PRP Records

Probable Primes Top 10000

(277054 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
7512^750725+60227225991Enzo Doria02/2016
7522^750525-113743225931Enzo Doria09/2014
753(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
7542^749444-1861889225606Enzo Doria12/2015
755tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
7562^749096+1876861225501Enzo Doria07/2016
757(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
7582^748657+79607225369Enzo Doria06/2016
7592^746653-291583224765Enzo Doria07/2015
7602^746461-114043224708Enzo Doria11/2014
7612^745098-350471224297Enzo Doria06/2015
762(154*10^224061-1)/9224063Serge Batalov12/2014
7632^744211-1845787224030Enzo Doria07/2015
7642^743592-134579223844Hans Havermann10/2018
7652^742452+3223501Paul Bourdelais06/2019
766234178^9+9^234178223463Anatoly F. Selevich07/2011
7672^741651-461197223260Enzo Doria07/2015
7682^741362-1845251223173Enzo Doria07/2015
7692^740455-1863877222900Enzo Doria12/2015
7702^739636-2792219222653Enzo Doria02/2016
77111^213654-180222498Enzo Doria01/2013
7722^738957-1859743222449Enzo Doria11/2015
773(54^128189+1)/55222073Paul Bourdelais11/2018
774(10^221654+179)/9221654Serge Batalov12/2014
7752^736281+79817221643Enzo Doria06/2016
77610^221631+247617221632Patrick De Geest10/2013
77710^221631-9221631Alexander Gramolin02/2011
7782^735970-1839821221550Enzo Doria06/2015
7792^735367+60293221368Enzo Doria03/2016
780(29^151153+1)/30221045Paul Bourdelais09/2017
7812^733264-2784089220735Enzo Doria10/2015
7822^733114-24555220690Enzo Doria09/2013
7832^731891-636259220322Enzo Doria12/2013
7842^731124-25539220091Enzo Doria09/2013
7852^730972-462029220045Enzo Doria07/2015
7862^730833+1868627220003Enzo Doria04/2016
7872^730645-2787133219947Enzo Doria11/2015
7882^730547-25581219917Enzo Doria09/2013
7892^730460+82291219891Enzo Doria09/2016
790(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
791L(1051849)219824Renaud Lifchitz03/2009
79211^210961-240219694Enzo Doria01/2013
7932^729611-113437219635Enzo Doria08/2014
794F(1049897)219416Henri Lifchitz10/2008
7952^728604+1879321219332Enzo Doria10/2016
79633^144412+2219292Robert Price04/2015
7972^728277-183313219234Hans Havermann10/2018
7982^727998-1862711219150Enzo Doria12/2015
7992^727729-114073219069Enzo Doria12/2014
8002^727496-1851809218999Enzo Doria08/2015
8012^726591+2793143218726Enzo Doria02/2016
8022^725534-2791931218408Enzo Doria02/2016
803Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
8042^722184+1877821217400Enzo Doria08/2016
805(109*10^217360-1)/9217362Serge Batalov12/2014
806281*499979#/46410-2702372216849Robert Smith08/2016
807281*499979#/46410+2400766216849Robert Smith08/2016
808tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
8092^718756-114107216368Enzo Doria12/2014
8102^717305+80327215931Enzo Doria07/2016
8112^717069-59773215860Enzo Doria10/2015
81230^146021-29^146021215691Jean-Louis Charton09/2018
813277^88301-276^88301215674Jean-Louis Charton06/2012
814227^91413-40215372Enzo Doria04/2015
8152^714717+782897215152Enzo Doria11/2016
816tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
8172^713241+1879157214707Enzo Doria08/2016
81811^206081-10^206081214612Jean-Louis Charton10/2011
8192^712801-69553214575Enzo Doria01/2016
8202^712603-25357214515Enzo Doria09/2013
8212^711721-1846723214250Enzo Doria07/2015
8222^710730-396765213952Enzo Doria09/2013
8232^708468-114329213271Enzo Doria02/2015
824(163*10^212779-1)/9212781Serge Batalov12/2014
8252^706838-69041212780Enzo Doria11/2015
8262^704577-113871212099Enzo Doria10/2014
8272^704110-2792441211959Enzo Doria02/2016
8282^703943-1862947211908Enzo Doria12/2015
829(60^119083+1)/61211746Paul Bourdelais10/2018
830(10^211610-91)/9211610Serge Batalov12/2014
831227^89797+2211565Lelio R Paula08/2012
8322^702194-3211382Paul Bourdelais03/2012
8332^702064+1874911211343Enzo Doria07/2016
8342^701968-113873211314Enzo Doria10/2014
8352^701713-113779211237Enzo Doria09/2014
8362^701449-25201211158Enzo Doria09/2013
8372^701403-2786977211144Enzo Doria11/2015
8382^701189-25423211079Enzo Doria09/2013
8392^701162-459161211071Enzo Doria05/2015
840(24^152783-1)/23210872Paul Bourdelais04/2018
8412^700400+9385210842Lelio R Paula01/2014
8422^700131+1874693210761Enzo Doria06/2016
843(2^700095+225414)/2210750Stefano Morozzi04/2020
844(2^700090+278254)/2210748Stefano Morozzi04/2020
845(2^700075+303666)/2210744Stefano Morozzi04/2020
846(2^700073+75882)/2210743Stefano Morozzi04/2020
847(2^700074+328890)/2210743Stefano Morozzi04/2020
848(2^700052+79162)/2210737Stefano Morozzi04/2020
849(2^700052+304458)/2210737Stefano Morozzi04/2020
850(2^700048+376578)/2210736Stefano Morozzi04/2020
85111^202357-1140210734Enzo Doria12/2012
852(2^700021+25874)/2210728Stefano Morozzi04/2020
853(2^700018+377518)/2210727Stefano Morozzi04/2020
8542^698929-2788423210399Enzo Doria11/2015
855(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
8562^698316+1878601210215Enzo Doria08/2016
8572^697036+1878751209829Enzo Doria08/2016
858(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
8592^696254-115151209594Enzo Doria06/2015
860(35^135623+1)/36209410Paul Bourdelais07/2018
8612^694633+1887257209106Enzo Doria05/2017
8622^693959+180923208903Enzo Doria07/2016
8632^693462-1847561208753Enzo Doria07/2015
8642^690890-59981207979Enzo Doria11/2015
865(38^131591+1)/39207884Paul Bourdelais07/2018
8662^690163+1877063207760Enzo Doria07/2016
8672^689286-29381207496Enzo Doria08/2015
8682^689122-114521207447Enzo Doria04/2015
8692^688373+6077207221Enzo Doria02/2016
8702^688201+1875527207170Enzo Doria07/2016
871(42^127609+1)/43207140Paul Bourdelais07/2018
8722^687619+81563206994Enzo Doria08/2016
8732^686572-1845299206679Enzo Doria07/2015
874(21^156217-1)/20206552Paul Bourdelais04/2010
875(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
8762^685578+3206380Paul Bourdelais04/2012
8772^684836-49349206157Enzo Doria10/2015
878(73^110603-1)/72206088Paul Bourdelais06/2018
8792^684163-2790967205954Enzo Doria12/2015
880326^81943-325^81943205941Jean-Louis Charton07/2012
881(2^684127-1)/23765203727205933Jens K. Andersen04/2009
8824^341233-3^341233205443Jean-Louis Charton01/2006
8832^681545+467205166Lelio R Paula11/2013
8842^681306+81049205094Enzo Doria07/2016
8852^680697+1877057204911Enzo Doria07/2016
8862^680415+71783204826Enzo Doria04/2016
8872^679860-459995204659Enzo Doria06/2015
8882^679593+1879547204578Enzo Doria09/2016
8892^678651+1875023204295Enzo Doria07/2016
8902^678561+678561204268Henri Lifchitz05/2006
8912^678101-114043204129Enzo Doria11/2014
8922^678028+1875631204107Enzo Doria06/2016
8932^676992-59783203795Enzo Doria10/2015
8942^676972+1866871203789Enzo Doria03/2016
8952^676761-9203726Robert Price01/2017
8962^676563-2792407203666Enzo Doria02/2016
8972^676306-114713203589Enzo Doria04/2015
898(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
8992^674627-25161203083Enzo Doria09/2013
9002^674603-69337203076Enzo Doria12/2015
9012^674459+74213203033Enzo Doria04/2016
9022^674116-458879202930Enzo Doria04/2015
9032^674076-114755202918Enzo Doria04/2015
9045^289937-4^289937202658Jean-Louis Charton03/2013
905(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
9062^672556-1835519202460Enzo Doria04/2015
9072^671446-351401202126Enzo Doria07/2015
9082^671373+77747202104Enzo Doria05/2016
9092^670726-114845201909Enzo Doria05/2015
9102^670539-25045201853Enzo Doria09/2013
91143284^43519-43519^43284201769Norbert Schneider08/2018
9122^670213+282317201755Enzo Doria09/2016
9132^669854-113501201647Enzo Doria08/2014
9142^669718+81619201606Enzo Doria08/2016
915(145*10^201504-1)/9201506Serge Batalov12/2014
9162^668938-1839821201371Enzo Doria06/2015
9172^668492+1879303201237Enzo Doria08/2016
9186^258413-5^258413201085Jean-Louis Charton03/2013
91910194^50161-50161^10194201063Norbert Schneider09/2020
9202^667894+1875589201057Enzo Doria06/2016
9212^667569-1836559200959Enzo Doria05/2015
922(172*10^200746-1)/9200748Serge Batalov12/2014
9232^666430+782569200616Enzo Doria10/2016
924(86^103471+1)/87200163Paul Bourdelais05/2018
925103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
926103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
927numbpart(32235776596)200002Serge Batalov04/2017
928(10^200001+149)/3200001Serge Batalov12/2014
92910^200000+571791200001Patrick De Geest08/2019
930(3^419180-621444)/3200000Stefano Morozzi06/2019
931(3^419180-1941384)/3200000Stefano Morozzi08/2019
93210^200000-45557200000Patrick De Geest08/2019
933(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
934(299*10^199801-17)/3199803Robert Price04/2020
9356*10^199788+77199789Robert Price06/2020
936(14*10^199447+73)/3199448Robert Price12/2018
9372^662103-29287199313Enzo Doria08/2015
938(2*10^199283+457)/9199283Robert Price01/2018
939(10^199248-19)/9199248Robert Price01/2018
940(194*10^199146-17)/3199148Robert Price09/2020
941(151*10^199003-1)/3199005Robert Price03/2020
9429*10^198946-73198947Robert Price01/2021
94345*10^198931-7198933Robert Price07/2020
9442^660482-2891198825Yves Minet05/2016
9452^659583+1879223198555Enzo Doria08/2016
946(53*10^198529+1)/9198530Serge Batalov07/2010
947(49*10^198403+311)/9198404Robert Price06/2019
9482^658828-29819198327Enzo Doria08/2015
9492^658776-2791229198312Enzo Doria01/2016
950(35*10^198294-377)/9198295Robert Price07/2018
951(4*10^198268+137)/3198269Robert Price03/2018
9522^658544-1854029198242Enzo Doria09/2015
953(157^90239-1)/156198154Alexander Zhirkov06/2016
954(4*10^197778+173)/3197779Robert Price02/2018
95578*10^197702-7197704Robert Price10/2020
956(29*10^197629-77)/3197630Robert Price02/2020
9572^656462+1874419197615Enzo Doria06/2016
958(89^101363+1)/90197595Paul Bourdelais11/2017
9592^655893-344563197444Enzo Doria07/2015
9602^655875+71333197439Enzo Doria04/2016
9612^655845-9197430Robert Price01/2017
962(299*10^197426+1)/3197428Robert Price04/2020
9632^655682-1849121197380Enzo Doria08/2015
9644*10^197268-89197269Robert Price11/2018
9652^655045-49603197189Enzo Doria10/2015
9662^655000-2784089197175Enzo Doria10/2015
967(18^157051-1)/17197141Paul Bourdelais03/2010
9682^654400-39719196995Enzo Doria09/2015
969(14*10^196965-221)/9196966Robert Price04/2018
9702^654216-459995196939Enzo Doria06/2015
971(17*10^196921+31)/3196922Robert Price01/2019
972(14*10^196885-89)/3196886Robert Price05/2020
9733*10^196881-59196882Robert Price09/2018
9742^653851+82295196829Enzo Doria09/2016
975(38*10^196792+691)/9196793Robert Price10/2018
9762^653636-29429196765Enzo Doria08/2015
9772^653601-69673196754Enzo Doria02/2016
978(44*10^196684+1)/9196685Serge Batalov07/2010
9792^652786-1852571196509Enzo Doria08/2015
9802^652752-1325196498Yves Minet07/2015
9812^652470-1859141196414Enzo Doria10/2015
9822^652307+1877483196364Enzo Doria08/2016
9832^652293-115273196360Enzo Doria06/2015
984(47*10^196281+403)/9196282Robert Price03/2019
9856*10^196070+73196071Robert Price04/2019
9862^651218-1868201196037Enzo Doria04/2016
9872^651047-49687195985Enzo Doria10/2015
9882^650285-2785333195756Enzo Doria10/2015
989(69^106397-1)/68195647Paul Bourdelais10/2017
9902^649811+1877573195613Enzo Doria08/2016
9912^649662-170531195568Hans Havermann10/2018
9922^649586+182839195545Enzo Doria11/2016
9932^649537-1867363195531Enzo Doria04/2016
9942^649536-1861499195530Enzo Doria12/2015
995(103*10^195478-1)/3195480Serge Batalov12/2014
9962^649102-59351195400Enzo Doria10/2015
997(2*10^195399+529)/9195399Robert Price01/2018
998(202*10^195383-13)/9195385Robert Price01/2020
9992^648988+1178971195365Enzo Doria06/2016
10002^648975-114319195361Enzo Doria02/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!