PRP Records

Probable Primes Top 10000

(211563 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 (> 30000) Who ? When ?
7512^655875+71333197439Enzo Doria04/2016
7522^655845-9197430Robert Price01/2017
7532^655682-1849121197380Enzo Doria08/2015
7542^655045-49603197189Enzo Doria10/2015
7552^655000-2784089197175Enzo Doria10/2015
756(18^157051-1)/17197141Paul Bourdelais03/2010
7572^654400-39719196995Enzo Doria09/2015
758(14*10^196965-221)/9196966Robert Price04/2018
7592^654216-459995196939Enzo Doria06/2015
7602^653851+82295196829Enzo Doria09/2016
7612^653636-29429196765Enzo Doria08/2015
7622^653601-69673196754Enzo Doria02/2016
763(44*10^196684+1)/9196685Serge Batalov07/2010
7642^652786-1852571196509Enzo Doria08/2015
7652^652752-1325196498Yves Minet07/2015
7662^652470-1859141196414Enzo Doria10/2015
7672^652307+1877483196364Enzo Doria08/2016
7682^652293-115273196360Enzo Doria06/2015
7692^651218-1868201196037Enzo Doria04/2016
7702^651047-49687195985Enzo Doria10/2015
7712^650285-2785333195756Enzo Doria10/2015
772(69^106397-1)/68195647Paul Bourdelais10/2017
7732^649811+1877573195613Enzo Doria08/2016
7742^649586+182839195545Enzo Doria11/2016
7752^649537-1867363195531Enzo Doria04/2016
7762^649536-1861499195530Enzo Doria12/2015
777(103*10^195478-1)/3195480Serge Batalov12/2014
7782^649102-59351195400Enzo Doria10/2015
779(2*10^195399+529)/9195399Robert Price01/2018
7802^648988+1178971195365Enzo Doria06/2016
7812^648975-114319195361Enzo Doria02/2015
782(11*10^195350-137)/9195351Robert Price01/2018
7832^648619-24835195254Enzo Doria09/2013
7842^648190-24737195125Enzo Doria09/2013
785(57^111119+1)/58195110Paul Bourdelais10/2017
78611^187185-90194934Enzo Doria09/2012
7872^647068+77281194787Enzo Doria05/2016
78815^165559-14^165559194713Jean-Louis Charton03/2011
789F(931517)194676Henri Lifchitz09/2008
7902^646589+1179407194643Enzo Doria06/2016
7912^646289-114621194553Enzo Doria05/2015
7922^646236-39659194537Enzo Doria09/2015
7932^646161-59833194514Enzo Doria11/2015
7942*10^194413+3194414Robert Price07/2015
7952^645360-1848599194273Enzo Doria08/2015
796(112*10^194150-1)/3194152Serge Batalov12/2014
7972*10^193981-43193982Robert Price04/2018
7982^644382+75169193979Enzo Doria04/2016
7992^644304-1861409193955Enzo Doria11/2015
8005*10^193907-9193908Robert Price05/2015
8012^644043+1876703193877Enzo Doria07/2016
8022^643735+1879733193784Enzo Doria09/2016
803(5^277183+1)/6193742Paul Bourdelais07/2010
8042^643216-286565193628Enzo Doria07/2015
8052^642888-24965193529Enzo Doria09/2013
8062^642448-114825193397Enzo Doria05/2015
8072^642437-1856623193393Enzo Doria10/2015
8082^642039-59797193273Enzo Doria11/2015
80910^193230-8001193230Robert Price03/2018
8102^641692-286349193169Enzo Doria07/2015
8112^641690-24737193168Enzo Doria09/2013
8122^641514+1876549193115Enzo Doria07/2016
8132^640888-2785619192927Enzo Doria10/2015
8142^640874-2783741192923Enzo Doria09/2015
8152^640181+467192714Lelio R Paula08/2013
8162^639536-1850249192520Enzo Doria08/2015
8172^639110-2792441192392Enzo Doria02/2016
8182^638955-29827192345Enzo Doria08/2015
8192^638713-2784223192272Enzo Doria10/2015
8202^638490-113507192205Enzo Doria08/2014
8212^638189-39943192115Enzo Doria09/2015
8222^638110+1877119192091Enzo Doria07/2016
8232^638066-2785211192078Enzo Doria10/2015
8242^637475-115309191900Enzo Doria07/2015
8252^636661+1876577191655Enzo Doria07/2016
826(34^125101-1)/33191589Paul Bourdelais11/2017
8272^636177-1855123191509Enzo Doria09/2015
8282^636158-113627191503Enzo Doria08/2014
829(37*25^136966+63)/4191472Curtis Bright05/2015
8302^636035+79823191466Enzo Doria06/2016
8312^636011-1860847191459Enzo Doria11/2015
8322^635926-1860611191433Enzo Doria11/2015
8333*10^191152-7191153Robert Price08/2015
8342^634883-1865677191119Enzo Doria02/2016
8352^634801+1871957191095Enzo Doria05/2016
836(35*10^191073+1)/9191074Serge Batalov07/2010
8372^634470-59861190995Enzo Doria11/2015
8382^634368-29519190964Enzo Doria08/2015
8392^634188-350609190910Enzo Doria06/2015
840(7*10^190683+143)/3190684Robert Price03/2018
8412^633088-113879190579Enzo Doria10/2014
8422^633064+1874911190572Enzo Doria06/2016
8432^632795-351205190491Enzo Doria06/2015
8442^632156+78391190298Enzo Doria06/2016
8452^632082-1851971190276Enzo Doria08/2015
8462^632020+1880311190257Enzo Doria09/2016
8472^631637-462373190142Enzo Doria08/2015
8482^631122-39251189987Enzo Doria08/2015
849(26*10^189928-89)/9189929Robert Price06/2018
8502^630839-97189902Yves Minet07/2017
8512^630359+1788953189757Enzo Doria05/2016
8522^630228+1871971189718Enzo Doria05/2016
8532^630108+781189682Lelio R Paula08/2013
8542^629870-1867811189610Enzo Doria04/2016
855(359^74189-1)/358189558Alexander Zhirkov11/2017
8562^629326+2792929189447Enzo Doria02/2016
857(10^189385-61)/3189385Serge Batalov12/2014
8582^629036+1874011189359Enzo Doria06/2016
8592^628930+80779189327Enzo Doria07/2016
8602^628582+1179439189223Enzo Doria06/2016
8612^627037-2785843188757Enzo Doria10/2015
862L(901657)188436Renaud Lifchitz11/2008
8632^625651+74213188340Enzo Doria04/2016
8642^625584-460919188320Enzo Doria06/2015
865(10^188164+359)/9188164Serge Batalov12/2014
8662^624481-113611187988Enzo Doria08/2014
8672^624077-112723187866Enzo Doria07/2014
8682^624008+1874941187846Enzo Doria06/2016
8692^623870+78679187804Enzo Doria05/2016
8702^623714-114035187757Enzo Doria11/2014
8712^623651-1834251187738Enzo Doria07/2015
872(7*10^187645+53)/3187646Robert Price05/2018
8732^623146+1879609187586Enzo Doria09/2016
874(5*10^187471+91)/3187472Robert Price04/2018
8752^622500+81931187392Enzo Doria08/2016
8762^622300-1861739187331Enzo Doria12/2015
8772^622052+76771187257Enzo Doria05/2016
8782^622005-24091187243Enzo Doria08/2013
8792^621879-351787187205Enzo Doria07/2015
8802^621700+79411187151Enzo Doria06/2016
881(2*10^187062-71)/3187062Robert Price12/2017
8822^620929-113203186919Enzo Doria07/2014
88310^186842-8001186842Robert Price03/2018
8842^620347-1777186744Lelio R Paula07/2013
88511^179143-4170186559Enzo Doria12/2012
886(5^266863+1)/6186529Paul Bourdelais07/2010
8872^619297-2792353186427Enzo Doria02/2016
8882^618940-460139186320Enzo Doria06/2015
8892^618046+74179186051Enzo Doria04/2016
8902*10^185930-3185931Robert Price07/2015
891(82^97151+1)/83185928Paul Bourdelais10/2017
8922^617250+9385185811Lelio R Paula07/2013
89339^116749+2185756Robert Price04/2015
8942^616924-39719185713Enzo Doria09/2015
8952^616712+1867621185649Enzo Doria04/2016
896(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
8974*10^185355+9185356Robert Price05/2015
8982^615622+76639185321Enzo Doria05/2016
8992^615591+1879223185312Enzo Doria08/2016
9002^615503+1876643185285Enzo Doria07/2016
9015^265007-4^265007185232Jean-Louis Charton02/2013
902(4*10^185221-91)/3185222Robert Price03/2018
9032^614783-2790097185069Enzo Doria12/2015
9042^614745-29323185057Enzo Doria07/2015
905(((((((((((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
906(14*10^184950+211)/9184951Robert Price04/2018
9072^614315+81353184928Enzo Doria08/2016
9082^614294-1849961184921Enzo Doria08/2015
9092^614266+1877809184913Enzo Doria08/2016
9102^613715-1860727184747Enzo Doria11/2015
9112*10^184723+41184724Robert Price05/2018
9122^613487-349987184678Enzo Doria07/2015
913(95^93377+1)/96184672Paul Bourdelais11/2017
91414^161089-161089^14184629Serge Batalov05/2016
9152^613033-114621184542Enzo Doria05/2015
916(9^193247+1)/10184404Paul Bourdelais02/2010
9172^612341-1604809184334Enzo Doria05/2015
918(2^611999-1)/18464214225958267477777390354183184199Dario Alpern06/2017
9193*10^184124-7184125Robert Price08/2015
9202^611628-24537184119Enzo Doria08/2013
9212^611460+71881184068Enzo Doria04/2016
9222^610982-1867301183924Enzo Doria03/2016
9232^610597+1178897183809Enzo Doria05/2016
924(28*10^183760-1)/9183761Serge Batalov10/2014
9252^610401+1277183750Lelio R Paula07/2013
9262^610356-1849019183736Enzo Doria08/2015
927(63^102103+1)/64183717Paul Bourdelais10/2017
928(4*10^183659+149)/9183659Robert Price04/2018
9292^609846-1834251183582Enzo Doria07/2015
93011^176176-240183469Enzo Doria11/2012
931(41^113749+1)/42183451Paul Bourdelais11/2017
932(101^91463+1)/102183320Paul Bourdelais11/2017
9332^608965-113989183317Enzo Doria10/2014
934A005165(43592)183312Serge Batalov07/2017
9352^608814-461261183272Enzo Doria06/2015
936(163*10^183227-1)/9183229Serge Batalov12/2014
9372^608541-608541^2183190Henri Lifchitz02/2018
9382^608293+143807183115Enzo Doria10/2016
9392^608164-462419183076Enzo Doria08/2015
9402^607950-1862303183012Enzo Doria12/2015
9412^607101+1871987182756Enzo Doria05/2016
9422^606869-69175182686Enzo Doria11/2015
9432^606560-357182593Enzo Doria05/2014
9442^605687+1866983182330Enzo Doria03/2016
9452^605655-114445182321Enzo Doria02/2015
946(20^140053+1)/21182212Paul Bourdelais04/2010
947(14*10^182177-221)/9182178Robert Price04/2018
9482^605174-112751182176Enzo Doria06/2014
9492^604761+1874507182052Enzo Doria06/2016
9502^604705+1871957182035Enzo Doria05/2016
951(14*10^182000+229)/9182001Robert Price03/2018
952(10^181996+41)/3181996Robert Price12/2017
953(5*10^181950-101)/3181951Robert Price04/2018
9542^603915+75233181797Enzo Doria04/2016
95511^174145-360181354Enzo Doria10/2012
9562^602351-396765181326Enzo Doria08/2013
9572^601957-113833181208Enzo Doria09/2014
95866^99581-65^99581181193Robert Price09/2013
95910^181182+383973181183Patrick De Geest04/2016
96010^181182-21181182Serge Batalov12/2014
961(5*10^181127-29)/3181128Robert Price03/2018
9622^601521-29143181076Enzo Doria07/2015
9632^601442-2797811181053Enzo Doria04/2016
9645*10^180992-9180993Robert Price05/2015
96510^180979+79477180980Patrick De Geest04/2016
96610^180979+107739180980Patrick De Geest04/2016
96710^180979-11180979Serge Batalov12/2014
9682^601023-113851180926Enzo Doria10/2014
9693*10^180852+29180853Robert Price05/2018
9702^600300-1852559180709Enzo Doria08/2015
971(10^180689+71)/9180689Serge Batalov07/2015
9722^600209+76487180681Enzo Doria05/2016
9732^599702-369885180529Enzo Doria11/2013
974Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
975(2951*29^123418-3)/4180490Curtis Bright05/2015
9762^598942+80779180300Enzo Doria07/2016
9772^598591-1844797180194Enzo Doria06/2015
978(100^90089+1)/101180176Paul Bourdelais08/2017
979(4*10^179963-79)/3179964Robert Price02/2018
980Gamma-Prime(179849)179849Eric W. Weisstein06/2011
9812^597424-1859729179843Enzo Doria11/2015
982Phi(180683,10)179760Maksym Voznyy09/2015
983(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
984(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
9852^596690-461261179622Enzo Doria07/2015
9862^596684-113939179620Enzo Doria10/2014
9872*10^179602+63179603Robert Price05/2018
9883^375887-112696179344Enzo Doria07/2014
9892^595144-1850429179157Enzo Doria08/2015
9902^594531+82253178972Enzo Doria09/2016
9912^594260-2787899178891Enzo Doria11/2015
9922^593631+101381178701Jorge Menendez04/2018
99310^178695+136719178696Patrick De Geest05/2016
99410^178695-71178695Serge Batalov12/2014
995(2^148330+1)^4-2178608Cletus Emmanuel12/2003
9962^593222-14145178578Jorge Menendez10/2017
9972^593178+1867219178565Enzo Doria03/2016
998(18^142031-1)/17178287Paul Bourdelais03/2010
999(5*10^178206+91)/3178207Robert Price04/2018
10002^591872-291929178172Enzo Doria07/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!