PRP Records

Probable Primes Top 10000

(252675 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 ?
7512^676992-59783203795Enzo Doria10/2015
7522^676972+1866871203789Enzo Doria03/2016
7532^676761-9203726Robert Price01/2017
7542^676563-2792407203666Enzo Doria02/2016
7552^676306-114713203589Enzo Doria04/2015
756(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
7572^674627-25161203083Enzo Doria09/2013
7582^674603-69337203076Enzo Doria12/2015
7592^674459+74213203033Enzo Doria04/2016
7602^674116-458879202930Enzo Doria04/2015
7612^674076-114755202918Enzo Doria04/2015
7625^289937-4^289937202658Jean-Louis Charton03/2013
7632^672556-1835519202460Enzo Doria04/2015
7642^671446-351401202126Enzo Doria07/2015
7652^671373+77747202104Enzo Doria05/2016
7662^670726-114845201909Enzo Doria05/2015
7672^670539-25045201853Enzo Doria09/2013
76843284^43519-43519^43284201769Norbert Schneider08/2018
7692^670213+282317201755Enzo Doria09/2016
7702^669854-113501201647Enzo Doria08/2014
7712^669718+81619201606Enzo Doria08/2016
772(145*10^201504-1)/9201506Serge Batalov12/2014
7732^668938-1839821201371Enzo Doria06/2015
7742^668492+1879303201237Enzo Doria08/2016
7756^258413-5^258413201085Jean-Louis Charton03/2013
7762^667894+1875589201057Enzo Doria06/2016
7772^667569-1836559200959Enzo Doria05/2015
778(172*10^200746-1)/9200748Serge Batalov12/2014
7792^666430+782569200616Enzo Doria10/2016
780(86^103471+1)/87200163Paul Bourdelais05/2018
781103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
782103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
783numbpart(32235776596)200002Serge Batalov04/2017
784(10^200001+149)/3200001Serge Batalov12/2014
785(14*10^199447+73)/3199448Robert Price12/2018
7862^662103-29287199313Enzo Doria08/2015
787(2*10^199283+457)/9199283Robert Price01/2018
788(10^199248-19)/9199248Robert Price01/2018
7892^660482-2891198825Yves Minet05/2016
7902^659583+1879223198555Enzo Doria08/2016
791(53*10^198529+1)/9198530Serge Batalov07/2010
7922^658828-29819198327Enzo Doria08/2015
7932^658776-2791229198312Enzo Doria01/2016
794(35*10^198294-377)/9198295Robert Price07/2018
795(4*10^198268+137)/3198269Robert Price03/2018
7962^658544-1854029198242Enzo Doria09/2015
797(157^90239-1)/156198154Alexander Zhirkov06/2016
798(4*10^197778+173)/3197779Robert Price02/2018
7992^656462+1874419197615Enzo Doria06/2016
800(89^101363+1)/90197595Paul Bourdelais11/2017
8012^655893-344563197444Enzo Doria07/2015
8022^655875+71333197439Enzo Doria04/2016
8032^655845-9197430Robert Price01/2017
8042^655682-1849121197380Enzo Doria08/2015
8054*10^197268-89197269Robert Price11/2018
8062^655045-49603197189Enzo Doria10/2015
8072^655000-2784089197175Enzo Doria10/2015
808(18^157051-1)/17197141Paul Bourdelais03/2010
8092^654400-39719196995Enzo Doria09/2015
810(14*10^196965-221)/9196966Robert Price04/2018
8112^654216-459995196939Enzo Doria06/2015
812(17*10^196921+31)/3196922Robert Price01/2019
8133*10^196881-59196882Robert Price09/2018
8142^653851+82295196829Enzo Doria09/2016
815(38*10^196792+691)/9196793Robert Price10/2018
8162^653636-29429196765Enzo Doria08/2015
8172^653601-69673196754Enzo Doria02/2016
818(44*10^196684+1)/9196685Serge Batalov07/2010
8192^652786-1852571196509Enzo Doria08/2015
8202^652752-1325196498Yves Minet07/2015
8212^652470-1859141196414Enzo Doria10/2015
8222^652307+1877483196364Enzo Doria08/2016
8232^652293-115273196360Enzo Doria06/2015
824(47*10^196281+403)/9196282Robert Price03/2019
8256*10^196070+73196071Robert Price04/2019
8262^651218-1868201196037Enzo Doria04/2016
8272^651047-49687195985Enzo Doria10/2015
8282^650285-2785333195756Enzo Doria10/2015
829(69^106397-1)/68195647Paul Bourdelais10/2017
8302^649811+1877573195613Enzo Doria08/2016
8312^649662-170531195568Hans Havermann10/2018
8322^649586+182839195545Enzo Doria11/2016
8332^649537-1867363195531Enzo Doria04/2016
8342^649536-1861499195530Enzo Doria12/2015
835(103*10^195478-1)/3195480Serge Batalov12/2014
8362^649102-59351195400Enzo Doria10/2015
837(2*10^195399+529)/9195399Robert Price01/2018
8382^648988+1178971195365Enzo Doria06/2016
8392^648975-114319195361Enzo Doria02/2015
840(11*10^195350-137)/9195351Robert Price01/2018
8412^648619-24835195254Enzo Doria09/2013
842(14*10^195234-83)/3195235Robert Price12/2018
8435*10^195221+81195222Robert Price03/2019
8442^648190-24737195125Enzo Doria09/2013
845(57^111119+1)/58195110Paul Bourdelais10/2017
84611^187185-90194934Enzo Doria09/2012
8472^647068+77281194787Enzo Doria05/2016
84815^165559-14^165559194713Jean-Louis Charton03/2011
849F(931517)194676Henri Lifchitz09/2008
8504*10^194668+49194669Robert Price01/2019
8512^646589+1179407194643Enzo Doria06/2016
8522^646289-114621194553Enzo Doria05/2015
8532^646236-39659194537Enzo Doria09/2015
854(16*10^194536+53)/3194537Robert Price03/2019
8552^646161-59833194514Enzo Doria11/2015
856(17*10^194502+31)/3194503Robert Price01/2019
8572*10^194413+3194414Robert Price07/2015
8582^645360-1848599194273Enzo Doria08/2015
859(112*10^194150-1)/3194152Serge Batalov12/2014
8602*10^193981-43193982Robert Price04/2018
8612^644382+75169193979Enzo Doria04/2016
8622^644304-1861409193955Enzo Doria11/2015
8635*10^193907-9193908Robert Price05/2015
8642^644043+1876703193877Enzo Doria07/2016
8652^643735+1879733193784Enzo Doria09/2016
866(5^277183+1)/6193742Paul Bourdelais07/2010
8672^643216-286565193628Enzo Doria07/2015
8682^642888-24965193529Enzo Doria09/2013
8692^642448-114825193397Enzo Doria05/2015
8702^642437-1856623193393Enzo Doria10/2015
8712^642039-59797193273Enzo Doria11/2015
87210^193230+513861193231Patrick De Geest07/2018
87310^193230-8001193230Robert Price03/2018
8742^641692-286349193169Enzo Doria07/2015
8752^641690-24737193168Enzo Doria09/2013
8762^641514+1876549193115Enzo Doria07/2016
8772^640888-2785619192927Enzo Doria10/2015
8782^640874-2783741192923Enzo Doria09/2015
879(46*10^192841+683)/9192842Robert Price03/2019
8802^640181+467192714Lelio R Paula08/2013
8812^639536-1850249192520Enzo Doria08/2015
8825*10^192422-43192423Robert Price01/2019
8832^639110-2792441192392Enzo Doria02/2016
8842^638955-29827192345Enzo Doria08/2015
8852^638713-2784223192272Enzo Doria10/2015
8862^638490-113507192205Enzo Doria08/2014
8872^638189-39943192115Enzo Doria09/2015
8882^638110+1877119192091Enzo Doria07/2016
8892^638066-2785211192078Enzo Doria10/2015
8902^637475-115309191900Enzo Doria07/2015
8912^636661+1876577191655Enzo Doria07/2016
892(34^125101-1)/33191589Paul Bourdelais11/2017
8932^636177-1855123191509Enzo Doria09/2015
8942^636158-113627191503Enzo Doria08/2014
895(37*25^136966+63)/4191472Curtis Bright05/2015
8962^636035+79823191466Enzo Doria06/2016
8972^636011-1860847191459Enzo Doria11/2015
8982^635926-1860611191433Enzo Doria11/2015
8993*10^191152-7191153Robert Price08/2015
9002^634883-1865677191119Enzo Doria02/2016
9012^634801+1871957191095Enzo Doria05/2016
902(35*10^191073+1)/9191074Serge Batalov07/2010
9032^634470-59861190995Enzo Doria11/2015
9042^634368-29519190964Enzo Doria08/2015
9052^634188-350609190910Enzo Doria06/2015
906(13*10^190732-61)/3190733Robert Price11/2018
907(7*10^190683+143)/3190684Robert Price03/2018
9082^633088-113879190579Enzo Doria10/2014
9092^633064+1874911190572Enzo Doria06/2016
910(43*10^190547+83)/9190548Robert Price11/2018
9112^632795-351205190491Enzo Doria06/2015
912(16*10^190420-19)/3190421Robert Price02/2019
913(43*10^190351+101)/9190352Robert Price11/2018
9142^632156+78391190298Enzo Doria06/2016
9152^632082-1851971190276Enzo Doria08/2015
9162^632020+1880311190257Enzo Doria09/2016
9172^631637-462373190142Enzo Doria08/2015
9182^631122-39251189987Enzo Doria08/2015
919(26*10^189928-89)/9189929Robert Price06/2018
9202^630839-97189902Yves Minet07/2017
9212^630359+1788953189757Enzo Doria05/2016
9222^630228+1871971189718Enzo Doria05/2016
9232^630108+781189682Lelio R Paula08/2013
9242^629870-1867811189610Enzo Doria04/2016
925(359^74189-1)/358189558Alexander Zhirkov11/2017
9262^629326+2792929189447Enzo Doria02/2016
927(10^189385-61)/3189385Serge Batalov12/2014
9282^629036+1874011189359Enzo Doria06/2016
9292^628930+80779189327Enzo Doria07/2016
9302^628582+1179439189223Enzo Doria06/2016
931(44*10^188999-503)/9189000Robert Price12/2018
9322^627037-2785843188757Enzo Doria10/2015
933(16*10^188457+161)/3188458Robert Price02/2019
934L(901657)188436Renaud Lifchitz11/2008
9352^625651+74213188340Enzo Doria04/2016
9362^625584-460919188320Enzo Doria06/2015
937(10^188164+359)/9188164Serge Batalov12/2014
9382^624481-113611187988Enzo Doria08/2014
9392^624077-112723187866Enzo Doria07/2014
9402^624008+1874941187846Enzo Doria06/2016
9412^623870+78679187804Enzo Doria05/2016
9422^623714-114035187757Enzo Doria11/2014
9432^623651-1834251187738Enzo Doria07/2015
944(7*10^187645+53)/3187646Robert Price05/2018
9452^623146+1879609187586Enzo Doria09/2016
946(5*10^187471+91)/3187472Robert Price04/2018
9472^622500+81931187392Enzo Doria08/2016
9482^622300-1861739187331Enzo Doria12/2015
949(38*10^187281+349)/9187282Robert Price10/2018
9502^622052+76771187257Enzo Doria05/2016
9512^622005-24091187243Enzo Doria08/2013
9522^621879-351787187205Enzo Doria07/2015
9532^621700+79411187151Enzo Doria06/2016
954(2*10^187062-71)/3187062Robert Price12/2017
9552^620929-113203186919Enzo Doria07/2014
95610^186842+168223186843Patrick De Geest07/2018
95710^186842-8001186842Robert Price03/2018
9582^620347-1777186744Lelio R Paula07/2013
95911^179143-4170186559Enzo Doria12/2012
960(5^266863+1)/6186529Paul Bourdelais07/2010
9612^619297-2792353186427Enzo Doria02/2016
962(49*10^186409+383)/9186410Robert Price04/2019
9632^618940-460139186320Enzo Doria06/2015
9642^618046+74179186051Enzo Doria04/2016
9653*10^186019+11186020Robert Price07/2018
966(16*10^185978-19)/3185979Robert Price02/2019
9672*10^185930-3185931Robert Price07/2015
968(82^97151+1)/83185928Paul Bourdelais10/2017
9694*10^185905+91185906Robert Price08/2018
970(37*10^185811+377)/9185812Robert Price11/2018
9712^617250+9385185811Lelio R Paula07/2013
97239^116749+2185756Robert Price04/2015
9732^616924-39719185713Enzo Doria09/2015
9742^616712+1867621185649Enzo Doria04/2016
975(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
9764*10^185355+9185356Robert Price05/2015
9772^615622+76639185321Enzo Doria05/2016
9782^615591+1879223185312Enzo Doria08/2016
9792^615503+1876643185285Enzo Doria07/2016
9805^265007-4^265007185232Jean-Louis Charton02/2013
981(4*10^185221-91)/3185222Robert Price03/2018
9822^614783-2790097185069Enzo Doria12/2015
9832^614745-29323185057Enzo Doria07/2015
984(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840185052Serge Batalov07/2013
985(49*10^184993-67)/9184994Robert Price03/2019
986(14*10^184950+211)/9184951Robert Price04/2018
9872^614315+81353184928Enzo Doria08/2016
9882^614294-1849961184921Enzo Doria08/2015
9892^614266+1877809184913Enzo Doria08/2016
9902^613715-1860727184747Enzo Doria11/2015
9912*10^184723+41184724Robert Price05/2018
9922^613487-349987184678Enzo Doria07/2015
993(95^93377+1)/96184672Paul Bourdelais11/2017
99414^161089-161089^14184629Serge Batalov05/2016
9952^613033-114621184542Enzo Doria05/2015
996(9^193247+1)/10184404Paul Bourdelais02/2010
9972^612341-1604809184334Enzo Doria05/2015
998(2^611999-1)/18464214225958267477777390354183184199Dario Alpern06/2017
999(14*10^184150+37)/3184151Robert Price12/2018
10002^611731-4837184150Yves Minet08/2018


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!