PRP Records

Probable Primes Top 10000

(190562 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 ?
1751331^50339-10004126846Enzo Doria07/2012
17522^421363-2790757126843Enzo Doria03/2016
1753(106*10^126839-1)/3126841Serge Batalov12/2014
1754(7*2^421243+1)/39126807Lelio R Paula05/2014
17552^421161-286183126783Enzo Doria06/2015
17562^420939-113935126716Enzo Doria10/2014
1757177^56363-2126703Lelio R Paula10/2017
17582^420741-113659126656Enzo Doria08/2014
17592^420694-21126642Lelio R Paula05/2017
1760(31*2^420556+1)/7126601Lelio R Paula05/2014
17612^420424-59189126561Enzo Doria10/2015
17622^420126+71893126471Enzo Doria04/2016
17632^419866+1877059126393Enzo Doria07/2016
1764F(604711)126377Henri Lifchitz02/2005
17652^419757+72707126360Enzo Doria04/2016
17662^419720-21569126349Enzo Doria07/2013
17672^419637+29126324Henri Lifchitz02/2006
17682^419612+1876741126316Enzo Doria07/2016
17692^419520+2793271126289Enzo Doria03/2016
1770(2^419447-5)/369126264Lelio R Paula05/2014
17712^419328-1859939126231Enzo Doria03/2016
17722^419282-1851507126217Enzo Doria08/2015
17732^419251+1866143126208Enzo Doria03/2016
177411^121185+2126202Robert Price05/2014
1775(23*2^419036-1)/1393126141Lelio R Paula05/2014
17762^418851+23126087Robert Price09/2015
1777(2^418849-9)/2681126083Lelio R Paula05/2014
17782^418829+167126081Lelio R Paula01/2012
1779(31*2^418782-1)/75891126063Lelio R Paula05/2014
1780(19*2^418754-1)/15126058Lelio R Paula05/2014
17812^418319-109501125927Enzo Doria04/2014
17822^418316-112373125926Enzo Doria06/2014
17832^417968+1869811125821Enzo Doria06/2016
17842^417902+63125802Lelio R Paula09/2015
1785(10^125792-91)/9125792Serge Batalov12/2014
17862^417704+77011125742Enzo Doria05/2016
1787(10^125706+149)/3125706Serge Batalov12/2014
17882^417419-115309125656Enzo Doria07/2015
17892^417300+77281125620Enzo Doria05/2016
17902^417095-1657125559Yves Minet07/2014
17912^416773-25125462Lelio R Paula09/2015
1792(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
1793(11*2^416691+1)/43125436Lelio R Paula05/2014
1794(21*2^416566-1)/17125399Lelio R Paula05/2014
17952^416530+1870429125389Enzo Doria05/2016
17962^416490+1875109125376Enzo Doria09/2016
17972^416416-114929125354Enzo Doria05/2015
1798(172*10^125292-1)/9125294Serge Batalov12/2014
17992^416134+1865899125269Enzo Doria03/2016
1800(9*2^415992+1)/13560845125220Lelio R Paula05/2014
1801(23^91943-1)/22125201Robert Price01/2012
180243125^27010-106125185Enzo Doria08/2012
18032^415765-112603125158Enzo Doria06/2014
18042^415290-113591125015Enzo Doria08/2014
18052^415276-460919125011Enzo Doria06/2015
18062^415259+77243125006Enzo Doria05/2016
18072^415144-3683124971Yves Minet10/2011
18082^414874+79124890Lelio R Paula01/2015
1809(2^414765+7)/1389124854Lelio R Paula05/2014
18102^414618+79459124813Enzo Doria06/2016
18112^414432-1846709124757Enzo Doria07/2015
1812(13*2^414274-1)/153124708Lelio R Paula05/2014
18142^414032-5124637Henri Lifchitz07/2006
18132^414032+1872331124637Enzo Doria05/2016
181514120^30009-30009^14120124533Norbert Schneider02/2015
181664^68909-63^68909124463Robert Price07/2013
18172^413387+76253124442Enzo Doria04/2016
1818287117#+391613124424Nicolas PALAU01/2017
1819(27*2^413207-1)/108335124385Lelio R Paula05/2014
18202^412868-120599124286Paul Bourdelais02/2012
182145^75145-2124231Lelio R Paula08/2015
18222^412645-112213124219Enzo Doria06/2014
18232^412248+74611124100Enzo Doria04/2016
18242^412192-3329124083Yves Minet12/2014
1825(25*2^412191-1)/23124082Lelio R Paula05/2014
1826F(593689)124074Henri Lifchitz01/2005
1827(11*2^412161+1)/19124073Lelio R Paula05/2014
18282^411884-113279123990Enzo Doria07/2014
1829(2^411832+1)/257123972Lelio R Paula05/2014
18302^411790-1853531123962Enzo Doria08/2015
1831(5^177337+1)/6123953Paul Bourdelais11/2008
18322^411711-113257123938Enzo Doria07/2014
1833(23*2^411675-1)/3123928Lelio R Paula05/2014
18342^411325-351103123822Enzo Doria06/2015
18352^411052+1872481123739Enzo Doria05/2016
18362^410997+39123723Lelio R Paula05/2014
18372^410596-39123602Lelio R Paula05/2014
18382^410540-115079123585Enzo Doria06/2015
1839(3*2^410392-1)/9229123537Lelio R Paula05/2014
18402^410206-113081123485Enzo Doria07/2014
1841(25*2^410192+1)/10397123478Lelio R Paula04/2014
18422^409909-189123395Enzo Doria05/2014
18432^409896-109043123391Enzo Doria04/2014
18442^409890+75409123390Enzo Doria04/2016
1845133^58076-2123345Lelio R Paula10/2017
1846F(590041)123311Henri Lifchitz01/2005
18472^409566-113501123292Enzo Doria08/2014
18482^409533+77747123282Enzo Doria05/2016
18492^409436-112799123253Enzo Doria06/2014
18502^409225+1873787123189Enzo Doria06/2016
18512^409174+73009123174Enzo Doria04/2016
18522^409058-112685123139Enzo Doria06/2014
18532^408778+77689123055Enzo Doria05/2016
18542^408690-75123028Lelio R Paula11/2013
18552^408574-2787341122994Enzo Doria03/2016
1856Phi(157825,10)122961Maksym Voznyy06/2015
1857(13*2^408283+1)/1665122904Lelio R Paula05/2014
1858(11*2^408100-1)/35122850Lelio R Paula04/2014
1859(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
1860(21*2^407604-1)/215122701Lelio R Paula04/2014
1861(21*2^407433-1)/13122650Lelio R Paula04/2014
1862(73*10^122592-1)/9122593Robert Price01/2015
18632^407179-112075122574Enzo Doria06/2014
1864(21*2^407131+1)/207517523122552Lelio R Paula04/2014
1865(66^67349+1)/67122543Paul Bourdelais09/2017
18662^407008-1867919122522Enzo Doria04/2016
186711^117642-300122512Enzo Doria10/2012
1868(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
18692^406949+72197122504Enzo Doria04/2016
18702^406826-65122467Lelio R Paula11/2013
18712^406821-2797363122466Enzo Doria04/2016
18722^406758-17122447Lelio R Paula11/2013
1873(30^82883-1)/29122427Robert Price12/2011
1874(2^406583-1)/813167122388Jens K. Andersen02/2009
187597^61575-2122336Lelio R Paula12/2014
18762^406298+2799109122308Enzo Doria04/2016
1877(27*2^406241-1)/10277122289Lelio R Paula04/2014
18782^406229-1849993122288Enzo Doria08/2015
18793*10^122274+7122275Robert Price07/2015
18802^406117+1876577122254Enzo Doria07/2016
18813^256199-2^256199122238Mike Oakes06/2005
18822^405774+179149122151Enzo Doria06/2016
18832^405514-3311122072Yves Minet12/2014
18842^405514-115511122072Enzo Doria07/2015
18852^405422-113261122045Enzo Doria07/2014
18862^405173+71237121970Enzo Doria04/2016
1887(2^405016+1)/257121920Lelio R Paula04/2014
18882^404858+71329121875Enzo Doria04/2016
18892^404813-114703121861Enzo Doria04/2015
18902^404764+77791121847Enzo Doria05/2016
1891317^48694+48694^317121787Norbert Schneider08/2015
18922^404536-115259121778Enzo Doria06/2015
18932^404501-631121767Yves Minet07/2012
189463^67620+2121672Lelio R Paula08/2015
1895(17*10^121621+1)/9121622Serge Batalov05/2010
1896(15*2^403912+1)/271121589Lelio R Paula05/2014
18972^403676+76831121519Enzo Doria05/2016
18982^403363-113635121425Enzo Doria08/2014
18992^403336-1861469121417Enzo Doria03/2016
1900p(24442)#/2-64121381Robert Price04/2017
190111^116555-720121380Enzo Doria11/2012
19022^403100-461267121346Enzo Doria07/2015
19032^403093-112213121344Enzo Doria06/2014
1904(316^48539+1)/317121330Eric Chen10/2017
19052^403004+1866361121317Enzo Doria03/2016
19062^402953+89121301Lelio R Paula10/2013
19072^402944-2788319121299Enzo Doria03/2016
1908(27*2^402865+1)/5121276Lelio R Paula04/2014
19092^402828-113183121264Enzo Doria07/2014
1910(17*10^121242+1)/9121243Serge Batalov05/2010
1911(15*2^402757+1)/101121242Lelio R Paula05/2014
19122^402715+1874223121230Enzo Doria06/2016
1913(91^61879+1)/92121222Paul Bourdelais09/2017
19147*10^121144+9121145Robert Price09/2015
19152^401725-113251120932Enzo Doria07/2014
1916(15*2^401677-1)/19120917Lelio R Paula05/2014
19172^401652+73711120910Enzo Doria04/2016
1918(2^401632+3)/79120902Lelio R Paula04/2014
19192^401406-2791331120836Enzo Doria03/2016
1920(28^83497+1)/29120832Robert Price07/2013
19212^401369+1867367120825Enzo Doria03/2016
1922(10^120782+29)/3120782Serge Batalov12/2014
19232^401215-1657120778Yves Minet07/2014
19242^401159+53120761Lelio R Paula10/2013
19252^401031-113047120723Enzo Doria07/2014
1926(29*2^400909-1)/303120685Lelio R Paula04/2014
19272^400571-15120584Lelio R Paula10/2013
1928(10^120574+359)/9120574Serge Batalov12/2014
19292^400424-216413120540Enzo Doria04/2013
1930(17*2^400200-1)/587120471Lelio R Paula05/2014
19312^400166+1874899120462Enzo Doria06/2016
1932(3*2^400045-1)/865120424Lelio R Paula04/2014
19332^399966+73759120402Enzo Doria04/2016
1934(112*10^120395-1)/3120397Serge Batalov12/2014
19352^399918-95120388Lelio R Paula04/2013
19362^399792-1849259120350Enzo Doria08/2015
19379*10^120342-7120343Robert Price09/2015
19382^399526-1861721120270Enzo Doria11/2015
1939(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
19402^399322-2798111120208Enzo Doria04/2016
194172^64693-71^64693120157Robert Price03/2014
19422^399111-28489120145Enzo Doria08/2015
19442^398877+105120074Donovan Johnson01/2006
1943(101*10^120072-87)/7120074Hans Havermann02/2015
1945(88^61751+1)/89120072Paul Bourdelais09/2017
19462^398710+57120024Lelio R Paula04/2013
19472^398691-115057120018Enzo Doria06/2015
1948L(574219)120005Renaud Lifchitz03/2004
19492^398571+60413119982Yves Minet03/2011
1950p(24179)#/2-64119949Robert Price04/2017
19512^398448+1872001119945Enzo Doria05/2016
19528*10^119930-3119931Ray Chandler04/2011
1953(10^119880+179)/9119880Serge Batalov12/2014
1954(9*2^398145+1)/73119853Lelio R Paula04/2014
19552^398029+1872527119819Enzo Doria05/2016
19562^397897-113541119779Enzo Doria08/2014
1957(21*2^397661-1)/27593119705Lelio R Paula04/2014
1958(58^67853-1)/57119653Paul Bourdelais09/2017
19592^397426+73849119638Enzo Doria04/2016
19602^396933-112723119489Enzo Doria06/2014
196111^114738-150119488Enzo Doria10/2012
19622^396790-21119446Lelio R Paula04/2013
1963(2^396633-7)/5119398Lelio R Paula04/2014
1964105^59050+104119352Norbert Schneider11/2016
19652^396374+73729119321Enzo Doria04/2016
19662^396258-459491119286Enzo Doria05/2015
1967(2^395986+5)/76881119199Lelio R Paula04/2014
1968(23*2^395942-1)/91119190Lelio R Paula04/2014
1969(11*2^395548+1)/3119073Lelio R Paula04/2014
1970(30^80599+1)/31119054Robert Price07/2013
19712^395062-109121118926Enzo Doria04/2014
1972(2^394918+78557)/3118882Lelio R Paula01/2015
1973(2^394739+3)/1883118826Lelio R Paula04/2014
19742^394266+71389118686Enzo Doria04/2016
19755^169727+2118635Lelio R Paula08/2013
19762^394034-3118617M. Frind & P. Underwood09/2002
19773^248572-6242118599Enzo Doria05/2014
1978(3*2^393964-1)/181118594Lelio R Paula04/2014
19797^140303-6118570Robert Price11/2014
19802^393427+75683118434Enzo Doria04/2016
19812^393376-114749118418Enzo Doria04/2015
19822^393180+73118359Lelio R Paula04/2013
1983p(23881)#/2+256118328Robert Price05/2017
1984(10^118324+359)/9118324Serge Batalov12/2014
1985p(23879)#/2+64118317Robert Price03/2017
1986(53*10^118216+1)/9118217Serge Batalov11/2010
1987(7*2^392697+1)/15118214Renaud Lifchitz03/2011
1988(157^53819-1)/156118179Alexander Zhirkov06/2016
1989(19*2^392551+1)/3118171Lelio R Paula04/2014
19902^392516-29219118160Enzo Doria07/2015
1991Phi(177231,10)118152Maksym Voznyy09/2015
19922^392413-112123118129Enzo Doria06/2014
1993(2^392342+5)/27118106Lelio R Paula04/2014
19942^392300-1841429118095Enzo Doria06/2015
19952^392220+75241118070Enzo Doria04/2016
19962^391933+5897117984Yves Minet02/2011
19972^391912-1849259117978Enzo Doria08/2015
1998(2^391812+5)/14181117944Lelio R Paula04/2014
1999(7*2^391521+1)/285117858Lelio R Paula04/2014
20002^391324+90901117801Yves Minet02/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 17 2017 23:50 (Time in France)

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