PRP Records

Probable Primes Top 10000

(172213 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 ?
175111^116555-720121380Enzo Doria11/2012
17522^403100-461267121346Enzo Doria07/2015
17532^403093-112213121344Enzo Doria06/2014
17542^403004+1866361121317Enzo Doria03/2016
17552^402953+89121301Lelio R Paula10/2013
17562^402944-2788319121299Enzo Doria03/2016
1757(27*2^402865+1)/5121276Lelio R Paula04/2014
17582^402828-113183121264Enzo Doria07/2014
1759(17*10^121242+1)/9121243Serge Batalov05/2010
1760(15*2^402757+1)/101121242Lelio R Paula05/2014
17612^402715+1874223121230Enzo Doria06/2016
17627*10^121144+9121145Robert Price09/2015
17632^401725-113251120932Enzo Doria07/2014
1764(15*2^401677-1)/19120917Lelio R Paula05/2014
17652^401652+73711120910Enzo Doria04/2016
1766(2^401632+3)/79120902Lelio R Paula04/2014
17672^401406-2791331120836Enzo Doria03/2016
1768(28^83497+1)/29120832Robert Price07/2013
17692^401369+1867367120825Enzo Doria03/2016
1770(10^120782+29)/3120782Serge Batalov12/2014
17712^401215-1657120778Yves Minet07/2014
17722^401159+53120761Lelio R Paula10/2013
17732^401031-113047120723Enzo Doria07/2014
1774(29*2^400909-1)/303120685Lelio R Paula04/2014
17752^400571-15120584Lelio R Paula10/2013
1776(10^120574+359)/9120574Serge Batalov12/2014
17772^400424-216413120540Enzo Doria04/2013
1778(17*2^400200-1)/587120471Lelio R Paula05/2014
17792^400166+1874899120462Enzo Doria06/2016
1780(3*2^400045-1)/865120424Lelio R Paula04/2014
17812^399966+73759120402Enzo Doria04/2016
1782(112*10^120395-1)/3120397Serge Batalov12/2014
17832^399918-95120388Lelio R Paula04/2013
17842^399792-1849259120350Enzo Doria08/2015
17859*10^120342-7120343Robert Price09/2015
17862^399526-1861721120270Enzo Doria11/2015
1787(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
17882^399322-2798111120208Enzo Doria04/2016
178972^64693-71^64693120157Robert Price03/2014
17902^399111-28489120145Enzo Doria08/2015
17922^398877+105120074Donovan Johnson01/2006
1791(101*10^120072-87)/7120074Hans Havermann02/2015
17932^398710+57120024Lelio R Paula04/2013
17942^398691-115057120018Enzo Doria06/2015
1795L(574219)120005Renaud Lifchitz03/2004
17962^398571+60413119982Yves Minet03/2011
17972^398448+1872001119945Enzo Doria05/2016
17988*10^119930-3119931Ray Chandler04/2011
1799(10^119880+179)/9119880Serge Batalov12/2014
1800(9*2^398145+1)/73119853Lelio R Paula04/2014
18012^398029+1872527119819Enzo Doria05/2016
18022^397897-113541119779Enzo Doria08/2014
1803(21*2^397661-1)/27593119705Lelio R Paula04/2014
18042^397426+73849119638Enzo Doria04/2016
18052^396933-112723119489Enzo Doria06/2014
180611^114738-150119488Enzo Doria10/2012
18072^396790-21119446Lelio R Paula04/2013
1808(2^396633-7)/5119398Lelio R Paula04/2014
1809105^59050+104119352Norbert Schneider11/2016
18102^396374+73729119321Enzo Doria04/2016
18112^396258-459491119286Enzo Doria05/2015
1812(2^395986+5)/76881119199Lelio R Paula04/2014
1813(23*2^395942-1)/91119190Lelio R Paula04/2014
1814(11*2^395548+1)/3119073Lelio R Paula04/2014
1815(30^80599+1)/31119054Robert Price07/2013
18162^395062-109121118926Enzo Doria04/2014
1817(2^394918+78557)/3118882Lelio R Paula01/2015
1818(2^394739+3)/1883118826Lelio R Paula04/2014
18192^394266+71389118686Enzo Doria04/2016
18205^169727+2118635Lelio R Paula08/2013
18212^394034-3118617M. Frind & P. Underwood09/2002
18223^248572-6242118599Enzo Doria05/2014
1823(3*2^393964-1)/181118594Lelio R Paula04/2014
18247^140303-6118570Robert Price11/2014
18252^393427+75683118434Enzo Doria04/2016
18262^393376-114749118418Enzo Doria04/2015
18272^393180+73118359Lelio R Paula04/2013
1828(10^118324+359)/9118324Serge Batalov12/2014
1829(53*10^118216+1)/9118217Serge Batalov11/2010
1830(7*2^392697+1)/15118214Renaud Lifchitz03/2011
1831(157^53819-1)/156118179Alexander Zhirkov06/2016
1832(19*2^392551+1)/3118171Lelio R Paula04/2014
18332^392516-29219118160Enzo Doria07/2015
1834Phi(177231,10)118152Maksym Voznyy09/2015
18352^392413-112123118129Enzo Doria06/2014
1836(2^392342+5)/27118106Lelio R Paula04/2014
18372^392300-1841429118095Enzo Doria06/2015
18382^392220+75241118070Enzo Doria04/2016
18392^391933+5897117984Yves Minet02/2011
18402^391912-1849259117978Enzo Doria08/2015
1841(2^391812+5)/14181117944Lelio R Paula04/2014
1842(7*2^391521+1)/285117858Lelio R Paula04/2014
18432^391324+90901117801Yves Minet02/2011
18442^391301-1859923117794Enzo Doria03/2016
1845(2^391115-7)/11791117734Lelio R Paula04/2014
18462^390960+1880881117691Enzo Doria11/2016
18472^390897-1860553117672Enzo Doria11/2015
18482^390889-115003117670Enzo Doria06/2015
18492^390779-30337117637Paul Bourdelais02/2012
185011^112916-780117590Enzo Doria12/2012
1851(16^97613-5^97613)/11117537Robert Price07/2013
1852(17*2^390272+1)/1983117482Lelio R Paula04/2014
185331^78759-30117459Theodore Burton02/2007
18542^389998+37117402Lelio R Paula03/2013
18552^389478+43117245Lelio R Paula03/2013
1856(29*2^389351-1)/9117207Lelio R Paula04/2014
1857(2^389341-7)/3865117200Lelio R Paula03/2014
18582^389033-12797413117111Enzo Doria04/2016
18592^388960-109505117089Enzo Doria04/2014
1860(2^388928-5)/569117077Lelio R Paula03/2014
18612^388888-1529117067Yves Minet01/2013
186210^117059+28879117060Patrick De Geest05/2016
1863(10^117059-71)/1117059Serge Batalov12/2014
18643^245154-6256116969Enzo Doria05/2014
18652^388536-113495116961Enzo Doria08/2014
18662^388469-43116941Lelio R Paula03/2013
1867(7*2^388372-1)/111116911Lelio R Paula04/2014
1868(7*2^388335-1)/25116900Lelio R Paula04/2014
18692^388180+93116854Donovan Johnson07/2008
1870(2^388081+7)/1179116821Lelio R Paula03/2014
18712^387946-113261116784Enzo Doria07/2014
18722^387745+75557116723Enzo Doria04/2016
18732^387554+71455116666Enzo Doria04/2016
1874(2^387447+78557)/365116631Lelio R Paula12/2014
1875(145*10^116610-1)/9116612Serge Batalov12/2014
1876(17*2^387284-1)/59116584Lelio R Paula04/2014
1877(31*2^386968+1)/7116490Lelio R Paula03/2014
18782^386947+1869143116483Enzo Doria05/2016
1879(30^78857-1)/29116480Robert Price12/2011
1880(2^386903-3)/5116469Lelio R Paula03/2014
18812^386389-1864783116315Enzo Doria03/2016
1882(31*2^386231-1)/1711116266Lelio R Paula03/2014
1883(2^386087-5)/40959116220Lelio R Paula03/2014
18842^385969-823116189Yves Minet05/2012
188557^66162+2116173Lelio R Paula08/2013
18862^385854+75049116154Enzo Doria04/2016
18872^385775-109587116130Enzo Doria04/2014
18882^385622+71839116084Enzo Doria04/2016
18892^385564+781116067Lelio R Paula01/2012
18902^385410+71893116020Enzo Doria04/2016
1891(25*2^385091+1)/27115924Lelio R Paula04/2014
18922^384953-111943115883Paul Bourdelais02/2012
189343^70942-2115882Lelio R Paula04/2014
18947*10^115863+3115864Robert Price08/2015
18952^384834+93115847Donovan Johnson07/2008
18962^384809+71297115840Enzo Doria04/2016
1897(7*2^384759-1)/5115825Lelio R Paula04/2014
1898(71*10^115810-17)/9115811Ray Chandler08/2011
1899(97*10^115794-1)/3115796Serge Batalov12/2014
19002^384530+1874305115756Enzo Doria06/2016
1901(3*2^384524-1)/7631115750Lelio R Paula03/2014
19022^384312+81091115690Yves Minet02/2010
19033^242337-4042115625Enzo Doria05/2014
1904(11*2^383859-13)/15115553Renaud Lifchitz03/2011
19052^383780-3149115530Yves Minet10/2014
19062^383560-455115464Yves Minet03/2012
1907(2^383544+5)/3115458Lelio R Paula03/2014
190889^59221-88^59221115445Robert Price06/2015
19092^383347+1869413115399Enzo Doria05/2016
1910(2^383130-7)/131793115329Lelio R Paula03/2014
1911(12^106859+1)/13115320Paul Bourdelais02/2010
19122^383039+1869509115307Enzo Doria05/2016
1913(13*2^382968+1)/7115286Lelio R Paula04/2014
19142^382633+73697115185Enzo Doria04/2016
19152^382509-113593115147Enzo Doria08/2014
19162^382502-2791721115145Enzo Doria03/2016
19179^120590-120590115073Robert Price03/2014
19182^382198+9115054Lelio R Paula03/2013
19192^381883-59197114959Enzo Doria10/2015
19212^381806-4481114936Yves Minet07/2011
19202^381808-1851507114936Enzo Doria08/2015
19222^381774-112373114926Enzo Doria06/2014
19232^381555-109051114860Enzo Doria04/2014
19242^381546-113501114857Enzo Doria08/2014
19252^381360-110429114801Enzo Doria05/2014
19262^381252-115079114769Enzo Doria06/2015
19272^381209-29323114756Enzo Doria07/2015
1928569^41651-568^41651114754Jean-Louis Charton11/2009
19292^381201+1873205114753Enzo Doria06/2016
19302^380974-112991114685Enzo Doria07/2014
193188^58949-87114626Norbert Schneider11/2015
19322^380700+91114603Lelio R Paula03/2013
193310^114575+3^114576114576Mike Oakes09/2010
193410^114575+66561114576Patrick De Geest02/2017
193510^114575-581081114575Patrick De Geest02/2017
19362^380587-115315114569Enzo Doria06/2015
19372^380513-216925114546Enzo Doria05/2014
19382^380451-1840087114528Enzo Doria06/2015
1939(15*2^380388-1)/539114507Lelio R Paula04/2014
19402^380279-461347114476Enzo Doria07/2015
19412^380021+1871147114398Enzo Doria05/2016
19422^380005+1869707114393Enzo Doria05/2016
19432^379958-113297114379Enzo Doria07/2014
19442^379881-109105114356Enzo Doria04/2014
1945(21*2^379857-1)/13114349Lelio R Paula03/2014
194688^58773-87114284Norbert Schneider11/2015
19472^379529-2790283114250Enzo Doria03/2016
19482^379522+1869115114248Enzo Doria05/2016
1949(145*10^114226-1)/9114228Serge Batalov12/2014
19502^379317-115033114186Enzo Doria06/2015
1951(17*2^379246-1)/17407114162Lelio R Paula03/2014
19522*10^113941+9113942Dmitry Domanov11/2010
19532^378272-16565113872Enzo Doria04/2013
19542^378217-109075113855Enzo Doria04/2014
19552^378198+67113849Lelio R Paula03/2013
19562^378173-3249113842Yves Minet12/2014
1957(2^378155-5)/6597113833Lelio R Paula03/2014
19582^378128-262977113828Enzo Doria05/2014
19592^378123-113215113827Enzo Doria07/2014
19606^146274-18893113824Enzo Doria03/2013
19612^378078+75113813Lelio R Paula03/2013
19622^377940+63113772Lelio R Paula03/2013
19632^377941-2785843113772Enzo Doria04/2016
19642^377810+1875109113733Enzo Doria09/2016
19652^377803-1838635113731Enzo Doria05/2015
19662^377799+52223113729Yves Minet08/2010
196711^109190-270113710Enzo Doria12/2012
19687*10^113693+9113694Robert Price09/2015
19692^377408-2798279113612Enzo Doria04/2016
19702^377222+93679113556Yves Minet02/2011
1971262147#+316847113552Makoto Morimoto02/2016
19722^377026-458903113497Enzo Doria04/2015
197335^73477-34^73477113454Robert Price05/2012
19742^376790+27113426Lelio R Paula03/2013
19752^376786-112701113424Enzo Doria06/2014
19762^376731+21113408Lelio R Paula03/2013
19772^376634+1871245113379Enzo Doria05/2016
1978(4^188318+17)/3113379Robert Price02/2017
19792^376576-344369113361Enzo Doria07/2015
1980(17*2^376526-1)/223113345Lelio R Paula03/2014
1981(27*2^376441-1)/811113319Lelio R Paula03/2014
19822^376128-21237113226Enzo Doria06/2013
19832^375638-1787171113079Enzo Doria03/2016
19842^375537+4847113048Yves Minet02/2011
1985(17^91837+16^91837)/33113000Robert Price08/2013
19865*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
19872^375350-3221112992Yves Minet07/2011
1988(13*2^375306+1)/7112979Lelio R Paula03/2014
19892^375305+76757112979Enzo Doria05/2016
19902^375258+1874989112964Enzo Doria07/2016
1991(29^77237-1)/28112950Robert Price04/2012
19922^375154+74959112933Enzo Doria04/2016
19932^374993-2787163112885Enzo Doria11/2015
1994123^53970+2112793Lelio R Paula06/2013
19952^374441-21049112718Enzo Doria06/2013
1996(2^374321+1)/3112682H.&R. Lifchitz12/2000
1997(13^101089-1)/12112607Paul Bourdelais03/2010
19983^236011-8828112606Enzo Doria05/2014
199939^70666+2112435Lelio R Paula11/2013
2000(2^373350-7)/3112390Lelio R Paula03/2014


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!