PRP Records

Probable Primes Top 10000

(202632 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 (> 30000) Who ? When ?
20012^398710+57120024Lelio R Paula04/2013
20022^398691-115057120018Enzo Doria06/2015
2003L(574219)120005Renaud Lifchitz03/2004
20042^398571+60413119982Yves Minet03/2011
2005p(24179)#/2-64119949Robert Price04/2017
20062^398448+1872001119945Enzo Doria05/2016
20078*10^119930-3119931Ray Chandler04/2011
2008(10^119880+179)/9119880Serge Batalov12/2014
2009(9*2^398145+1)/73119853Lelio R Paula04/2014
2010(10^119836+77)/3119836Robert Price01/2018
20112^398029+1872527119819Enzo Doria05/2016
20122^397897-113541119779Enzo Doria08/2014
2013(21*2^397661-1)/27593119705Lelio R Paula04/2014
2014(58^67853-1)/57119653Paul Bourdelais09/2017
20152^397426+73849119638Enzo Doria04/2016
20162^396933-112723119489Enzo Doria06/2014
201711^114738-150119488Enzo Doria10/2012
20182^396790-21119446Lelio R Paula04/2013
2019(2^396633-7)/5119398Lelio R Paula04/2014
2020105^59050+104119352Norbert Schneider11/2016
20212^396374+73729119321Enzo Doria04/2016
20222^396258-459491119286Enzo Doria05/2015
2023(2^395986+5)/76881119199Lelio R Paula04/2014
2024(23*2^395942-1)/91119190Lelio R Paula04/2014
2025(11*2^395548+1)/3119073Lelio R Paula04/2014
2026(30^80599+1)/31119054Robert Price07/2013
20272^395062-109121118926Enzo Doria04/2014
2028(2^394918+78557)/3118882Lelio R Paula01/2015
2029(2^394739+3)/1883118826Lelio R Paula04/2014
20302^394266+71389118686Enzo Doria04/2016
20315^169727+2118635Lelio R Paula08/2013
20322^394034-3118617M. Frind & P. Underwood09/2002
20333^248572-6242118599Enzo Doria05/2014
2034(3*2^393964-1)/181118594Lelio R Paula04/2014
20357^140303-6118570Robert Price11/2014
20362^393427+75683118434Enzo Doria04/2016
20372^393376-114749118418Enzo Doria04/2015
20382^393180+73118359Lelio R Paula04/2013
2039p(23881)#/2+256118328Robert Price05/2017
2040(10^118324+359)/9118324Serge Batalov12/2014
2041p(23879)#/2+64118317Robert Price03/2017
2042(53*10^118216+1)/9118217Serge Batalov11/2010
2043(7*2^392697+1)/15118214Renaud Lifchitz03/2011
2044(157^53819-1)/156118179Alexander Zhirkov06/2016
2045(19*2^392551+1)/3118171Lelio R Paula04/2014
20462^392516-29219118160Enzo Doria07/2015
2047Phi(177231,10)118152Maksym Voznyy09/2015
20482^392413-112123118129Enzo Doria06/2014
2049(2^392342+5)/27118106Lelio R Paula04/2014
20502^392300-1841429118095Enzo Doria06/2015
20512^392220+75241118070Enzo Doria04/2016
205210^118009-20001118009Robert Price01/2018
20532^391933+5897117984Yves Minet02/2011
20542^391912-1849259117978Enzo Doria08/2015
2055(2^391812+5)/14181117944Lelio R Paula04/2014
2056(7*2^391521+1)/285117858Lelio R Paula04/2014
20572^391324+90901117801Yves Minet02/2011
20582^391301-1859923117794Enzo Doria03/2016
2059(2^391115-7)/11791117734Lelio R Paula04/2014
20602^390960+1880881117691Enzo Doria11/2016
20612^390897-1860553117672Enzo Doria11/2015
20622^390889-115003117670Enzo Doria06/2015
20632^390779-30337117637Paul Bourdelais02/2012
206411^112916-780117590Enzo Doria12/2012
2065(16^97613-5^97613)/11117537Robert Price07/2013
2066(17*2^390272+1)/1983117482Lelio R Paula04/2014
206731^78759-30117459Theodore Burton02/2007
20682^389998+37117402Lelio R Paula03/2013
20692^389478+43117245Lelio R Paula03/2013
2070(29*2^389351-1)/9117207Lelio R Paula04/2014
2071(2^389341-7)/3865117200Lelio R Paula03/2014
207210^117135-401117135Robert Price01/2018
20732^389033-12797413117111Enzo Doria04/2016
20742^388960-109505117089Enzo Doria04/2014
2075(2^388928-5)/569117077Lelio R Paula03/2014
20762^388888-1529117067Yves Minet01/2013
207710^117059+28879117060Patrick De Geest05/2016
2078(10^117059-71)/1117059Serge Batalov12/2014
20793^245154-6256116969Enzo Doria05/2014
20802^388536-113495116961Enzo Doria08/2014
20812^388469-43116941Lelio R Paula03/2013
2082(7*2^388372-1)/111116911Lelio R Paula04/2014
2083(7*2^388335-1)/25116900Lelio R Paula04/2014
20842^388180+93116854Donovan Johnson07/2008
2085(2^388081+7)/1179116821Lelio R Paula03/2014
20862^387946-113261116784Enzo Doria07/2014
20872^387745+75557116723Enzo Doria04/2016
20882^387554+71455116666Enzo Doria04/2016
2089(2^387447+78557)/365116631Lelio R Paula12/2014
2090(145*10^116610-1)/9116612Serge Batalov12/2014
2091(17*2^387284-1)/59116584Lelio R Paula04/2014
2092(31*2^386968+1)/7116490Lelio R Paula03/2014
20932^386947+1869143116483Enzo Doria05/2016
2094(30^78857-1)/29116480Robert Price12/2011
2095(2^386903-3)/5116469Lelio R Paula03/2014
20962^386389-1864783116315Enzo Doria03/2016
2097(31*2^386231-1)/1711116266Lelio R Paula03/2014
2098(2^386087-5)/40959116220Lelio R Paula03/2014
20992^385969-823116189Yves Minet05/2012
210057^66162+2116173Lelio R Paula08/2013
21012^385854+75049116154Enzo Doria04/2016
21022^385775-109587116130Enzo Doria04/2014
21032^385622+71839116084Enzo Doria04/2016
21042^385564+781116067Lelio R Paula01/2012
21052^385410+71893116020Enzo Doria04/2016
2106(25*2^385091+1)/27115924Lelio R Paula04/2014
21072^384953-111943115883Paul Bourdelais02/2012
210843^70942-2115882Lelio R Paula04/2014
21097*10^115863+3115864Robert Price08/2015
21102^384834+93115847Donovan Johnson07/2008
21112^384809+71297115840Enzo Doria04/2016
2112(7*2^384759-1)/5115825Lelio R Paula04/2014
2113(71*10^115810-17)/9115811Ray Chandler08/2011
2114(97*10^115794-1)/3115796Serge Batalov12/2014
21152^384530+1874305115756Enzo Doria06/2016
2116(3*2^384524-1)/7631115750Lelio R Paula03/2014
21172^384312+81091115690Yves Minet02/2010
2118(4*10^115668-79)/3115669Robert Price02/2018
2119(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
21203^242337-4042115625Enzo Doria05/2014
2121(11*2^383859-13)/15115553Renaud Lifchitz03/2011
21222^383780-3149115530Yves Minet10/2014
21232^383560-455115464Yves Minet03/2012
2124(2^383544+5)/3115458Lelio R Paula03/2014
212589^59221-88^59221115445Robert Price06/2015
21262^383347+1869413115399Enzo Doria05/2016
2127(2^383130-7)/131793115329Lelio R Paula03/2014
2128(12^106859+1)/13115320Paul Bourdelais02/2010
21292^383039+1869509115307Enzo Doria05/2016
2130(13*2^382968+1)/7115286Lelio R Paula04/2014
21312^382633+73697115185Enzo Doria04/2016
21322^382509-113593115147Enzo Doria08/2014
21332^382502-2791721115145Enzo Doria03/2016
21349^120590-120590115073Robert Price03/2014
21352^382198+9115054Lelio R Paula03/2013
21362^381883-59197114959Enzo Doria10/2015
21382^381806-4481114936Yves Minet07/2011
21372^381808-1851507114936Enzo Doria08/2015
21392^381774-112373114926Enzo Doria06/2014
21402^381555-109051114860Enzo Doria04/2014
21412^381546-113501114857Enzo Doria08/2014
21422^381360-110429114801Enzo Doria05/2014
2143(66^63079+1)/67114774Paul Bourdelais09/2017
21442^381252-115079114769Enzo Doria06/2015
21452^381209-29323114756Enzo Doria07/2015
2146569^41651-568^41651114754Jean-Louis Charton11/2009
21472^381201+1873205114753Enzo Doria06/2016
21482^380974-112991114685Enzo Doria07/2014
214988^58949-87114626Norbert Schneider11/2015
21502^380700+91114603Lelio R Paula03/2013
215110^114575+3^114576114576Mike Oakes09/2010
215210^114575+66561114576Patrick De Geest02/2017
215310^114575-581081114575Patrick De Geest02/2017
21542^380587-115315114569Enzo Doria06/2015
21552^380513-216925114546Enzo Doria05/2014
21562^380451-1840087114528Enzo Doria06/2015
2157(15*2^380388-1)/539114507Lelio R Paula04/2014
21582^380279-461347114476Enzo Doria07/2015
21592^380021+1871147114398Enzo Doria05/2016
21602^380005+1869707114393Enzo Doria05/2016
21612^379958-113297114379Enzo Doria07/2014
21622^379881-109105114356Enzo Doria04/2014
2163(21*2^379857-1)/13114349Lelio R Paula03/2014
2164(4*10^114340+83)/3114341Robert Price02/2018
216588^58773-87114284Norbert Schneider11/2015
21662^379529-2790283114250Enzo Doria03/2016
21672^379522+1869115114248Enzo Doria05/2016
2168(145*10^114226-1)/9114228Serge Batalov12/2014
21692^379317-115033114186Enzo Doria06/2015
2170(17*2^379246-1)/17407114162Lelio R Paula03/2014
21712*10^113941+9113942Dmitry Domanov11/2010
21722^378272-16565113872Enzo Doria04/2013
21732^378217-109075113855Enzo Doria04/2014
21742^378198+67113849Lelio R Paula03/2013
21752^378173-3249113842Yves Minet12/2014
2176(2^378155-5)/6597113833Lelio R Paula03/2014
217792941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
21782^378128-262977113828Enzo Doria05/2014
21792^378123-113215113827Enzo Doria07/2014
21806^146274-18893113824Enzo Doria03/2013
21812^378078+75113813Lelio R Paula03/2013
21822^377940+63113772Lelio R Paula03/2013
21832^377941-2785843113772Enzo Doria04/2016
21842^377810+1875109113733Enzo Doria09/2016
21852^377803-1838635113731Enzo Doria05/2015
21862^377799+52223113729Yves Minet08/2010
218711^109190-270113710Enzo Doria12/2012
21887*10^113693+9113694Robert Price09/2015
2189(2*10^113631+529)/9113631Robert Price01/2018
21902^377408-2798279113612Enzo Doria04/2016
21912^377222+93679113556Yves Minet02/2011
2192262147#+316847113552Makoto Morimoto02/2016
21932^377026-458903113497Enzo Doria04/2015
219435^73477-34^73477113454Robert Price05/2012
21952^376790+27113426Lelio R Paula03/2013
21962^376786-112701113424Enzo Doria06/2014
21972^376731+21113408Lelio R Paula03/2013
21982^376634+1871245113379Enzo Doria05/2016
2199(4^188318+17)/3113379Robert Price02/2017
22002^376576-344369113361Enzo Doria07/2015
2201(17*2^376526-1)/223113345Lelio R Paula03/2014
2202(27*2^376441-1)/811113319Lelio R Paula03/2014
22032^376128-21237113226Enzo Doria06/2013
22042^375638-1787171113079Enzo Doria03/2016
22052^375537+4847113048Yves Minet02/2011
2206(17^91837+16^91837)/33113000Robert Price08/2013
22075*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
22082^375350-3221112992Yves Minet07/2011
2210(13*2^375306+1)/7112979Lelio R Paula03/2014
22092^375305+76757112979Enzo Doria05/2016
22112^375258+1874989112964Enzo Doria07/2016
2212(29^77237-1)/28112950Robert Price04/2012
22132^375154+74959112933Enzo Doria04/2016
22142^374993-2787163112885Enzo Doria11/2015
2215123^53970+2112793Lelio R Paula06/2013
2216p(22852)#/2+512112745Robert Price05/2017
22172^374441-21049112718Enzo Doria06/2013
2218(2^374321+1)/3112682H.&R. Lifchitz12/2000
2219(13^101089-1)/12112607Paul Bourdelais03/2010
22203^236011-8828112606Enzo Doria05/2014
222139^70666+2112435Lelio R Paula11/2013
2222(2^373350-7)/3112390Lelio R Paula03/2014
22232^373306-1840931112377Enzo Doria06/2015
22242^373117+1872107112320Enzo Doria05/2016
22252^373040+2792761112297Enzo Doria03/2016
2226EPrime(112280)112280Eric W. Weisstein10/2010
22272^372950+7112270Lelio R Paula03/2013
22282^372945+1872167112268Enzo Doria05/2016
22292^372695+72113112193Enzo Doria04/2016
22302^372689-2563112191Yves Minet07/2014
22312^372638-1859441112176Enzo Doria03/2016
22323^235074-113056112159Enzo Doria07/2014
2233(91*10^112098-1)/9112100Robert Price04/2015
22342^372310-85061112077Paul Bourdelais02/2012
2235(10^112067+53)/9112067Serge Batalov07/2015
223675^59760+2112054Lelio R Paula08/2013
22372^372108+74221112016Enzo Doria04/2016
22382^371970-459491111975Enzo Doria05/2015
223941^69427-40^69427111971Robert Price07/2012
2240(10^111902+71)/9111902Serge Batalov07/2015
22412^371440-112865111815Enzo Doria06/2014
22422^371426-459161111811Enzo Doria05/2015
22432^371276-461267111766Enzo Doria07/2015
22442^371098-113261111712Enzo Doria07/2014
2245(7*10^111706-61)/9111706Erik Branger01/2011
22462^371044+1869391111696Enzo Doria05/2016
224788^57416+87111645Norbert Schneider11/2015
22482^370829-109693111631Enzo Doria04/2014
224915^94906-2111619Lelio R Paula11/2013
2250(2^370655-5)/2439111575Lelio R Paula03/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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