PRP Records

Probable Primes Top 10000

(193013 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 ?
2001p(23879)#/2+64118317Robert Price03/2017
2002(53*10^118216+1)/9118217Serge Batalov11/2010
2003(7*2^392697+1)/15118214Renaud Lifchitz03/2011
2004(157^53819-1)/156118179Alexander Zhirkov06/2016
2005(19*2^392551+1)/3118171Lelio R Paula04/2014
20062^392516-29219118160Enzo Doria07/2015
2007Phi(177231,10)118152Maksym Voznyy09/2015
20082^392413-112123118129Enzo Doria06/2014
2009(2^392342+5)/27118106Lelio R Paula04/2014
20102^392300-1841429118095Enzo Doria06/2015
20112^392220+75241118070Enzo Doria04/2016
20122^391933+5897117984Yves Minet02/2011
20132^391912-1849259117978Enzo Doria08/2015
2014(2^391812+5)/14181117944Lelio R Paula04/2014
2015(7*2^391521+1)/285117858Lelio R Paula04/2014
20162^391324+90901117801Yves Minet02/2011
20172^391301-1859923117794Enzo Doria03/2016
2018(2^391115-7)/11791117734Lelio R Paula04/2014
20192^390960+1880881117691Enzo Doria11/2016
20202^390897-1860553117672Enzo Doria11/2015
20212^390889-115003117670Enzo Doria06/2015
20222^390779-30337117637Paul Bourdelais02/2012
202311^112916-780117590Enzo Doria12/2012
2024(16^97613-5^97613)/11117537Robert Price07/2013
2025(17*2^390272+1)/1983117482Lelio R Paula04/2014
202631^78759-30117459Theodore Burton02/2007
20272^389998+37117402Lelio R Paula03/2013
20282^389478+43117245Lelio R Paula03/2013
2029(29*2^389351-1)/9117207Lelio R Paula04/2014
2030(2^389341-7)/3865117200Lelio R Paula03/2014
20312^389033-12797413117111Enzo Doria04/2016
20322^388960-109505117089Enzo Doria04/2014
2033(2^388928-5)/569117077Lelio R Paula03/2014
20342^388888-1529117067Yves Minet01/2013
203510^117059+28879117060Patrick De Geest05/2016
2036(10^117059-71)/1117059Serge Batalov12/2014
20373^245154-6256116969Enzo Doria05/2014
20382^388536-113495116961Enzo Doria08/2014
20392^388469-43116941Lelio R Paula03/2013
2040(7*2^388372-1)/111116911Lelio R Paula04/2014
2041(7*2^388335-1)/25116900Lelio R Paula04/2014
20422^388180+93116854Donovan Johnson07/2008
2043(2^388081+7)/1179116821Lelio R Paula03/2014
20442^387946-113261116784Enzo Doria07/2014
20452^387745+75557116723Enzo Doria04/2016
20462^387554+71455116666Enzo Doria04/2016
2047(2^387447+78557)/365116631Lelio R Paula12/2014
2048(145*10^116610-1)/9116612Serge Batalov12/2014
2049(17*2^387284-1)/59116584Lelio R Paula04/2014
2050(31*2^386968+1)/7116490Lelio R Paula03/2014
20512^386947+1869143116483Enzo Doria05/2016
2052(30^78857-1)/29116480Robert Price12/2011
2053(2^386903-3)/5116469Lelio R Paula03/2014
20542^386389-1864783116315Enzo Doria03/2016
2055(31*2^386231-1)/1711116266Lelio R Paula03/2014
2056(2^386087-5)/40959116220Lelio R Paula03/2014
20572^385969-823116189Yves Minet05/2012
205857^66162+2116173Lelio R Paula08/2013
20592^385854+75049116154Enzo Doria04/2016
20602^385775-109587116130Enzo Doria04/2014
20612^385622+71839116084Enzo Doria04/2016
20622^385564+781116067Lelio R Paula01/2012
20632^385410+71893116020Enzo Doria04/2016
2064(25*2^385091+1)/27115924Lelio R Paula04/2014
20652^384953-111943115883Paul Bourdelais02/2012
206643^70942-2115882Lelio R Paula04/2014
20677*10^115863+3115864Robert Price08/2015
20682^384834+93115847Donovan Johnson07/2008
20692^384809+71297115840Enzo Doria04/2016
2070(7*2^384759-1)/5115825Lelio R Paula04/2014
2071(71*10^115810-17)/9115811Ray Chandler08/2011
2072(97*10^115794-1)/3115796Serge Batalov12/2014
20732^384530+1874305115756Enzo Doria06/2016
2074(3*2^384524-1)/7631115750Lelio R Paula03/2014
20752^384312+81091115690Yves Minet02/2010
2076(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
20773^242337-4042115625Enzo Doria05/2014
2078(11*2^383859-13)/15115553Renaud Lifchitz03/2011
20792^383780-3149115530Yves Minet10/2014
20802^383560-455115464Yves Minet03/2012
2081(2^383544+5)/3115458Lelio R Paula03/2014
208289^59221-88^59221115445Robert Price06/2015
20832^383347+1869413115399Enzo Doria05/2016
2084(2^383130-7)/131793115329Lelio R Paula03/2014
2085(12^106859+1)/13115320Paul Bourdelais02/2010
20862^383039+1869509115307Enzo Doria05/2016
2087(13*2^382968+1)/7115286Lelio R Paula04/2014
20882^382633+73697115185Enzo Doria04/2016
20892^382509-113593115147Enzo Doria08/2014
20902^382502-2791721115145Enzo Doria03/2016
20919^120590-120590115073Robert Price03/2014
20922^382198+9115054Lelio R Paula03/2013
20932^381883-59197114959Enzo Doria10/2015
20952^381806-4481114936Yves Minet07/2011
20942^381808-1851507114936Enzo Doria08/2015
20962^381774-112373114926Enzo Doria06/2014
20972^381555-109051114860Enzo Doria04/2014
20982^381546-113501114857Enzo Doria08/2014
20992^381360-110429114801Enzo Doria05/2014
2100(66^63079+1)/67114774Paul Bourdelais09/2017
21012^381252-115079114769Enzo Doria06/2015
21022^381209-29323114756Enzo Doria07/2015
2103569^41651-568^41651114754Jean-Louis Charton11/2009
21042^381201+1873205114753Enzo Doria06/2016
21052^380974-112991114685Enzo Doria07/2014
210688^58949-87114626Norbert Schneider11/2015
21072^380700+91114603Lelio R Paula03/2013
210910^114575+3^114576114576Mike Oakes09/2010
210810^114575+66561114576Patrick De Geest02/2017
211010^114575-581081114575Patrick De Geest02/2017
21112^380587-115315114569Enzo Doria06/2015
21122^380513-216925114546Enzo Doria05/2014
21132^380451-1840087114528Enzo Doria06/2015
2114(15*2^380388-1)/539114507Lelio R Paula04/2014
21152^380279-461347114476Enzo Doria07/2015
21162^380021+1871147114398Enzo Doria05/2016
21172^380005+1869707114393Enzo Doria05/2016
21182^379958-113297114379Enzo Doria07/2014
21192^379881-109105114356Enzo Doria04/2014
2120(21*2^379857-1)/13114349Lelio R Paula03/2014
212188^58773-87114284Norbert Schneider11/2015
21222^379529-2790283114250Enzo Doria03/2016
21232^379522+1869115114248Enzo Doria05/2016
2124(145*10^114226-1)/9114228Serge Batalov12/2014
21252^379317-115033114186Enzo Doria06/2015
2126(17*2^379246-1)/17407114162Lelio R Paula03/2014
21272*10^113941+9113942Dmitry Domanov11/2010
21282^378272-16565113872Enzo Doria04/2013
21292^378217-109075113855Enzo Doria04/2014
21302^378198+67113849Lelio R Paula03/2013
21312^378173-3249113842Yves Minet12/2014
2132(2^378155-5)/6597113833Lelio R Paula03/2014
213392941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
21342^378128-262977113828Enzo Doria05/2014
21352^378123-113215113827Enzo Doria07/2014
21366^146274-18893113824Enzo Doria03/2013
21372^378078+75113813Lelio R Paula03/2013
21382^377940+63113772Lelio R Paula03/2013
21392^377941-2785843113772Enzo Doria04/2016
21402^377810+1875109113733Enzo Doria09/2016
21412^377803-1838635113731Enzo Doria05/2015
21422^377799+52223113729Yves Minet08/2010
214311^109190-270113710Enzo Doria12/2012
21447*10^113693+9113694Robert Price09/2015
21452^377408-2798279113612Enzo Doria04/2016
21462^377222+93679113556Yves Minet02/2011
2147262147#+316847113552Makoto Morimoto02/2016
21482^377026-458903113497Enzo Doria04/2015
214935^73477-34^73477113454Robert Price05/2012
21502^376790+27113426Lelio R Paula03/2013
21512^376786-112701113424Enzo Doria06/2014
21522^376731+21113408Lelio R Paula03/2013
21542^376634+1871245113379Enzo Doria05/2016
2153(4^188318+17)/3113379Robert Price02/2017
21552^376576-344369113361Enzo Doria07/2015
2156(17*2^376526-1)/223113345Lelio R Paula03/2014
2157(27*2^376441-1)/811113319Lelio R Paula03/2014
21582^376128-21237113226Enzo Doria06/2013
21592^375638-1787171113079Enzo Doria03/2016
21602^375537+4847113048Yves Minet02/2011
2161(17^91837+16^91837)/33113000Robert Price08/2013
21625*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
21632^375350-3221112992Yves Minet07/2011
2164(13*2^375306+1)/7112979Lelio R Paula03/2014
21652^375305+76757112979Enzo Doria05/2016
21662^375258+1874989112964Enzo Doria07/2016
2167(29^77237-1)/28112950Robert Price04/2012
21682^375154+74959112933Enzo Doria04/2016
21692^374993-2787163112885Enzo Doria11/2015
2170123^53970+2112793Lelio R Paula06/2013
2171p(22852)#/2+512112745Robert Price05/2017
21722^374441-21049112718Enzo Doria06/2013
2173(2^374321+1)/3112682H.&R. Lifchitz12/2000
2174(13^101089-1)/12112607Paul Bourdelais03/2010
21753^236011-8828112606Enzo Doria05/2014
217639^70666+2112435Lelio R Paula11/2013
2177(2^373350-7)/3112390Lelio R Paula03/2014
21782^373306-1840931112377Enzo Doria06/2015
21792^373117+1872107112320Enzo Doria05/2016
21802^373040+2792761112297Enzo Doria03/2016
2181EPrime(112280)112280Eric W. Weisstein10/2010
21822^372950+7112270Lelio R Paula03/2013
21832^372945+1872167112268Enzo Doria05/2016
21842^372695+72113112193Enzo Doria04/2016
21852^372689-2563112191Yves Minet07/2014
21862^372638-1859441112176Enzo Doria03/2016
21873^235074-113056112159Enzo Doria07/2014
2188(91*10^112098-1)/9112100Robert Price04/2015
21892^372310-85061112077Paul Bourdelais02/2012
2190(10^112067+53)/9112067Serge Batalov07/2015
219175^59760+2112054Lelio R Paula08/2013
21922^372108+74221112016Enzo Doria04/2016
21932^371970-459491111975Enzo Doria05/2015
219441^69427-40^69427111971Robert Price07/2012
2195(10^111902+71)/9111902Serge Batalov07/2015
21962^371440-112865111815Enzo Doria06/2014
21972^371426-459161111811Enzo Doria05/2015
21982^371276-461267111766Enzo Doria07/2015
21992^371098-113261111712Enzo Doria07/2014
2200(7*10^111706-61)/9111706Erik Branger01/2011
22012^371044+1869391111696Enzo Doria05/2016
220288^57416+87111645Norbert Schneider11/2015
22032^370829-109693111631Enzo Doria04/2014
220415^94906-2111619Lelio R Paula11/2013
22062^370643-37111575Yves Minet01/2012
2205(2^370655-5)/2439111575Lelio R Paula03/2014
22072^370610-3911111565Yves Minet04/2017
2208286^45405+45405^286111532Norbert Schneider04/2015
22094*5^159563-9111531Lelio R Paula11/2014
22102^370393-2797093111500Enzo Doria03/2016
2211(21*2^370382-1)/629111495Lelio R Paula03/2014
22122^370292-2791979111469Enzo Doria03/2016
22132^370177-461551111435Enzo Doria07/2015
2214109^54683-108111413Norbert Schneider02/2017
2215numbpart(10^10+76282)111391Serge Batalov04/2015
22162^369974+733111374Lelio R Paula05/2013
22172^369915-286267111356Enzo Doria07/2015
22182^369855-1615111338Lelio R Paula05/2017
22197*10^111325+3111326Robert Price08/2015
222051^65176+2111293Lelio R Paula08/2013
22212^369643-1865767111274Enzo Doria03/2016
22222^369603+885111262Lelio R Paula05/2017
2223L(532277)111240Renaud Lifchitz03/2004
2224105^55033-2111233Lelio R Paula10/2017
22252^369392+29835111199Lelio R Paula05/2017
22262^369354-3413111187Yves Minet12/2016
22272^369296-27111170Lelio R Paula02/2013
22282^369239-109837111153Enzo Doria05/2014
22292^369224-291839111148Enzo Doria07/2015
22302^369216+2798881111146Enzo Doria04/2016
223110^111111+163849111112Patrick De Geest03/2017
223210^111111-312911111111Patrick De Geest03/2017
22332^369092-216923111108Enzo Doria05/2014
22342^369081-55111105Lelio R Paula02/2013
223588^57124-87111077Norbert Schneider11/2015
22362^368980+753111075Lelio R Paula05/2013
22372^368946-3623111064Yves Minet03/2017
22382^368929+29835111059Lelio R Paula05/2017
22394^184463-3^184463111058Jean-Louis Charton12/2004
2240111^54298+110111057Norbert Schneider04/2017
2241(4*10^111032-7)/3111033Ray Chandler04/2011
22422^368641-460303110972Enzo Doria06/2015
22432^368619-109087110966Enzo Doria04/2014
22443*2^368489+7110927Lelio R Paula09/2014
224597411!4-2110913Robert Price07/2017
2246(9179*2^368330-1)/35110881Lelio R Paula05/2015
2247(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
22482^368050-64875110795Lelio R Paula05/2017
22492^368048+25110794Lelio R Paula02/2013
225069^60239-2110771Lelio R Paula10/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 09 2017 09:21 (Time in France)

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