PRP Records

Probable Primes Top 10000

(300935 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 ?
2001(238*10^209715-1)/3209717Robert Price09/2023
20026^269407+5209640Paul Bourdelais02/2021
2003(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
20042^696254-115151209594Enzo Doria06/2015
20052^695841+225209470Henri Lifchitz01/2025
2006(35^135623+1)/36209410Paul Bourdelais07/2018
20077*10^209161+39209162Robert Price01/2023
20082^694633+1887257209106Enzo Doria05/2017
2009fibonacci(999790)-4208944Jon Grantham08/2023
20102^693959+180923208903Enzo Doria07/2016
2011(2^693747-11)/3208839Stefano Morozzi08/2022
20122^693462-1847561208753Enzo Doria07/2015
20132^690890-59981207979Enzo Doria11/2015
2014(38^131591+1)/39207884Paul Bourdelais07/2018
20153*2^690484+5207857Jon Grantham07/2023
20162^690163+1877063207760Enzo Doria07/2016
20177^245608-2207563Paul Bourdelais01/2021
2018(67*10^207556+23)/9207557Serge Batalov01/2023
20192^689286-29381207496Enzo Doria08/2015
20202^689122-114521207447Enzo Doria04/2015
20219*10^207254-89207255Robert Price02/2023
20222^688373+6077207221Enzo Doria02/2016
20232^688201+1875527207170Enzo Doria07/2016
2024(42^127609+1)/43207140Paul Bourdelais07/2018
20252^687938+213589207090Enzo Doria10/2023
20262^687619+81563206994Enzo Doria08/2016
20273*10^206927+37206928Robert Price08/2023
20282^687383+21803206923Enzo Doria09/2023
2029(11*10^206688+19)/3206689Robert Price07/2024
20302^686572-1845299206679Enzo Doria07/2015
2031(21^156217-1)/20206552Paul Bourdelais04/2010
20322^685970+39415206498Enzo Doria11/2024
2033(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
20342^685578+3206380Paul Bourdelais04/2012
20352^685078+218599206230Enzo Doria01/2024
20362^684836-49349206157Enzo Doria10/2015
2037(73^110603-1)/72206088Paul Bourdelais06/2018
20382^684163-2790967205954Enzo Doria12/2015
2039326^81943-325^81943205941Jean-Louis Charton07/2012
2040(2^684127-1)/23765203727205933Jens K. Andersen04/2009
2041(68*10^205510+13)/9205511Serge Batalov01/2023
20424^341233-3^341233205443Jean-Louis Charton01/2006
20432^682414+215029205428Enzo Doria11/2023
2044(963^68821-1)/962205334Jinyuan Wang01/2024
2045(43*10^205183-421)/9205184Robert Price10/2023
20462^681545+467205166Lelio R Paula11/2013
20472^681306+81049205094Enzo Doria07/2016
20482^680697+1877057204911Enzo Doria07/2016
20492^680415+71783204826Enzo Doria04/2016
205010^204764-8001204764Robert Price03/2023
2051(26*10^204730-77)/3204731Robert Price03/2023
20522^679860-459995204659Enzo Doria06/2015
20532^679593+1879547204578Enzo Doria09/2016
20542^678899+220073204369Enzo Doria03/2024
20552^678753+21677204326Enzo Doria08/2023
20562^678651+1875023204295Enzo Doria07/2016
20572^678561+678561204268Henri Lifchitz05/2006
20585*3^427884+2^427884204154Jon Grantham08/2023
20592^678101-114043204129Enzo Doria11/2014
20602^678028+1875631204107Enzo Doria06/2016
20612^677721+28607204015Enzo Doria01/2024
2062(19*10^203798-7)/3203799Robert Price12/2023
20632^676992-59783203795Enzo Doria10/2015
20642^676972+1866871203789Enzo Doria03/2016
20652^676815+22583203742Enzo Doria09/2023
20662^676761-9203726Robert Price01/2017
20672^676592-23203675Stefano Morozzi07/2022
20682^676563-2792407203666Enzo Doria02/2016
20692^676306-114713203589Enzo Doria04/2015
2070(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
20716*10^203365+53203366Robert Price09/2023
207210247^50678-50678^10247203250Norbert Schneider03/2022
20732^675106-73241203228Stefano Morozzi02/2025
20742^675103-188727203227Stefano Morozzi02/2025
20752^675104-16199203227Stefano Morozzi02/2025
20762^675104-195303203227Stefano Morozzi02/2025
20772^675105-94521203227Stefano Morozzi02/2025
20782^675100-2775203226Stefano Morozzi02/2025
20792^675098-170703203225Stefano Morozzi02/2025
20802^675093-162123203224Stefano Morozzi02/2025
20812^675093-48955203224Stefano Morozzi02/2025
20822^675095-73591203224Stefano Morozzi02/2025
20832^675095-89937203224Stefano Morozzi02/2025
20842^675092-144539203223Stefano Morozzi02/2025
20852^675086-186387203222Stefano Morozzi02/2025
20862^675088-68505203222Stefano Morozzi02/2025
20872^675083-149199203221Stefano Morozzi02/2025
20882^675081-91425203220Stefano Morozzi02/2025
20892^675082-80213203220Stefano Morozzi02/2025
20902^675077-152683203219Stefano Morozzi02/2025
20912^675077-79213203219Stefano Morozzi02/2025
20922^675073-149065203218Stefano Morozzi02/2025
20932^675073-19663203218Stefano Morozzi02/2025
20942^675069-147135203217Stefano Morozzi02/2025
20952^675069-161461203217Stefano Morozzi02/2025
20962^675071-175189203217Stefano Morozzi02/2025
20972^675060+119983203214Stefano Morozzi02/2025
20982^675060+161301203214Stefano Morozzi02/2025
20992^675061-187773203214Stefano Morozzi02/2025
21002^675062-92193203214Stefano Morozzi02/2025
21012^675058-10403203213Stefano Morozzi01/2025
21022^675058-40337203213Stefano Morozzi01/2025
21032^675057+123557203213Stefano Morozzi02/2025
21042^675057+172475203213Stefano Morozzi02/2025
21052^675053-4801203212Stefano Morozzi01/2025
21062^675054-174341203212Stefano Morozzi01/2025
21072^675054-53697203212Stefano Morozzi01/2025
21082^675054+24825203212Stefano Morozzi02/2025
21092^675055+160265203212Stefano Morozzi02/2025
21102^675050-30015203211Stefano Morozzi01/2025
21112^675051-85941203211Stefano Morozzi01/2025
21122^675051+30885203211Stefano Morozzi02/2025
21132^675052+12537203211Stefano Morozzi02/2025
21142^675047-100299203210Stefano Morozzi01/2025
21152^675048-97313203210Stefano Morozzi01/2025
21162^675046+118119203210Stefano Morozzi02/2025
21172^675048+128941203210Stefano Morozzi02/2025
21182^675049+136359203210Stefano Morozzi02/2025
21192^675044-81087203209Stefano Morozzi01/2025
21202^675042-179811203208Stefano Morozzi01/2025
21212^675036-192939203207Stefano Morozzi01/2025
21222^675037-17853203207Stefano Morozzi01/2025
21232^675036+47101203207Stefano Morozzi02/2025
21242^675038+189589203207Stefano Morozzi02/2025
21252^675034-169727203206Stefano Morozzi01/2025
21262^675035-173055203206Stefano Morozzi01/2025
21272^675035-73551203206Stefano Morozzi01/2025
21282^675033+79109203206Stefano Morozzi02/2025
21292^675034+154057203206Stefano Morozzi02/2025
21302^675030+109245203205Stefano Morozzi01/2025
21312^675030-160047203205Stefano Morozzi01/2025
21322^675027+106733203204Stefano Morozzi01/2025
21332^675026-67377203204Stefano Morozzi01/2025
21342^675021+13335203202Stefano Morozzi01/2025
21352^675020-180497203202Stefano Morozzi01/2025
21362^675016+174777203201Stefano Morozzi01/2025
21372^675017+128379203201Stefano Morozzi01/2025
21382^675017+171249203201Stefano Morozzi01/2025
21392^675018+86517203201Stefano Morozzi01/2025
21402^675019+125891203201Stefano Morozzi01/2025
21412^675019+163251203201Stefano Morozzi01/2025
21422^675016-170847203201Stefano Morozzi01/2025
21432^675019-44755203201Stefano Morozzi01/2025
21442^675015+120225203200Stefano Morozzi01/2025
21452^675013-69831203200Stefano Morozzi01/2025
21462^675014-3897203200Stefano Morozzi01/2025
21472^675006+75357203198Stefano Morozzi01/2025
21482^675008+112231203198Stefano Morozzi01/2025
21492^675007-123309203198Stefano Morozzi01/2025
21502^675003+52529203197Stefano Morozzi01/2025
21512^675002+50595203196Stefano Morozzi01/2025
21522^674627-25161203083Enzo Doria09/2013
21532^674603-69337203076Enzo Doria12/2015
2154(182*10^203048+1)/3203050Robert Price09/2023
21552^674459+74213203033Enzo Doria04/2016
21562^674116-458879202930Enzo Doria04/2015
21572^674076-114755202918Enzo Doria04/2015
21585^289937-4^289937202658Jean-Louis Charton03/2013
21595^289926-289926^5202650Henri Lifchitz07/2024
2160(2^673184-7)/3202649Stefano Morozzi08/2022
2161(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
2162(155^92479-1)/154202558Anonymous06/2024
21632^672773+219407202525Enzo Doria03/2024
21641374^64531-64531^1374202498Henri Lifchitz10/2024
21652^672556-1835519202460Enzo Doria04/2015
2166(7*10^202267+179)/3202268Robert Price02/2023
21672^671446-351401202126Enzo Doria07/2015
21682^671373+77747202104Enzo Doria05/2016
2169(2*10^202059+7)/9202059Rytis Slatkevicius01/2023
217098*10^202021-9202023Robert Price05/2023
21712^670726-114845201909Enzo Doria05/2015
21722^670539-25045201853Enzo Doria09/2013
217310^201801-93201801Robert Price02/2023
217443284^43519-43519^43284201769Norbert Schneider08/2018
21752^670213+282317201755Enzo Doria09/2016
21762^670133+89201731Stefano Morozzi05/2021
21772^669854-113501201647Enzo Doria08/2014
21782^669718+81619201606Enzo Doria08/2016
2179(299*10^201547-17)/3201549Robert Price02/2023
2180(145*10^201504-1)/9201506Serge Batalov12/2014
21812^668938-1839821201371Enzo Doria06/2015
2182(198^87623-1)/197201239Anonymous06/2024
21832^668492+1879303201237Enzo Doria08/2016
21847*10^201140-87201141Robert Price03/2023
21856^258413-5^258413201085Jean-Louis Charton03/2013
218610194^50161-50161^10194201063Norbert Schneider09/2020
21872^667894+1875589201057Enzo Doria06/2016
21882^667569-1836559200959Enzo Doria05/2015
2189(172*10^200746-1)/9200748Serge Batalov12/2014
2190(166^90407-1)/165200712Anonymous06/2024
21912^666430+782569200616Enzo Doria10/2016
2192(13*10^200610-43)/3200611Robert Price08/2023
2193(8*10^200408-11)/3200409Robert Price07/2023
2194p(38635)#-p(38635+1)200356Henri Lifchitz11/2024
2195(19*10^200260+101)/3200261Robert Price06/2023
219643183^43183+4^4200167Serge Batalov04/2024
2197(86^103471+1)/87200163Paul Bourdelais05/2018
2198(10^(2*100072+1)+36*10^100072-1)/9200145Robert Price09/2023
21992^664778+34789200119Enzo Doria07/2024
2200103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
2201103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
2202numbpart(32235776596)200002Serge Batalov04/2017
2203(10^200001+149)/3200001Serge Batalov12/2014
220410^200000+571791200001Patrick De Geest08/2019
2205(3^419180-621444)/3200000Stefano Morozzi06/2019
2206(3^419180-1941384)/3200000Stefano Morozzi08/2019
220710^200000-45557200000Patrick De Geest08/2019
2208(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
22092593604092947240127723272^8192+2593604092947240127722755^8192200000Youcef Lemsafer01/2023
2210(2593604092947240127723019^8192+2593604092947240127723011^8192)/2199999Youcef Lemsafer01/2023
2211(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457199994Youcef Lemsafer01/2023
2212(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986199989Youcef Lemsafer01/2023
2213(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169199986Youcef Lemsafer01/2023
221492*10^199980-9199982Robert Price12/2021
2215(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649199977Youcef Lemsafer01/2023
2216(85*10^199951-139)/9199952Robert Price08/2021
2217(10^199926+7)/29/373/2339199919Alfred Reich08/2021
22182^663838+25819199836Enzo Doria11/2023
221923*10^199833-9199835Robert Price10/2021
2220fibonacci(956176)-4199829Jon Grantham08/2023
2221(299*10^199801-17)/3199803Robert Price04/2020
22226*10^199788+77199789Robert Price06/2020
2223(2^663604+1)/270750449199757Anonymous10/2024
2224(23*10^199615+37)/3199616Robert Price02/2022
2225(17*10^199607-167)/3199608Robert Price05/2022
22262^663020-933075199589Paul Bourdelais06/2021
22272^663007+29963199585Enzo Doria03/2024
22283*2^662703-5199494Jon Grantham07/2023
2229(14*10^199447+73)/3199448Robert Price12/2018
2230(2^662424-15)/7199409Stefano Morozzi08/2022
22312^662194+22189199341Enzo Doria09/2023
22322^662103-29287199313Enzo Doria08/2015
2233(2*10^199283+457)/9199283Robert Price01/2018
2234(10^199248-19)/9199248Robert Price01/2018
2235(83*10^199213+529)/9199214Robert Price12/2021
2236(194*10^199146-17)/3199148Robert Price09/2020
2237(151*10^199003-1)/3199005Robert Price03/2020
22389*10^198946-73198947Robert Price01/2021
223945*10^198931-7198933Robert Price07/2020
22402^660482-2891198825Yves Minet05/2016
22412^659594+37729198558Enzo Doria10/2024
22422^659589-21198557Stefano Morozzi07/2022
22432^659583+1879223198555Enzo Doria08/2016
2244(53*10^198529+1)/9198530Serge Batalov07/2010
2245(49*10^198403+311)/9198404Robert Price06/2019
224696*10^198376-7198378Robert Price03/2021
2247(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
22482^658828-29819198327Enzo Doria08/2015
22492^658776-2791229198312Enzo Doria01/2016
2250(35*10^198294-377)/9198295Robert Price07/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 07 2025 10:37 (Time in France)

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