10^212779-1)/9212781Serge Batalov12/2014
11492^706838-69041212780Enzo Doria11/2015
115022*10^212339+7212341Robert Price10/2022
11512^704577-113871212099Enzo Doria10/2014
1152(2^704548-19)/3212090Stefano Morozzi08/2022
11532^704110-2792441211959Enzo Doria02/2016
11542^703943-1862947211908Enzo Doria12/2015
1155(60^119083+1)/61211746Paul Bourdelais10/2018
1156(184*10^211682-1)/3211684Robert Price12/2022
1157(10^211610-91)/9211610Serge Batalov12/2014
1158227^89797+2211565Lelio R Paula08/2012
11592^702194-3211382Paul Bourdelais03/2012
11602^702064+1874911211343Enzo Doria07/2016
11612^701968-113873211314Enzo Doria10/2014
1162(14*10^211262-41)/9211263Serge Batalov01/2023
11632^701713-113779211237Enzo Doria09/2014
11642^701449-25201211158Enzo Doria09/2013
11652^701403-2786977211144Enzo Doria11/2015
11662^701189-25423211079Enzo Doria09/2013
11672^701162-459161211071Enzo Doria05/2015
1168(24^152783-1)/23210872Paul Bourdelais04/2018
11692^700400+9385210842Lelio R Paula01/2014
11702^700304-17210813Stefano Morozzi07/2022
11712^700131+1874693210761Enzo Doria06/2016
1172(2^700095+225414)/2210750Stefano Morozzi04/2020
1173(2^700090+278254)/2210748Stefano Morozzi04/2020
1174(2^700075+303666)/2210744Stefano Morozzi04/2020
1175(2^700073+75882)/2210743Stefano Morozzi04/2020
1176(2^700074+328890)/2210743Stefano Morozzi04/2020
1177(2^700052+79162)/2210737Stefano Morozzi04/2020
1178(2^700052+304458)/2210737Stefano Morozzi04/2020
1179(2^700048+376578)/2210736Stefano Morozzi04/2020
118011^202357-1140210734Enzo Doria12/2012
1181(2^700021+25874)/2210728Stefano Morozzi04/2020
1182(2^700018+377518)/2210727Stefano Morozzi04/2020
11832^699740+25210643Stefano Morozzi05/2021
11842^698929-2788423210399Enzo Doria11/2015
1185(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
11862^698316+1878601210215Enzo Doria08/2016
11872^697036+1878751209829Enzo Doria08/2016
11886^269407+5209640Paul Bourdelais02/2021
1189(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
11902^696254-115151209594Enzo Doria06/2015
1191(35^135623+1)/36209410Paul Bourdelais07/2018
11927*10^209161+39209162Robert Price01/2023
11932^694633+1887257209106Enzo Doria05/2017
11942^693959+180923208903Enzo Doria07/2016
1195(2^693747-11)/3208839Stefano Morozzi08/2022
11962^693462-1847561208753Enzo Doria07/2015
11972^690890-59981207979Enzo Doria11/2015
1198(38^131591+1)/39207884Paul Bourdelais07/2018
11992^690163+1877063207760Enzo Doria07/2016
12007^245608-2207563Paul Bourdelais01/2021
1201(67*10^207556+23)/9207557Serge Batalov01/2023
12022^689286-29381207496Enzo Doria08/2015
12032^689122-114521207447Enzo Doria04/2015
12042^688373+6077207221Enzo Doria02/2016
12052^688201+1875527207170Enzo Doria07/2016
1206(42^127609+1)/43207140Paul Bourdelais07/2018
12072^687619+81563206994Enzo Doria08/2016
12082^686572-1845299206679Enzo Doria07/2015
1209(21^156217-1)/20206552Paul Bourdelais04/2010
1210(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
12112^685578+3206380Paul Bourdelais04/2012
12122^684836-49349206157Enzo Doria10/2015
1213(73^110603-1)/72206088Paul Bourdelais06/2018
12142^684163-2790967205954Enzo Doria12/2015
1215326^81943-325^81943205941Jean-Louis Charton07/2012
1216(2^684127-1)/23765203727205933Jens K. Andersen04/2009
1217(68*10^205510+13)/9205511Serge Batalov01/2023
12184^341233-3^341233205443Jean-Louis Charton01/2006
12192^681545+467205166Lelio R Paula11/2013
12202^681306+81049205094Enzo Doria07/2016
12212^680697+1877057204911Enzo Doria07/2016
12222^680415+71783204826Enzo Doria04/2016
12232^679860-459995204659Enzo Doria06/2015
12242^679593+1879547204578Enzo Doria09/2016
12252^678651+1875023204295Enzo Doria07/2016
12262^678561+678561204268Henri Lifchitz05/2006
12272^678101-114043204129Enzo Doria11/2014
12282^678028+1875631204107Enzo Doria06/2016
12292^676992-59783203795Enzo Doria10/2015
12302^676972+1866871203789Enzo Doria03/2016
12312^676761-9203726Robert Price01/2017
12322^676592-23203675Stefano Morozzi07/2022
12332^676563-2792407203666Enzo Doria02/2016
12342^676306-114713203589Enzo Doria04/2015
1235(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
123610247^50678-50678^10247203250Norbert Schneider03/2022
12372^674627-25161203083Enzo Doria09/2013
12382^674603-69337203076Enzo Doria12/2015
12392^674459+74213203033Enzo Doria04/2016
12402^674116-458879202930Enzo Doria04/2015
12412^674076-114755202918Enzo Doria04/2015
12425^289937-4^289937202658Jean-Louis Charton03/2013
1243(2^673184-7)/3202649Stefano Morozzi08/2022
1244(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
12452^672556-1835519202460Enzo Doria04/2015
12462^671446-351401202126Enzo Doria07/2015
12472^671373+77747202104Enzo Doria05/2016
1248(2*10^202059+7)/9202059Rytis Slatkevicius01/2023
12492^670726-114845201909Enzo Doria05/2015
12502^670539-25045201853Enzo Doria09/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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