PRP Records

Probable Primes Top 10000

(280932 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 ?
751(20^177967+1)/21231540Paul Bourdelais05/2013
7522^767622-9221231078Lelio R Paula01/2016
7532^767344+1880311230994Enzo Doria09/2016
754(3^483611-1)/2230741Paul Bourdelais02/2010
755(10^230706+179)/9230706Serge Batalov12/2014
7562^766309+1875257230682Enzo Doria06/2016
7572^765635+1879883230480Enzo Doria09/2016
7582^764348-113697230092Enzo Doria09/2014
7592^764131+78863230027Enzo Doria05/2016
7602^763701+60197229897Enzo Doria03/2016
7612^762841-25905229639Enzo Doria10/2013
7622^761117-113569229120Enzo Doria08/2014
763(98^114859+1)/99228709Paul Bourdelais12/2018
764(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
7652^757985-2790013228177Enzo Doria12/2015
7662^757038-1862081227892Enzo Doria12/2015
7672^756839+95849227832Makoto Morimoto10/2013
768(2^756839+6989)/756091227826Makoto Morimoto09/2016
769(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
7702^756773-112723227812Enzo Doria07/2014
771524309#+616367227431Makoto Morimoto02/2016
7722^755097-114193227307Enzo Doria12/2014
7732^754473-2791513227120Enzo Doria01/2016
7742^751426-764321226202Enzo Doria12/2013
775(18^180181-1)/17226176Andy Steward04/2007
7762^750740-3225996Paul Bourdelais03/2012
7772^750725+60227225991Enzo Doria02/2016
7782^750525-113743225931Enzo Doria09/2014
779(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
7802^749444-1861889225606Enzo Doria12/2015
781tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
7822^749096+1876861225501Enzo Doria07/2016
783(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
7842^748657+79607225369Enzo Doria06/2016
7852^746653-291583224765Enzo Doria07/2015
7862^746461-114043224708Enzo Doria11/2014
7872^745098-350471224297Enzo Doria06/2015
7882^745039-4897224280Yves Minet03/2021
789(154*10^224061-1)/9224063Serge Batalov12/2014
7902^744211-1845787224030Enzo Doria07/2015
7912^743592-134579223844Hans Havermann10/2018
7922^742452+3223501Paul Bourdelais06/2019
793234178^9+9^234178223463Anatoly F. Selevich07/2011
7942^741651-461197223260Enzo Doria07/2015
7952^741362-1845251223173Enzo Doria07/2015
7962^740455-1863877222900Enzo Doria12/2015
7972^739636-2792219222653Enzo Doria02/2016
79811^213654-180222498Enzo Doria01/2013
7992^738957-1859743222449Enzo Doria11/2015
800(54^128189+1)/55222073Paul Bourdelais11/2018
801(10^221654+179)/9221654Serge Batalov12/2014
8022^736281+79817221643Enzo Doria06/2016
80310^221631+247617221632Patrick De Geest10/2013
80410^221631-9221631Alexander Gramolin02/2011
8052^735970-1839821221550Enzo Doria06/2015
8062^735367+60293221368Enzo Doria03/2016
807(29^151153+1)/30221045Paul Bourdelais09/2017
8082^733264-2784089220735Enzo Doria10/2015
8092^733114-24555220690Enzo Doria09/2013
8102^731891-636259220322Enzo Doria12/2013
8112^731124-25539220091Enzo Doria09/2013
8122^730972-462029220045Enzo Doria07/2015
8132^730833+1868627220003Enzo Doria04/2016
8142^730645-2787133219947Enzo Doria11/2015
8152^730547-25581219917Enzo Doria09/2013
8162^730460+82291219891Enzo Doria09/2016
817(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
818L(1051849)219824Renaud Lifchitz03/2009
81911^210961-240219694Enzo Doria01/2013
8202^729611-113437219635Enzo Doria08/2014
8217^259710-2219481Paul Bourdelais01/2021
822F(1049897)219416Henri Lifchitz10/2008
8232^728604+1879321219332Enzo Doria10/2016
82433^144412+2219292Robert Price04/2015
8252^728277-183313219234Hans Havermann10/2018
8262^727998-1862711219150Enzo Doria12/2015
8272^727729-114073219069Enzo Doria12/2014
8282^727496-1851809218999Enzo Doria08/2015
8292^726591+2793143218726Enzo Doria02/2016
8302^725534-2791931218408Enzo Doria02/2016
831Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
8322^722184+1877821217400Enzo Doria08/2016
833(109*10^217360-1)/9217362Serge Batalov12/2014
8342^721721-4453217260Yves Minet03/2021
835281*499979#/46410-2702372216849Robert Smith08/2016
836281*499979#/46410+2400766216849Robert Smith08/2016
837tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
8382^718756-114107216368Enzo Doria12/2014
8392^717305+80327215931Enzo Doria07/2016
8402^717069-59773215860Enzo Doria10/2015
84130^146021-29^146021215691Jean-Louis Charton09/2018
842277^88301-276^88301215674Jean-Louis Charton06/2012
843227^91413-40215372Enzo Doria04/2015
8442^714717+782897215152Enzo Doria11/2016
845tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
8462^713241+1879157214707Enzo Doria08/2016
84711^206081-10^206081214612Jean-Louis Charton10/2011
8482^712801-69553214575Enzo Doria01/2016
8492^712603-25357214515Enzo Doria09/2013
8502^711721-1846723214250Enzo Doria07/2015
8512^710730-396765213952Enzo Doria09/2013
8522^708468-114329213271Enzo Doria02/2015
853(163*10^212779-1)/9212781Serge Batalov12/2014
8542^706838-69041212780Enzo Doria11/2015
8552^704577-113871212099Enzo Doria10/2014
8562^704110-2792441211959Enzo Doria02/2016
8572^703943-1862947211908Enzo Doria12/2015
858(60^119083+1)/61211746Paul Bourdelais10/2018
859(10^211610-91)/9211610Serge Batalov12/2014
860227^89797+2211565Lelio R Paula08/2012
8612^702194-3211382Paul Bourdelais03/2012
8622^702064+1874911211343Enzo Doria07/2016
8632^701968-113873211314Enzo Doria10/2014
8642^701713-113779211237Enzo Doria09/2014
8652^701449-25201211158Enzo Doria09/2013
8662^701403-2786977211144Enzo Doria11/2015
8672^701189-25423211079Enzo Doria09/2013
8682^701162-459161211071Enzo Doria05/2015
869(24^152783-1)/23210872Paul Bourdelais04/2018
8702^700400+9385210842Lelio R Paula01/2014
8712^700131+1874693210761Enzo Doria06/2016
872(2^700095+225414)/2210750Stefano Morozzi04/2020
873(2^700090+278254)/2210748Stefano Morozzi04/2020
874(2^700075+303666)/2210744Stefano Morozzi04/2020
875(2^700073+75882)/2210743Stefano Morozzi04/2020
876(2^700074+328890)/2210743Stefano Morozzi04/2020
877(2^700052+79162)/2210737Stefano Morozzi04/2020
878(2^700052+304458)/2210737Stefano Morozzi04/2020
879(2^700048+376578)/2210736Stefano Morozzi04/2020
88011^202357-1140210734Enzo Doria12/2012
881(2^700021+25874)/2210728Stefano Morozzi04/2020
882(2^700018+377518)/2210727Stefano Morozzi04/2020
8832^698929-2788423210399Enzo Doria11/2015
884(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
8852^698316+1878601210215Enzo Doria08/2016
8862^697036+1878751209829Enzo Doria08/2016
8876^269407+5209640Paul Bourdelais02/2021
888(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
8892^696254-115151209594Enzo Doria06/2015
890(35^135623+1)/36209410Paul Bourdelais07/2018
8912^694633+1887257209106Enzo Doria05/2017
8922^693959+180923208903Enzo Doria07/2016
8932^693462-1847561208753Enzo Doria07/2015
8942^690890-59981207979Enzo Doria11/2015
895(38^131591+1)/39207884Paul Bourdelais07/2018
8962^690163+1877063207760Enzo Doria07/2016
8977^245608-2207563Paul Bourdelais01/2021
8982^689286-29381207496Enzo Doria08/2015
8992^689122-114521207447Enzo Doria04/2015
9002^688373+6077207221Enzo Doria02/2016
9012^688201+1875527207170Enzo Doria07/2016
902(42^127609+1)/43207140Paul Bourdelais07/2018
9032^687619+81563206994Enzo Doria08/2016
9042^686572-1845299206679Enzo Doria07/2015
905(21^156217-1)/20206552Paul Bourdelais04/2010
906(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
9072^685578+3206380Paul Bourdelais04/2012
9082^684836-49349206157Enzo Doria10/2015
909(73^110603-1)/72206088Paul Bourdelais06/2018
9102^684163-2790967205954Enzo Doria12/2015
911326^81943-325^81943205941Jean-Louis Charton07/2012
912(2^684127-1)/23765203727205933Jens K. Andersen04/2009
9134^341233-3^341233205443Jean-Louis Charton01/2006
9142^681545+467205166Lelio R Paula11/2013
9152^681306+81049205094Enzo Doria07/2016
9162^680697+1877057204911Enzo Doria07/2016
9172^680415+71783204826Enzo Doria04/2016
9182^679860-459995204659Enzo Doria06/2015
9192^679593+1879547204578Enzo Doria09/2016
9202^678651+1875023204295Enzo Doria07/2016
9212^678561+678561204268Henri Lifchitz05/2006
9222^678101-114043204129Enzo Doria11/2014
9232^678028+1875631204107Enzo Doria06/2016
9242^676992-59783203795Enzo Doria10/2015
9252^676972+1866871203789Enzo Doria03/2016
9262^676761-9203726Robert Price01/2017
9272^676563-2792407203666Enzo Doria02/2016
9282^676306-114713203589Enzo Doria04/2015
929(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
9302^674627-25161203083Enzo Doria09/2013
9312^674603-69337203076Enzo Doria12/2015
9322^674459+74213203033Enzo Doria04/2016
9332^674116-458879202930Enzo Doria04/2015
9342^674076-114755202918Enzo Doria04/2015
9355^289937-4^289937202658Jean-Louis Charton03/2013
936(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
9372^672556-1835519202460Enzo Doria04/2015
9382^671446-351401202126Enzo Doria07/2015
9392^671373+77747202104Enzo Doria05/2016
9402^670726-114845201909Enzo Doria05/2015
9412^670539-25045201853Enzo Doria09/2013
94243284^43519-43519^43284201769Norbert Schneider08/2018
9432^670213+282317201755Enzo Doria09/2016
9442^669854-113501201647Enzo Doria08/2014
9452^669718+81619201606Enzo Doria08/2016
946(145*10^201504-1)/9201506Serge Batalov12/2014
9472^668938-1839821201371Enzo Doria06/2015
9482^668492+1879303201237Enzo Doria08/2016
9496^258413-5^258413201085Jean-Louis Charton03/2013
95010194^50161-50161^10194201063Norbert Schneider09/2020
9512^667894+1875589201057Enzo Doria06/2016
9522^667569-1836559200959Enzo Doria05/2015
953(172*10^200746-1)/9200748Serge Batalov12/2014
9542^666430+782569200616Enzo Doria10/2016
955(86^103471+1)/87200163Paul Bourdelais05/2018
957103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
956103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
958numbpart(32235776596)200002Serge Batalov04/2017
959(10^200001+149)/3200001Serge Batalov12/2014
96010^200000+571791200001Patrick De Geest08/2019
961(3^419180-621444)/3200000Stefano Morozzi06/2019
962(3^419180-1941384)/3200000Stefano Morozzi08/2019
96310^200000-45557200000Patrick De Geest08/2019
964(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
965(299*10^199801-17)/3199803Robert Price04/2020
9666*10^199788+77199789Robert Price06/2020
967(14*10^199447+73)/3199448Robert Price12/2018
9682^662103-29287199313Enzo Doria08/2015
969(2*10^199283+457)/9199283Robert Price01/2018
970(10^199248-19)/9199248Robert Price01/2018
971(194*10^199146-17)/3199148Robert Price09/2020
972(151*10^199003-1)/3199005Robert Price03/2020
9739*10^198946-73198947Robert Price01/2021
97445*10^198931-7198933Robert Price07/2020
9752^660482-2891198825Yves Minet05/2016
9762^659583+1879223198555Enzo Doria08/2016
977(53*10^198529+1)/9198530Serge Batalov07/2010
978(49*10^198403+311)/9198404Robert Price06/2019
97996*10^198376-7198378Robert Price03/2021
9802^658828-29819198327Enzo Doria08/2015
9812^658776-2791229198312Enzo Doria01/2016
982(35*10^198294-377)/9198295Robert Price07/2018
983(4*10^198268+137)/3198269Robert Price03/2018
9842^658544-1854029198242Enzo Doria09/2015
985(157^90239-1)/156198154Alexander Zhirkov06/2016
986(232*10^197897+17)/3197899Robert Price04/2021
987(4*10^197778+173)/3197779Robert Price02/2018
98878*10^197702-7197704Robert Price10/2020
989(17*10^197640-23)/3197641Robert Price03/2021
990(29*10^197629-77)/3197630Robert Price02/2020
9912^656462+1874419197615Enzo Doria06/2016
992(89^101363+1)/90197595Paul Bourdelais11/2017
9932^655893-344563197444Enzo Doria07/2015
9942^655875+71333197439Enzo Doria04/2016
9952^655845-9197430Robert Price01/2017
996(299*10^197426+1)/3197428Robert Price04/2020
9972^655682-1849121197380Enzo Doria08/2015
9984*10^197268-89197269Robert Price11/2018
9992^655045-49603197189Enzo Doria10/2015
10002^655000-2784089197175Enzo Doria10/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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