PRP Records

Probable Primes Top 10000

(253476 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 ?
7512^693462-1847561208753Enzo Doria07/2015
7522^690890-59981207979Enzo Doria11/2015
753(38^131591+1)/39207884Paul Bourdelais07/2018
7542^690163+1877063207760Enzo Doria07/2016
7552^689286-29381207496Enzo Doria08/2015
7562^689122-114521207447Enzo Doria04/2015
7572^688373+6077207221Enzo Doria02/2016
7582^688201+1875527207170Enzo Doria07/2016
759(42^127609+1)/43207140Paul Bourdelais07/2018
7602^687619+81563206994Enzo Doria08/2016
7612^686572-1845299206679Enzo Doria07/2015
762(21^156217-1)/20206552Paul Bourdelais04/2010
763(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
7642^685578+3206380Paul Bourdelais04/2012
7652^684836-49349206157Enzo Doria10/2015
766(73^110603-1)/72206088Paul Bourdelais06/2018
7672^684163-2790967205954Enzo Doria12/2015
768326^81943-325^81943205941Jean-Louis Charton07/2012
769(2^684127-1)/23765203727205933Jens K. Andersen04/2009
7704^341233-3^341233205443Jean-Louis Charton01/2006
7712^681545+467205166Lelio R Paula11/2013
7722^681306+81049205094Enzo Doria07/2016
7732^680697+1877057204911Enzo Doria07/2016
7742^680415+71783204826Enzo Doria04/2016
7752^679860-459995204659Enzo Doria06/2015
7762^679593+1879547204578Enzo Doria09/2016
7772^678651+1875023204295Enzo Doria07/2016
7782^678561+678561204268Henri Lifchitz05/2006
7792^678101-114043204129Enzo Doria11/2014
7802^678028+1875631204107Enzo Doria06/2016
7812^676992-59783203795Enzo Doria10/2015
7822^676972+1866871203789Enzo Doria03/2016
7832^676761-9203726Robert Price01/2017
7842^676563-2792407203666Enzo Doria02/2016
7852^676306-114713203589Enzo Doria04/2015
786(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
7872^674627-25161203083Enzo Doria09/2013
7882^674603-69337203076Enzo Doria12/2015
7892^674459+74213203033Enzo Doria04/2016
7902^674116-458879202930Enzo Doria04/2015
7912^674076-114755202918Enzo Doria04/2015
7925^289937-4^289937202658Jean-Louis Charton03/2013
793(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
7942^672556-1835519202460Enzo Doria04/2015
7952^671446-351401202126Enzo Doria07/2015
7962^671373+77747202104Enzo Doria05/2016
7972^670726-114845201909Enzo Doria05/2015
7982^670539-25045201853Enzo Doria09/2013
79943284^43519-43519^43284201769Norbert Schneider08/2018
8002^670213+282317201755Enzo Doria09/2016
8012^669854-113501201647Enzo Doria08/2014
8022^669718+81619201606Enzo Doria08/2016
803(145*10^201504-1)/9201506Serge Batalov12/2014
8042^668938-1839821201371Enzo Doria06/2015
8052^668492+1879303201237Enzo Doria08/2016
8066^258413-5^258413201085Jean-Louis Charton03/2013
8072^667894+1875589201057Enzo Doria06/2016
8082^667569-1836559200959Enzo Doria05/2015
809(172*10^200746-1)/9200748Serge Batalov12/2014
8102^666430+782569200616Enzo Doria10/2016
811(86^103471+1)/87200163Paul Bourdelais05/2018
813103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
812103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
814numbpart(32235776596)200002Serge Batalov04/2017
815(10^200001+149)/3200001Serge Batalov12/2014
81610^200000+571791200001Patrick De Geest08/2019
817(3^419180-621444)/3200000Stefano Morozzi06/2019
818(3^419180-1941384)/3200000Stefano Morozzi08/2019
81910^200000-45557200000Patrick De Geest08/2019
820(14*10^199447+73)/3199448Robert Price12/2018
8212^662103-29287199313Enzo Doria08/2015
822(2*10^199283+457)/9199283Robert Price01/2018
823(10^199248-19)/9199248Robert Price01/2018
8242^660482-2891198825Yves Minet05/2016
8252^659583+1879223198555Enzo Doria08/2016
826(53*10^198529+1)/9198530Serge Batalov07/2010
827(49*10^198403+311)/9198404Robert Price06/2019
8282^658828-29819198327Enzo Doria08/2015
8292^658776-2791229198312Enzo Doria01/2016
830(35*10^198294-377)/9198295Robert Price07/2018
831(4*10^198268+137)/3198269Robert Price03/2018
8322^658544-1854029198242Enzo Doria09/2015
833(157^90239-1)/156198154Alexander Zhirkov06/2016
834(4*10^197778+173)/3197779Robert Price02/2018
8352^656462+1874419197615Enzo Doria06/2016
836(89^101363+1)/90197595Paul Bourdelais11/2017
8372^655893-344563197444Enzo Doria07/2015
8382^655875+71333197439Enzo Doria04/2016
8392^655845-9197430Robert Price01/2017
8402^655682-1849121197380Enzo Doria08/2015
8414*10^197268-89197269Robert Price11/2018
8422^655045-49603197189Enzo Doria10/2015
8432^655000-2784089197175Enzo Doria10/2015
844(18^157051-1)/17197141Paul Bourdelais03/2010
8452^654400-39719196995Enzo Doria09/2015
846(14*10^196965-221)/9196966Robert Price04/2018
8472^654216-459995196939Enzo Doria06/2015
848(17*10^196921+31)/3196922Robert Price01/2019
8493*10^196881-59196882Robert Price09/2018
8502^653851+82295196829Enzo Doria09/2016
851(38*10^196792+691)/9196793Robert Price10/2018
8522^653636-29429196765Enzo Doria08/2015
8532^653601-69673196754Enzo Doria02/2016
854(44*10^196684+1)/9196685Serge Batalov07/2010
8552^652786-1852571196509Enzo Doria08/2015
8562^652752-1325196498Yves Minet07/2015
8572^652470-1859141196414Enzo Doria10/2015
8582^652307+1877483196364Enzo Doria08/2016
8592^652293-115273196360Enzo Doria06/2015
860(47*10^196281+403)/9196282Robert Price03/2019
8616*10^196070+73196071Robert Price04/2019
8622^651218-1868201196037Enzo Doria04/2016
8632^651047-49687195985Enzo Doria10/2015
8642^650285-2785333195756Enzo Doria10/2015
865(69^106397-1)/68195647Paul Bourdelais10/2017
8662^649811+1877573195613Enzo Doria08/2016
8672^649662-170531195568Hans Havermann10/2018
8682^649586+182839195545Enzo Doria11/2016
8692^649537-1867363195531Enzo Doria04/2016
8702^649536-1861499195530Enzo Doria12/2015
871(103*10^195478-1)/3195480Serge Batalov12/2014
8722^649102-59351195400Enzo Doria10/2015
873(2*10^195399+529)/9195399Robert Price01/2018
8742^648988+1178971195365Enzo Doria06/2016
8752^648975-114319195361Enzo Doria02/2015
876(11*10^195350-137)/9195351Robert Price01/2018
8772^648619-24835195254Enzo Doria09/2013
878(14*10^195234-83)/3195235Robert Price12/2018
8795*10^195221+81195222Robert Price03/2019
8802^648190-24737195125Enzo Doria09/2013
881(57^111119+1)/58195110Paul Bourdelais10/2017
88211^187185-90194934Enzo Doria09/2012
8832^647068+77281194787Enzo Doria05/2016
88415^165559-14^165559194713Jean-Louis Charton03/2011
885F(931517)194676Henri Lifchitz09/2008
8864*10^194668+49194669Robert Price01/2019
8872^646589+1179407194643Enzo Doria06/2016
8882^646289-114621194553Enzo Doria05/2015
8892^646236-39659194537Enzo Doria09/2015
890(16*10^194536+53)/3194537Robert Price03/2019
8912^646161-59833194514Enzo Doria11/2015
892(17*10^194502+31)/3194503Robert Price01/2019
8932*10^194413+3194414Robert Price07/2015
8942^645360-1848599194273Enzo Doria08/2015
895(112*10^194150-1)/3194152Serge Batalov12/2014
8962*10^193981-43193982Robert Price04/2018
8972^644382+75169193979Enzo Doria04/2016
8982^644304-1861409193955Enzo Doria11/2015
8995*10^193907-9193908Robert Price05/2015
9002^644043+1876703193877Enzo Doria07/2016
9012^643735+1879733193784Enzo Doria09/2016
902(5^277183+1)/6193742Paul Bourdelais07/2010
9032^643216-286565193628Enzo Doria07/2015
9042^642888-24965193529Enzo Doria09/2013
9052^642448-114825193397Enzo Doria05/2015
9062^642437-1856623193393Enzo Doria10/2015
9072^642039-59797193273Enzo Doria11/2015
90810^193230+513861193231Patrick De Geest07/2018
90910^193230-8001193230Robert Price03/2018
9102^641692-286349193169Enzo Doria07/2015
9112^641690-24737193168Enzo Doria09/2013
9122^641514+1876549193115Enzo Doria07/2016
9132^640888-2785619192927Enzo Doria10/2015
9142^640874-2783741192923Enzo Doria09/2015
915(46*10^192841+683)/9192842Robert Price03/2019
9162^640181+467192714Lelio R Paula08/2013
9172^639536-1850249192520Enzo Doria08/2015
9185*10^192422-43192423Robert Price01/2019
9192^639110-2792441192392Enzo Doria02/2016
9202^638955-29827192345Enzo Doria08/2015
9212^638713-2784223192272Enzo Doria10/2015
9222^638490-113507192205Enzo Doria08/2014
9232^638189-39943192115Enzo Doria09/2015
9242^638110+1877119192091Enzo Doria07/2016
9252^638066-2785211192078Enzo Doria10/2015
9262^637475-115309191900Enzo Doria07/2015
9272^636661+1876577191655Enzo Doria07/2016
928(34^125101-1)/33191589Paul Bourdelais11/2017
9292^636177-1855123191509Enzo Doria09/2015
9302^636158-113627191503Enzo Doria08/2014
931(37*25^136966+63)/4191472Curtis Bright05/2015
9322^636035+79823191466Enzo Doria06/2016
9332^636011-1860847191459Enzo Doria11/2015
9342^635926-1860611191433Enzo Doria11/2015
9353*10^191152-7191153Robert Price08/2015
9362^634883-1865677191119Enzo Doria02/2016
9372^634801+1871957191095Enzo Doria05/2016
938(35*10^191073+1)/9191074Serge Batalov07/2010
9392^634470-59861190995Enzo Doria11/2015
9402^634368-29519190964Enzo Doria08/2015
9412^634188-350609190910Enzo Doria06/2015
942(13*10^190732-61)/3190733Robert Price11/2018
943(7*10^190683+143)/3190684Robert Price03/2018
9442^633088-113879190579Enzo Doria10/2014
9452^633064+1874911190572Enzo Doria06/2016
946(43*10^190547+83)/9190548Robert Price11/2018
9472^632795-351205190491Enzo Doria06/2015
948(16*10^190420-19)/3190421Robert Price02/2019
949(43*10^190351+101)/9190352Robert Price11/2018
9502^632156+78391190298Enzo Doria06/2016
9512^632082-1851971190276Enzo Doria08/2015
9522^632020+1880311190257Enzo Doria09/2016
9532^631637-462373190142Enzo Doria08/2015
9542^631122-39251189987Enzo Doria08/2015
955(26*10^189928-89)/9189929Robert Price06/2018
9562^630839-97189902Yves Minet07/2017
9572^630359+1788953189757Enzo Doria05/2016
9582^630228+1871971189718Enzo Doria05/2016
9592^630108+781189682Lelio R Paula08/2013
9602^629870-1867811189610Enzo Doria04/2016
961(359^74189-1)/358189558Alexander Zhirkov11/2017
9622^629326+2792929189447Enzo Doria02/2016
963(10^189385-61)/3189385Serge Batalov12/2014
9642^629036+1874011189359Enzo Doria06/2016
9652^628930+80779189327Enzo Doria07/2016
9662^628582+1179439189223Enzo Doria06/2016
967(44*10^188999-503)/9189000Robert Price12/2018
968(16*10^188823+167)/3188824Robert Price06/2019
9692^627037-2785843188757Enzo Doria10/2015
970(16*10^188457+161)/3188458Robert Price02/2019
971L(901657)188436Renaud Lifchitz11/2008
9722^625651+74213188340Enzo Doria04/2016
9732^625584-460919188320Enzo Doria06/2015
974(10^188164+359)/9188164Serge Batalov12/2014
9752^624481-113611187988Enzo Doria08/2014
9762^624077-112723187866Enzo Doria07/2014
9772^624008+1874941187846Enzo Doria06/2016
9782^623870+78679187804Enzo Doria05/2016
9792^623714-114035187757Enzo Doria11/2014
9802^623651-1834251187738Enzo Doria07/2015
981(7*10^187645+53)/3187646Robert Price05/2018
9822^623146+1879609187586Enzo Doria09/2016
983(5*10^187471+91)/3187472Robert Price04/2018
9842^622500+81931187392Enzo Doria08/2016
9852^622300-1861739187331Enzo Doria12/2015
986(38*10^187281+349)/9187282Robert Price10/2018
9872^622052+76771187257Enzo Doria05/2016
9882^622005-24091187243Enzo Doria08/2013
9892^621879-351787187205Enzo Doria07/2015
9902^621700+79411187151Enzo Doria06/2016
991(2*10^187062-71)/3187062Robert Price12/2017
9922^620929-113203186919Enzo Doria07/2014
99310^186842+168223186843Patrick De Geest07/2018
99410^186842-8001186842Robert Price03/2018
9952^620347-1777186744Lelio R Paula07/2013
99611^179143-4170186559Enzo Doria12/2012
997(5^266863+1)/6186529Paul Bourdelais07/2010
9982^619297-2792353186427Enzo Doria02/2016
999(49*10^186409+383)/9186410Robert Price04/2019
10002^618940-460139186320Enzo Doria06/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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