PRP Records

Probable Primes Top 10000

(181746 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 ?
17512^415290-113591125015Enzo Doria08/2014
17522^415276-460919125011Enzo Doria06/2015
17532^415259+77243125006Enzo Doria05/2016
17542^415144-3683124971Yves Minet10/2011
17552^414874+79124890Lelio R Paula01/2015
1756(2^414765+7)/1389124854Lelio R Paula05/2014
17572^414618+79459124813Enzo Doria06/2016
17582^414432-1846709124757Enzo Doria07/2015
1759(13*2^414274-1)/153124708Lelio R Paula05/2014
17602^414032-5124637Henri Lifchitz07/2006
17612^414032+1872331124637Enzo Doria05/2016
176214120^30009-30009^14120124533Norbert Schneider02/2015
176364^68909-63^68909124463Robert Price07/2013
17642^413387+76253124442Enzo Doria04/2016
1765287117#+391613124424Nicolas PALAU01/2017
1766(27*2^413207-1)/108335124385Lelio R Paula05/2014
17672^412868-120599124286Paul Bourdelais02/2012
176845^75145-2124231Lelio R Paula08/2015
17692^412645-112213124219Enzo Doria06/2014
17702^412248+74611124100Enzo Doria04/2016
17712^412192-3329124083Yves Minet12/2014
1772(25*2^412191-1)/23124082Lelio R Paula05/2014
1773F(593689)124074Henri Lifchitz01/2005
1774(11*2^412161+1)/19124073Lelio R Paula05/2014
17752^411884-113279123990Enzo Doria07/2014
1776(2^411832+1)/257123972Lelio R Paula05/2014
17772^411790-1853531123962Enzo Doria08/2015
1778(5^177337+1)/6123953Paul Bourdelais11/2008
17792^411711-113257123938Enzo Doria07/2014
1780(23*2^411675-1)/3123928Lelio R Paula05/2014
17812^411325-351103123822Enzo Doria06/2015
17822^411052+1872481123739Enzo Doria05/2016
17832^410997+39123723Lelio R Paula05/2014
17842^410596-39123602Lelio R Paula05/2014
17852^410540-115079123585Enzo Doria06/2015
1786(3*2^410392-1)/9229123537Lelio R Paula05/2014
17872^410206-113081123485Enzo Doria07/2014
1788(25*2^410192+1)/10397123478Lelio R Paula04/2014
17892^409909-189123395Enzo Doria05/2014
17902^409896-109043123391Enzo Doria04/2014
17912^409890+75409123390Enzo Doria04/2016
1792F(590041)123311Henri Lifchitz01/2005
17932^409566-113501123292Enzo Doria08/2014
17942^409533+77747123282Enzo Doria05/2016
17952^409436-112799123253Enzo Doria06/2014
17962^409225+1873787123189Enzo Doria06/2016
17972^409174+73009123174Enzo Doria04/2016
17982^409058-112685123139Enzo Doria06/2014
17992^408778+77689123055Enzo Doria05/2016
18002^408690-75123028Lelio R Paula11/2013
18012^408574-2787341122994Enzo Doria03/2016
1802Phi(157825,10)122961Maksym Voznyy06/2015
1803(13*2^408283+1)/1665122904Lelio R Paula05/2014
1804(11*2^408100-1)/35122850Lelio R Paula04/2014
1805(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
1806(21*2^407604-1)/215122701Lelio R Paula04/2014
1807(21*2^407433-1)/13122650Lelio R Paula04/2014
1808(73*10^122592-1)/9122593Robert Price01/2015
18092^407179-112075122574Enzo Doria06/2014
1810(21*2^407131+1)/207517523122552Lelio R Paula04/2014
1811(66^67349+1)/67122543Paul Bourdelais09/2017
18122^407008-1867919122522Enzo Doria04/2016
181311^117642-300122512Enzo Doria10/2012
18142^406949+72197122504Enzo Doria04/2016
18152^406826-65122467Lelio R Paula11/2013
18162^406821-2797363122466Enzo Doria04/2016
18172^406758-17122447Lelio R Paula11/2013
1818(30^82883-1)/29122427Robert Price12/2011
1819(2^406583-1)/813167122388Jens K. Andersen02/2009
182097^61575-2122336Lelio R Paula12/2014
18212^406298+2799109122308Enzo Doria04/2016
1822(27*2^406241-1)/10277122289Lelio R Paula04/2014
18232^406229-1849993122288Enzo Doria08/2015
18243*10^122274+7122275Robert Price07/2015
18252^406117+1876577122254Enzo Doria07/2016
18263^256199-2^256199122238Mike Oakes06/2005
18272^405774+179149122151Enzo Doria06/2016
18282^405514-3311122072Yves Minet12/2014
18292^405514-115511122072Enzo Doria07/2015
18302^405422-113261122045Enzo Doria07/2014
18312^405173+71237121970Enzo Doria04/2016
1832(2^405016+1)/257121920Lelio R Paula04/2014
18332^404858+71329121875Enzo Doria04/2016
18342^404813-114703121861Enzo Doria04/2015
18352^404764+77791121847Enzo Doria05/2016
1836317^48694+48694^317121787Norbert Schneider08/2015
18372^404536-115259121778Enzo Doria06/2015
18382^404501-631121767Yves Minet07/2012
183963^67620+2121672Lelio R Paula08/2015
1840(17*10^121621+1)/9121622Serge Batalov05/2010
1841(15*2^403912+1)/271121589Lelio R Paula05/2014
18422^403676+76831121519Enzo Doria05/2016
18432^403363-113635121425Enzo Doria08/2014
18442^403336-1861469121417Enzo Doria03/2016
1845p(24442)#/2-64121381Robert Price04/2017
184611^116555-720121380Enzo Doria11/2012
18472^403100-461267121346Enzo Doria07/2015
18482^403093-112213121344Enzo Doria06/2014
18492^403004+1866361121317Enzo Doria03/2016
18502^402953+89121301Lelio R Paula10/2013
18512^402944-2788319121299Enzo Doria03/2016
1852(27*2^402865+1)/5121276Lelio R Paula04/2014
18532^402828-113183121264Enzo Doria07/2014
1854(17*10^121242+1)/9121243Serge Batalov05/2010
1855(15*2^402757+1)/101121242Lelio R Paula05/2014
18562^402715+1874223121230Enzo Doria06/2016
1857(91^61879+1)/92121222Paul Bourdelais09/2017
18587*10^121144+9121145Robert Price09/2015
18592^401725-113251120932Enzo Doria07/2014
1860(15*2^401677-1)/19120917Lelio R Paula05/2014
18612^401652+73711120910Enzo Doria04/2016
1862(2^401632+3)/79120902Lelio R Paula04/2014
18632^401406-2791331120836Enzo Doria03/2016
1864(28^83497+1)/29120832Robert Price07/2013
18652^401369+1867367120825Enzo Doria03/2016
1866(10^120782+29)/3120782Serge Batalov12/2014
18672^401215-1657120778Yves Minet07/2014
18682^401159+53120761Lelio R Paula10/2013
18692^401031-113047120723Enzo Doria07/2014
1870(29*2^400909-1)/303120685Lelio R Paula04/2014
18712^400571-15120584Lelio R Paula10/2013
1872(10^120574+359)/9120574Serge Batalov12/2014
18732^400424-216413120540Enzo Doria04/2013
1874(17*2^400200-1)/587120471Lelio R Paula05/2014
18752^400166+1874899120462Enzo Doria06/2016
1876(3*2^400045-1)/865120424Lelio R Paula04/2014
18772^399966+73759120402Enzo Doria04/2016
1878(112*10^120395-1)/3120397Serge Batalov12/2014
18792^399918-95120388Lelio R Paula04/2013
18802^399792-1849259120350Enzo Doria08/2015
18819*10^120342-7120343Robert Price09/2015
18822^399526-1861721120270Enzo Doria11/2015
1883(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
18842^399322-2798111120208Enzo Doria04/2016
188572^64693-71^64693120157Robert Price03/2014
18862^399111-28489120145Enzo Doria08/2015
18882^398877+105120074Donovan Johnson01/2006
1887(101*10^120072-87)/7120074Hans Havermann02/2015
1889(88^61751+1)/89120072Paul Bourdelais09/2017
18902^398710+57120024Lelio R Paula04/2013
18912^398691-115057120018Enzo Doria06/2015
1892L(574219)120005Renaud Lifchitz03/2004
18932^398571+60413119982Yves Minet03/2011
1894p(24179)#/2-64119949Robert Price04/2017
18952^398448+1872001119945Enzo Doria05/2016
18968*10^119930-3119931Ray Chandler04/2011
1897(10^119880+179)/9119880Serge Batalov12/2014
1898(9*2^398145+1)/73119853Lelio R Paula04/2014
18992^398029+1872527119819Enzo Doria05/2016
19002^397897-113541119779Enzo Doria08/2014
1901(21*2^397661-1)/27593119705Lelio R Paula04/2014
1902(58^67853-1)/57119653Paul Bourdelais09/2017
19032^397426+73849119638Enzo Doria04/2016
19042^396933-112723119489Enzo Doria06/2014
190511^114738-150119488Enzo Doria10/2012
19062^396790-21119446Lelio R Paula04/2013
1907(2^396633-7)/5119398Lelio R Paula04/2014
1908105^59050+104119352Norbert Schneider11/2016
19092^396374+73729119321Enzo Doria04/2016
19102^396258-459491119286Enzo Doria05/2015
1911(2^395986+5)/76881119199Lelio R Paula04/2014
1912(23*2^395942-1)/91119190Lelio R Paula04/2014
1913(11*2^395548+1)/3119073Lelio R Paula04/2014
1914(30^80599+1)/31119054Robert Price07/2013
19152^395062-109121118926Enzo Doria04/2014
1916(2^394918+78557)/3118882Lelio R Paula01/2015
1917(2^394739+3)/1883118826Lelio R Paula04/2014
19182^394266+71389118686Enzo Doria04/2016
19195^169727+2118635Lelio R Paula08/2013
19202^394034-3118617M. Frind & P. Underwood09/2002
19213^248572-6242118599Enzo Doria05/2014
1922(3*2^393964-1)/181118594Lelio R Paula04/2014
19237^140303-6118570Robert Price11/2014
19242^393427+75683118434Enzo Doria04/2016
19252^393376-114749118418Enzo Doria04/2015
19262^393180+73118359Lelio R Paula04/2013
1927p(23881)#/2+256118328Robert Price05/2017
1928(10^118324+359)/9118324Serge Batalov12/2014
1929p(23879)#/2+64118317Robert Price03/2017
1930(53*10^118216+1)/9118217Serge Batalov11/2010
1931(7*2^392697+1)/15118214Renaud Lifchitz03/2011
1932(157^53819-1)/156118179Alexander Zhirkov06/2016
1933(19*2^392551+1)/3118171Lelio R Paula04/2014
19342^392516-29219118160Enzo Doria07/2015
1935Phi(177231,10)118152Maksym Voznyy09/2015
19362^392413-112123118129Enzo Doria06/2014
1937(2^392342+5)/27118106Lelio R Paula04/2014
19382^392300-1841429118095Enzo Doria06/2015
19392^392220+75241118070Enzo Doria04/2016
19402^391933+5897117984Yves Minet02/2011
19412^391912-1849259117978Enzo Doria08/2015
1942(2^391812+5)/14181117944Lelio R Paula04/2014
1943(7*2^391521+1)/285117858Lelio R Paula04/2014
19442^391324+90901117801Yves Minet02/2011
19452^391301-1859923117794Enzo Doria03/2016
1946(2^391115-7)/11791117734Lelio R Paula04/2014
19472^390960+1880881117691Enzo Doria11/2016
19482^390897-1860553117672Enzo Doria11/2015
19492^390889-115003117670Enzo Doria06/2015
19502^390779-30337117637Paul Bourdelais02/2012
195111^112916-780117590Enzo Doria12/2012
1952(16^97613-5^97613)/11117537Robert Price07/2013
1953(17*2^390272+1)/1983117482Lelio R Paula04/2014
195431^78759-30117459Theodore Burton02/2007
19552^389998+37117402Lelio R Paula03/2013
19562^389478+43117245Lelio R Paula03/2013
1957(29*2^389351-1)/9117207Lelio R Paula04/2014
1958(2^389341-7)/3865117200Lelio R Paula03/2014
19592^389033-12797413117111Enzo Doria04/2016
19602^388960-109505117089Enzo Doria04/2014
1961(2^388928-5)/569117077Lelio R Paula03/2014
19622^388888-1529117067Yves Minet01/2013
196310^117059+28879117060Patrick De Geest05/2016
1964(10^117059-71)/1117059Serge Batalov12/2014
19653^245154-6256116969Enzo Doria05/2014
19662^388536-113495116961Enzo Doria08/2014
19672^388469-43116941Lelio R Paula03/2013
1968(7*2^388372-1)/111116911Lelio R Paula04/2014
1969(7*2^388335-1)/25116900Lelio R Paula04/2014
19702^388180+93116854Donovan Johnson07/2008
1971(2^388081+7)/1179116821Lelio R Paula03/2014
19722^387946-113261116784Enzo Doria07/2014
19732^387745+75557116723Enzo Doria04/2016
19742^387554+71455116666Enzo Doria04/2016
1975(2^387447+78557)/365116631Lelio R Paula12/2014
1976(145*10^116610-1)/9116612Serge Batalov12/2014
1977(17*2^387284-1)/59116584Lelio R Paula04/2014
1978(31*2^386968+1)/7116490Lelio R Paula03/2014
19792^386947+1869143116483Enzo Doria05/2016
1980(30^78857-1)/29116480Robert Price12/2011
1981(2^386903-3)/5116469Lelio R Paula03/2014
19822^386389-1864783116315Enzo Doria03/2016
1983(31*2^386231-1)/1711116266Lelio R Paula03/2014
1984(2^386087-5)/40959116220Lelio R Paula03/2014
19852^385969-823116189Yves Minet05/2012
198657^66162+2116173Lelio R Paula08/2013
19872^385854+75049116154Enzo Doria04/2016
19882^385775-109587116130Enzo Doria04/2014
19892^385622+71839116084Enzo Doria04/2016
19902^385564+781116067Lelio R Paula01/2012
19912^385410+71893116020Enzo Doria04/2016
1992(25*2^385091+1)/27115924Lelio R Paula04/2014
19932^384953-111943115883Paul Bourdelais02/2012
199443^70942-2115882Lelio R Paula04/2014
19957*10^115863+3115864Robert Price08/2015
19962^384834+93115847Donovan Johnson07/2008
19972^384809+71297115840Enzo Doria04/2016
1998(7*2^384759-1)/5115825Lelio R Paula04/2014
1999(71*10^115810-17)/9115811Ray Chandler08/2011
2000(97*10^115794-1)/3115796Serge Batalov12/2014


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!