PRP Records

Probable Primes Top 10000

(173006 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 ?
7512^634883-1865677191119Enzo Doria02/2016
7522^634801+1871957191095Enzo Doria05/2016
753(35*10^191073+1)/9191074Serge Batalov07/2010
7542^634470-59861190995Enzo Doria11/2015
7552^634368-29519190964Enzo Doria08/2015
7562^634188-350609190910Enzo Doria06/2015
7572^633088-113879190579Enzo Doria10/2014
7582^633064+1874911190572Enzo Doria06/2016
7592^632795-351205190491Enzo Doria06/2015
7602^632156+78391190298Enzo Doria06/2016
7612^632082-1851971190276Enzo Doria08/2015
7622^632020+1880311190257Enzo Doria09/2016
7632^631637-462373190142Enzo Doria08/2015
7642^631122-39251189987Enzo Doria08/2015
7652^630359+1788953189757Enzo Doria05/2016
7662^630228+1871971189718Enzo Doria05/2016
7672^630108+781189682Lelio R Paula08/2013
7682^629870-1867811189610Enzo Doria04/2016
7692^629326+2792929189447Enzo Doria02/2016
770(10^189385-61)/3189385Serge Batalov12/2014
7712^629036+1874011189359Enzo Doria06/2016
7722^628930+80779189327Enzo Doria07/2016
7732^628582+1179439189223Enzo Doria06/2016
7742^627037-2785843188757Enzo Doria10/2015
775L(901657)188436Renaud Lifchitz11/2008
7762^625651+74213188340Enzo Doria04/2016
7772^625584-460919188320Enzo Doria06/2015
778(10^188164+359)/9188164Serge Batalov12/2014
7792^624481-113611187988Enzo Doria08/2014
7802^624077-112723187866Enzo Doria07/2014
7812^624008+1874941187846Enzo Doria06/2016
7822^623870+78679187804Enzo Doria05/2016
7832^623714-114035187757Enzo Doria11/2014
7842^623651-1834251187738Enzo Doria07/2015
7852^623146+1879609187586Enzo Doria09/2016
7862^622500+81931187392Enzo Doria08/2016
7872^622300-1861739187331Enzo Doria12/2015
7882^622052+76771187257Enzo Doria05/2016
7892^622005-24091187243Enzo Doria08/2013
7902^621879-351787187205Enzo Doria07/2015
7912^621700+79411187151Enzo Doria06/2016
7922^620929-113203186919Enzo Doria07/2014
7932^620347-1777186744Lelio R Paula07/2013
79411^179143-4170186559Enzo Doria12/2012
795(5^266863+1)/6186529Paul Bourdelais07/2010
7962^619297-2792353186427Enzo Doria02/2016
7972^618940-460139186320Enzo Doria06/2015
7982^618046+74179186051Enzo Doria04/2016
7992*10^185930-3185931Robert Price07/2015
8002^617250+9385185811Lelio R Paula07/2013
80139^116749+2185756Robert Price04/2015
8022^616924-39719185713Enzo Doria09/2015
8032^616712+1867621185649Enzo Doria04/2016
804(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
8054*10^185355+9185356Robert Price05/2015
8062^615622+76639185321Enzo Doria05/2016
8072^615591+1879223185312Enzo Doria08/2016
8082^615503+1876643185285Enzo Doria07/2016
8095^265007-4^265007185232Jean-Louis Charton02/2013
8102^614783-2790097185069Enzo Doria12/2015
8112^614745-29323185057Enzo Doria07/2015
812(((((((((((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
8132^614315+81353184928Enzo Doria08/2016
8142^614294-1849961184921Enzo Doria08/2015
8152^614266+1877809184913Enzo Doria08/2016
8162^613715-1860727184747Enzo Doria11/2015
8172^613487-349987184678Enzo Doria07/2015
81814^161089-161089^14184629Serge Batalov05/2016
8192^613033-114621184542Enzo Doria05/2015
820(9^193247+1)/10184404Paul Bourdelais02/2010
8212^612341-1604809184334Enzo Doria05/2015
8223*10^184124-7184125Robert Price08/2015
8232^611628-24537184119Enzo Doria08/2013
8242^611460+71881184068Enzo Doria04/2016
8252^610982-1867301183924Enzo Doria03/2016
8262^610597+1178897183809Enzo Doria05/2016
827(28*10^183760-1)/9183761Serge Batalov10/2014
8282^610401+1277183750Lelio R Paula07/2013
8292^610356-1849019183736Enzo Doria08/2015
8302^609846-1834251183582Enzo Doria07/2015
83111^176176-240183469Enzo Doria11/2012
8322^608965-113989183317Enzo Doria10/2014
8332^608814-461261183272Enzo Doria06/2015
834(163*10^183227-1)/9183229Serge Batalov12/2014
8352^608293+143807183115Enzo Doria10/2016
8362^608164-462419183076Enzo Doria08/2015
8372^607950-1862303183012Enzo Doria12/2015
8382^607101+1871987182756Enzo Doria05/2016
8392^606869-69175182686Enzo Doria11/2015
8402^606560-357182593Enzo Doria05/2014
8412^605687+1866983182330Enzo Doria03/2016
8422^605655-114445182321Enzo Doria02/2015
843(20^140053+1)/21182212Paul Bourdelais04/2010
8442^605174-112751182176Enzo Doria06/2014
8452^604761+1874507182052Enzo Doria06/2016
8462^604705+1871957182035Enzo Doria05/2016
8472^603915+75233181797Enzo Doria04/2016
84811^174145-360181354Enzo Doria10/2012
8492^602351-396765181326Enzo Doria08/2013
8502^601957-113833181208Enzo Doria09/2014
85166^99581-65^99581181193Robert Price09/2013
85210^181182+383973181183Patrick De Geest04/2016
85310^181182-21181182Serge Batalov12/2014
8542^601521-29143181076Enzo Doria07/2015
8552^601442-2797811181053Enzo Doria04/2016
8565*10^180992-9180993Robert Price05/2015
85710^180979+79477180980Patrick De Geest04/2016
85810^180979+107739180980Patrick De Geest04/2016
85910^180979-11180979Serge Batalov12/2014
8602^601023-113851180926Enzo Doria10/2014
8612^600300-1852559180709Enzo Doria08/2015
862(10^180689+71)/9180689Serge Batalov07/2015
8632^600209+76487180681Enzo Doria05/2016
8642^599702-369885180529Enzo Doria11/2013
865Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
866(2951*29^123418-3)/4180490Curtis Bright05/2015
8672^598942+80779180300Enzo Doria07/2016
8682^598591-1844797180194Enzo Doria06/2015
869Gamma-Prime(179849)179849Eric W. Weisstein06/2011
8702^597424-1859729179843Enzo Doria11/2015
871Phi(180683,10)179760Maksym Voznyy09/2015
872(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
873(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
8742^596690-461261179622Enzo Doria07/2015
8752^596684-113939179620Enzo Doria10/2014
8763^375887-112696179344Enzo Doria07/2014
8772^595144-1850429179157Enzo Doria08/2015
8782^594531+82253178972Enzo Doria09/2016
8792^594260-2787899178891Enzo Doria11/2015
88010^178695+136719178696Patrick De Geest05/2016
88110^178695-71178695Serge Batalov12/2014
882(2^148330+1)^4-2178608Cletus Emmanuel12/2003
8832^593178+1867219178565Enzo Doria03/2016
884(18^142031-1)/17178287Paul Bourdelais03/2010
8852^591872-291929178172Enzo Doria07/2015
8862^591682-286871178115Enzo Doria07/2015
8874*10^178091+9178092Robert Price05/2015
888410747#+478483178007Makoto Morimoto02/2016
8892^590762-396765177838Enzo Doria08/2013
890(136*10^177754-1)/9177756Serge Batalov12/2014
891ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
8922^589204+1881151177369Enzo Doria11/2016
8932^589132-69479177347Enzo Doria01/2016
8942^588912-113519177281Enzo Doria08/2014
89515^150706+2177245Robert Price06/2015
8962^588194-1861001177065Enzo Doria11/2015
8972^587560-113699176874Enzo Doria09/2014
8985^252763-12862176674Enzo Doria05/2014
8992^586804+81721176646Enzo Doria08/2016
9002^586570+1874419176576Enzo Doria06/2016
9012^585994-3311176402Yves Minet12/2014
9022^585832-112799176354Enzo Doria07/2014
9032^585336-461039176204Enzo Doria06/2015
9042^585095-1848127176132Enzo Doria08/2015
9052^584950-115451176088Enzo Doria07/2015
9062^584671-3697176004Yves Minet03/2017
90710^175608+2971175609Mike Oakes05/2010
90810^175608-55829175608Patrick De Geest09/2013
9092^583051+1879793175516Enzo Doria09/2016
9102^582860-23829175459Enzo Doria08/2013
9112^582670-23913175402Enzo Doria08/2013
9122^582573-29563175372Enzo Doria08/2015
9132^582435-1862767175331Enzo Doria12/2015
9142^582072-1848599175222Enzo Doria08/2015
9152^581560+1874911175068Enzo Doria06/2016
9162^580528-114035174757Enzo Doria11/2014
9172^580046-459161174612Enzo Doria05/2015
9182^579992-39779174595Enzo Doria09/2015
919(2^578696+1)/257174203Lelio R Paula09/2015
9202^578656-1851809174193Enzo Doria08/2015
9212^578583-113917174171Enzo Doria10/2014
92215^148048-2174118Robert Price06/2015
9232^578346+2794249174100Enzo Doria03/2016
9242^577146-49877173739Enzo Doria10/2015
9252^576889+49727173661Enzo Doria09/2016
926(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
9272^576016-113919173399Enzo Doria11/2014
9282^575911-1849387173367Enzo Doria08/2015
9292^575196-114053173152Enzo Doria11/2014
9302^574591-115387172970Enzo Doria07/2015
9312^574328+81121172890Enzo Doria07/2016
932(115*10^172862-1)/3172864Serge Batalov12/2014
9334*5^247217-9172798Lelio R Paula10/2015
9342^573668-2782319172692Enzo Doria09/2015
9352^573444-1855109172624Enzo Doria09/2015
9363^361608+2172531Robert Price08/2014
9372^572592-114893172368Enzo Doria05/2015
9385^246497-4^246497172295Jean-Louis Charton11/2008
939(36^110503+1)/37171975Lelio R Paula04/2017
9402^570980-2782289171883Enzo Doria09/2015
941(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
9422^569563-1854607171456Enzo Doria09/2015
9432^568642+1876129171179Enzo Doria07/2016
944(58*10^170842+221)/9170843Robert Price02/2017
94511^164009-270170798Enzo Doria10/2012
9463^357706-112358170670Enzo Doria07/2014
947TheodorusPrime(170657)170657Eric W. Weisstein08/2013
9482^566871+1876163170646Enzo Doria07/2016
9492^566496+7170533Donovan Johnson07/2006
950(7^201653+1)/8170416Paul Bourdelais02/2010
9512^565183-352021170138Enzo Doria07/2015
9522^565143-114457170125Enzo Doria02/2015
9532^564976-49869170075Enzo Doria10/2015
9542^564526-351401169940Enzo Doria07/2015
95521^128327-20^128327169677Jean-Louis Charton11/2014
9562^562749+2793047169405Enzo Doria02/2016
957(154*10^169337-1)/9169339Serge Batalov12/2014
9582^562369-29503169290Enzo Doria08/2015
9592^560405-39943168699Enzo Doria09/2015
9602^559686-350471168483Enzo Doria06/2015
9612^559672-1855889168479Enzo Doria09/2015
9622^559000-59939168276Enzo Doria11/2015
9632^558640-114149168168Enzo Doria12/2014
9642^558498-1849277168125Enzo Doria08/2015
9652^558476-1850249168119Enzo Doria08/2015
9662^558150-1852211168020Enzo Doria08/2015
9672^558125-113661168013Enzo Doria09/2014
968393^64747-392^64747167980Jean-Louis Charton08/2012
96939^105456+2167788Robert Price04/2015
9702^556504-462059167525Enzo Doria07/2015
9715*10^167510+9167511Robert Price08/2015
9722^555343+1874333167175Enzo Doria06/2016
9732^555210-461261167135Enzo Doria07/2015
9742^554372+1880527166883Enzo Doria11/2016
9752^554299+72173166861Enzo Doria04/2016
9762^554037-2797063166782Enzo Doria03/2016
9772^553484-29819166616Enzo Doria08/2015
9782^553383-2784217166585Enzo Doria10/2015
9792^553069+76427166491Enzo Doria05/2016
980589^60089-588^60089166454Jean-Louis Charton09/2012
98111^159756-2424166369Mike Oakes06/2010
9822^552649-361275166364Enzo Doria05/2014
9832^552628-113669166358Enzo Doria09/2014
9842^552137+1879397166210Enzo Doria09/2016
9852^551542+19249166031Payam Samidoost08/2002
9862^551535-23821166029Enzo Doria08/2013
9872^551507-23557166021Enzo Doria08/2013
9887*10^165916-3165917Robert Price08/2015
98981^86837-80^86837165728Robert Price01/2015
9902^550270-69551165648Enzo Doria12/2015
9912^550000-23625165567Enzo Doria08/2013
9922^549675-1852057165469Enzo Doria08/2015
993-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
994(28*10^165358-1)/9165359Serge Batalov10/2014
9952^549278+1879669165350Enzo Doria09/2016
9962^549252-351269165342Enzo Doria06/2015
9972^549049+2797607165281Enzo Doria04/2016
9982^547178-1856501164717Enzo Doria10/2015
99911^158160-60164707Enzo Doria07/2012
10002^546398-59201164483Enzo Doria10/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!