PRP Records

Probable Primes Top 10000

(271067 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 ?
7512^730645-2787133219947Enzo Doria11/2015
7522^730547-25581219917Enzo Doria09/2013
7532^730460+82291219891Enzo Doria09/2016
754(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
755L(1051849)219824Renaud Lifchitz03/2009
75611^210961-240219694Enzo Doria01/2013
7572^729611-113437219635Enzo Doria08/2014
758F(1049897)219416Henri Lifchitz10/2008
7592^728604+1879321219332Enzo Doria10/2016
76033^144412+2219292Robert Price04/2015
7612^728277-183313219234Hans Havermann10/2018
7622^727998-1862711219150Enzo Doria12/2015
7632^727729-114073219069Enzo Doria12/2014
7642^727496-1851809218999Enzo Doria08/2015
7652^726591+2793143218726Enzo Doria02/2016
7662^725534-2791931218408Enzo Doria02/2016
7672^722184+1877821217400Enzo Doria08/2016
768(109*10^217360-1)/9217362Serge Batalov12/2014
769281*499979#/46410-2702372216849Robert Smith08/2016
770281*499979#/46410+2400766216849Robert Smith08/2016
771tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
7722^718756-114107216368Enzo Doria12/2014
7732^717305+80327215931Enzo Doria07/2016
7742^717069-59773215860Enzo Doria10/2015
77530^146021-29^146021215691Jean-Louis Charton09/2018
776277^88301-276^88301215674Jean-Louis Charton06/2012
777227^91413-40215372Enzo Doria04/2015
7782^714717+782897215152Enzo Doria11/2016
779tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
7802^713241+1879157214707Enzo Doria08/2016
78111^206081-10^206081214612Jean-Louis Charton10/2011
7822^712801-69553214575Enzo Doria01/2016
7832^712603-25357214515Enzo Doria09/2013
7842^711721-1846723214250Enzo Doria07/2015
7852^710730-396765213952Enzo Doria09/2013
7862^708468-114329213271Enzo Doria02/2015
787(163*10^212779-1)/9212781Serge Batalov12/2014
7882^706838-69041212780Enzo Doria11/2015
7892^704577-113871212099Enzo Doria10/2014
7902^704110-2792441211959Enzo Doria02/2016
7912^703943-1862947211908Enzo Doria12/2015
792(60^119083+1)/61211746Paul Bourdelais10/2018
793(10^211610-91)/9211610Serge Batalov12/2014
794227^89797+2211565Lelio R Paula08/2012
7952^702194-3211382Paul Bourdelais03/2012
7962^702064+1874911211343Enzo Doria07/2016
7972^701968-113873211314Enzo Doria10/2014
7982^701713-113779211237Enzo Doria09/2014
7992^701449-25201211158Enzo Doria09/2013
8002^701403-2786977211144Enzo Doria11/2015
8012^701189-25423211079Enzo Doria09/2013
8022^701162-459161211071Enzo Doria05/2015
803(24^152783-1)/23210872Paul Bourdelais04/2018
8042^700400+9385210842Lelio R Paula01/2014
8052^700131+1874693210761Enzo Doria06/2016
806(2^700095+225414)/2210750Stefano Morozzi04/2020
807(2^700090+278254)/2210748Stefano Morozzi04/2020
808(2^700075+303666)/2210744Stefano Morozzi04/2020
809(2^700073+75882)/2210743Stefano Morozzi04/2020
810(2^700074+328890)/2210743Stefano Morozzi04/2020
811(2^700052+79162)/2210737Stefano Morozzi04/2020
812(2^700052+304458)/2210737Stefano Morozzi04/2020
813(2^700048+376578)/2210736Stefano Morozzi04/2020
81411^202357-1140210734Enzo Doria12/2012
815(2^700021+25874)/2210728Stefano Morozzi04/2020
816(2^700018+377518)/2210727Stefano Morozzi04/2020
8172^698929-2788423210399Enzo Doria11/2015
818(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
8192^698316+1878601210215Enzo Doria08/2016
8202^697036+1878751209829Enzo Doria08/2016
821(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
8222^696254-115151209594Enzo Doria06/2015
823(35^135623+1)/36209410Paul Bourdelais07/2018
8242^694633+1887257209106Enzo Doria05/2017
8252^693959+180923208903Enzo Doria07/2016
8262^693462-1847561208753Enzo Doria07/2015
8272^690890-59981207979Enzo Doria11/2015
828(38^131591+1)/39207884Paul Bourdelais07/2018
8292^690163+1877063207760Enzo Doria07/2016
8302^689286-29381207496Enzo Doria08/2015
8312^689122-114521207447Enzo Doria04/2015
8322^688373+6077207221Enzo Doria02/2016
8332^688201+1875527207170Enzo Doria07/2016
834(42^127609+1)/43207140Paul Bourdelais07/2018
8352^687619+81563206994Enzo Doria08/2016
8362^686572-1845299206679Enzo Doria07/2015
837(21^156217-1)/20206552Paul Bourdelais04/2010
838(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
8392^685578+3206380Paul Bourdelais04/2012
8402^684836-49349206157Enzo Doria10/2015
841(73^110603-1)/72206088Paul Bourdelais06/2018
8422^684163-2790967205954Enzo Doria12/2015
843326^81943-325^81943205941Jean-Louis Charton07/2012
844(2^684127-1)/23765203727205933Jens K. Andersen04/2009
8454^341233-3^341233205443Jean-Louis Charton01/2006
8462^681545+467205166Lelio R Paula11/2013
8472^681306+81049205094Enzo Doria07/2016
8482^680697+1877057204911Enzo Doria07/2016
8492^680415+71783204826Enzo Doria04/2016
8502^679860-459995204659Enzo Doria06/2015
8512^679593+1879547204578Enzo Doria09/2016
8522^678651+1875023204295Enzo Doria07/2016
8532^678561+678561204268Henri Lifchitz05/2006
8542^678101-114043204129Enzo Doria11/2014
8552^678028+1875631204107Enzo Doria06/2016
8562^676992-59783203795Enzo Doria10/2015
8572^676972+1866871203789Enzo Doria03/2016
8582^676761-9203726Robert Price01/2017
8592^676563-2792407203666Enzo Doria02/2016
8602^676306-114713203589Enzo Doria04/2015
861(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
8622^674627-25161203083Enzo Doria09/2013
8632^674603-69337203076Enzo Doria12/2015
8642^674459+74213203033Enzo Doria04/2016
8652^674116-458879202930Enzo Doria04/2015
8662^674076-114755202918Enzo Doria04/2015
8675^289937-4^289937202658Jean-Louis Charton03/2013
868(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
8692^672556-1835519202460Enzo Doria04/2015
8702^671446-351401202126Enzo Doria07/2015
8712^671373+77747202104Enzo Doria05/2016
8722^670726-114845201909Enzo Doria05/2015
8732^670539-25045201853Enzo Doria09/2013
87443284^43519-43519^43284201769Norbert Schneider08/2018
8752^670213+282317201755Enzo Doria09/2016
8762^669854-113501201647Enzo Doria08/2014
8772^669718+81619201606Enzo Doria08/2016
878(145*10^201504-1)/9201506Serge Batalov12/2014
8792^668938-1839821201371Enzo Doria06/2015
8802^668492+1879303201237Enzo Doria08/2016
8816^258413-5^258413201085Jean-Louis Charton03/2013
88210194^50161-50161^10194201063Norbert Schneider09/2020
8832^667894+1875589201057Enzo Doria06/2016
8842^667569-1836559200959Enzo Doria05/2015
885(172*10^200746-1)/9200748Serge Batalov12/2014
8862^666430+782569200616Enzo Doria10/2016
887(86^103471+1)/87200163Paul Bourdelais05/2018
889103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
888103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
890numbpart(32235776596)200002Serge Batalov04/2017
891(10^200001+149)/3200001Serge Batalov12/2014
89210^200000+571791200001Patrick De Geest08/2019
893(3^419180-621444)/3200000Stefano Morozzi06/2019
894(3^419180-1941384)/3200000Stefano Morozzi08/2019
89510^200000-45557200000Patrick De Geest08/2019
896(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
897(299*10^199801-17)/3199803Robert Price04/2020
8986*10^199788+77199789Robert Price06/2020
899(14*10^199447+73)/3199448Robert Price12/2018
9002^662103-29287199313Enzo Doria08/2015
901(2*10^199283+457)/9199283Robert Price01/2018
902(10^199248-19)/9199248Robert Price01/2018
903(194*10^199146-17)/3199148Robert Price09/2020
904(151*10^199003-1)/3199005Robert Price03/2020
90545*10^198931-7198933Robert Price07/2020
9062^660482-2891198825Yves Minet05/2016
9072^659583+1879223198555Enzo Doria08/2016
908(53*10^198529+1)/9198530Serge Batalov07/2010
909(49*10^198403+311)/9198404Robert Price06/2019
9102^658828-29819198327Enzo Doria08/2015
9112^658776-2791229198312Enzo Doria01/2016
912(35*10^198294-377)/9198295Robert Price07/2018
913(4*10^198268+137)/3198269Robert Price03/2018
9142^658544-1854029198242Enzo Doria09/2015
915(157^90239-1)/156198154Alexander Zhirkov06/2016
916(4*10^197778+173)/3197779Robert Price02/2018
917(29*10^197629-77)/3197630Robert Price02/2020
9182^656462+1874419197615Enzo Doria06/2016
919(89^101363+1)/90197595Paul Bourdelais11/2017
9202^655893-344563197444Enzo Doria07/2015
9212^655875+71333197439Enzo Doria04/2016
9222^655845-9197430Robert Price01/2017
923(299*10^197426+1)/3197428Robert Price04/2020
9242^655682-1849121197380Enzo Doria08/2015
9254*10^197268-89197269Robert Price11/2018
9262^655045-49603197189Enzo Doria10/2015
9272^655000-2784089197175Enzo Doria10/2015
928(18^157051-1)/17197141Paul Bourdelais03/2010
9292^654400-39719196995Enzo Doria09/2015
930(14*10^196965-221)/9196966Robert Price04/2018
9312^654216-459995196939Enzo Doria06/2015
932(17*10^196921+31)/3196922Robert Price01/2019
933(14*10^196885-89)/3196886Robert Price05/2020
9343*10^196881-59196882Robert Price09/2018
9352^653851+82295196829Enzo Doria09/2016
936(38*10^196792+691)/9196793Robert Price10/2018
9372^653636-29429196765Enzo Doria08/2015
9382^653601-69673196754Enzo Doria02/2016
939(44*10^196684+1)/9196685Serge Batalov07/2010
9402^652786-1852571196509Enzo Doria08/2015
9412^652752-1325196498Yves Minet07/2015
9422^652470-1859141196414Enzo Doria10/2015
9432^652307+1877483196364Enzo Doria08/2016
9442^652293-115273196360Enzo Doria06/2015
945(47*10^196281+403)/9196282Robert Price03/2019
9466*10^196070+73196071Robert Price04/2019
9472^651218-1868201196037Enzo Doria04/2016
9482^651047-49687195985Enzo Doria10/2015
9492^650285-2785333195756Enzo Doria10/2015
950(69^106397-1)/68195647Paul Bourdelais10/2017
9512^649811+1877573195613Enzo Doria08/2016
9522^649662-170531195568Hans Havermann10/2018
9532^649586+182839195545Enzo Doria11/2016
9542^649537-1867363195531Enzo Doria04/2016
9552^649536-1861499195530Enzo Doria12/2015
956(103*10^195478-1)/3195480Serge Batalov12/2014
9572^649102-59351195400Enzo Doria10/2015
958(2*10^195399+529)/9195399Robert Price01/2018
959(202*10^195383-13)/9195385Robert Price01/2020
9602^648988+1178971195365Enzo Doria06/2016
9612^648975-114319195361Enzo Doria02/2015
962(11*10^195350-137)/9195351Robert Price01/2018
9632^648619-24835195254Enzo Doria09/2013
964(14*10^195234-83)/3195235Robert Price12/2018
9655*10^195221+81195222Robert Price03/2019
9662^648190-24737195125Enzo Doria09/2013
967(57^111119+1)/58195110Paul Bourdelais10/2017
96810^195060-40000000001195060Robert Price09/2020
96956*10^195032-3195034Robert Price03/2020
97011^187185-90194934Enzo Doria09/2012
9712^647068+77281194787Enzo Doria05/2016
97215^165559-14^165559194713Jean-Louis Charton03/2011
973F(931517)194676Henri Lifchitz09/2008
9744*10^194668+49194669Robert Price01/2019
9752^646589+1179407194643Enzo Doria06/2016
9762^646289-114621194553Enzo Doria05/2015
9772^646236-39659194537Enzo Doria09/2015
978(16*10^194536+53)/3194537Robert Price03/2019
9792^646161-59833194514Enzo Doria11/2015
980(17*10^194502+31)/3194503Robert Price01/2019
9812*10^194413+3194414Robert Price07/2015
9822^645360-1848599194273Enzo Doria08/2015
983(112*10^194150-1)/3194152Serge Batalov12/2014
9842*10^193981-43193982Robert Price04/2018
9852^644382+75169193979Enzo Doria04/2016
9862^644304-1861409193955Enzo Doria11/2015
9875*10^193907-9193908Robert Price05/2015
9882^644043+1876703193877Enzo Doria07/2016
9892^643735+1879733193784Enzo Doria09/2016
990(5^277183+1)/6193742Paul Bourdelais07/2010
9919*10^193712+71193713Robert Price08/2020
9922^643216-286565193628Enzo Doria07/2015
9932^642888-24965193529Enzo Doria09/2013
9942^642448-114825193397Enzo Doria05/2015
9952^642437-1856623193393Enzo Doria10/2015
9962^642039-59797193273Enzo Doria11/2015
99710^193230+513861193231Patrick De Geest07/2018
99810^193230-8001193230Robert Price03/2018
9992^641692-286349193169Enzo Doria07/2015
10002^641690-24737193168Enzo Doria09/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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