PRP Records

Probable Primes Top 10000

(218736 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 ?
200143125^27010-106125185Enzo Doria08/2012
20022^415765-112603125158Enzo Doria06/2014
20032^415290-113591125015Enzo Doria08/2014
20042^415276-460919125011Enzo Doria06/2015
20052^415259+77243125006Enzo Doria05/2016
20062^415144-3683124971Yves Minet10/2011
20072^414874+79124890Lelio R Paula01/2015
2008(2^414765+7)/1389124854Lelio R Paula05/2014
20092^414618+79459124813Enzo Doria06/2016
20102^414432-1846709124757Enzo Doria07/2015
20112*10^124751-51124752Robert Price04/2018
2012(13*2^414274-1)/153124708Lelio R Paula05/2014
2013(7*10^124648+197)/3124649Robert Price07/2018
20152^414032-5124637Henri Lifchitz07/2006
20142^414032+1872331124637Enzo Doria05/2016
201614120^30009-30009^14120124533Norbert Schneider02/2015
201764^68909-63^68909124463Robert Price07/2013
20182^413387+76253124442Enzo Doria04/2016
2019287117#+391613124424Nicolas PALAU01/2017
2020(4*10^124420+83)/3124421Robert Price02/2018
2021(27*2^413207-1)/108335124385Lelio R Paula05/2014
20222^412868-120599124286Paul Bourdelais02/2012
202345^75145-2124231Lelio R Paula08/2015
20242^412645-112213124219Enzo Doria06/2014
20252^412248+74611124100Enzo Doria04/2016
2026(22*10^124096-13)/9124097Robert Price06/2018
20272^412192-3329124083Yves Minet12/2014
2028(25*2^412191-1)/23124082Lelio R Paula05/2014
2029F(593689)124074Henri Lifchitz01/2005
2030(11*2^412161+1)/19124073Lelio R Paula05/2014
20312^411884-113279123990Enzo Doria07/2014
2032(2^411832+1)/257123972Lelio R Paula05/2014
2033(26*10^123970-89)/9123971Robert Price06/2018
20342^411790-1853531123962Enzo Doria08/2015
2035(5^177337+1)/6123953Paul Bourdelais11/2008
20362^411711-113257123938Enzo Doria07/2014
2037(23*2^411675-1)/3123928Lelio R Paula05/2014
20382^411325-351103123822Enzo Doria06/2015
20392^411052+1872481123739Enzo Doria05/2016
20402^410997+39123723Lelio R Paula05/2014
20412^410596-39123602Lelio R Paula05/2014
20422^410540-115079123585Enzo Doria06/2015
2043(7*10^123563+107)/3123564Robert Price02/2018
2044(3*2^410392-1)/9229123537Lelio R Paula05/2014
20452^410206-113081123485Enzo Doria07/2014
2046(25*2^410192+1)/10397123478Lelio R Paula04/2014
20472^409909-189123395Enzo Doria05/2014
20482^409896-109043123391Enzo Doria04/2014
20492^409890+75409123390Enzo Doria04/2016
2050133^58076-2123345Lelio R Paula10/2017
2051F(590041)123311Henri Lifchitz01/2005
20522^409566-113501123292Enzo Doria08/2014
20532^409533+77747123282Enzo Doria05/2016
20542^409436-112799123253Enzo Doria06/2014
20552^409225+1873787123189Enzo Doria06/2016
20562^409174+73009123174Enzo Doria04/2016
20572^409058-112685123139Enzo Doria06/2014
20582^408778+77689123055Enzo Doria05/2016
20592^408690-75123028Lelio R Paula11/2013
20602^408574-2787341122994Enzo Doria03/2016
2061Phi(157825,10)122961Maksym Voznyy06/2015
2062(13*2^408283+1)/1665122904Lelio R Paula05/2014
2063(11*2^408100-1)/35122850Lelio R Paula04/2014
2064(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2065(32*10^122733-77)/9122734Robert Price06/2018
2066(21*2^407604-1)/215122701Lelio R Paula04/2014
2067(21*2^407433-1)/13122650Lelio R Paula04/2014
2068(73*10^122592-1)/9122593Robert Price01/2015
2069(5*10^122592+91)/3122593Robert Price04/2018
20702^407179-112075122574Enzo Doria06/2014
2071(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2072(66^67349+1)/67122543Paul Bourdelais09/2017
20732^407008-1867919122522Enzo Doria04/2016
207411^117642-300122512Enzo Doria10/2012
2075(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
20762^406949+72197122504Enzo Doria04/2016
20772^406826-65122467Lelio R Paula11/2013
20782^406821-2797363122466Enzo Doria04/2016
20792^406758-17122447Lelio R Paula11/2013
2080(30^82883-1)/29122427Robert Price12/2011
2081(2^406583-1)/813167122388Jens K. Andersen02/2009
20823*10^122345-97122346Robert Price07/2018
208397^61575-2122336Lelio R Paula12/2014
20842^406298+2799109122308Enzo Doria04/2016
2085(27*2^406241-1)/10277122289Lelio R Paula04/2014
20862^406229-1849993122288Enzo Doria08/2015
20873*10^122274+7122275Robert Price07/2015
20882^406117+1876577122254Enzo Doria07/2016
20893^256199-2^256199122238Mike Oakes06/2005
20902^405992-78557122216Jorge Menendez03/2018
2091(8*10^122203+43)/3122204Robert Price06/2018
20922^405774+179149122151Enzo Doria06/2016
20932^405514-3311122072Yves Minet12/2014
20942^405514-115511122072Enzo Doria07/2015
20952^405422-113261122045Enzo Doria07/2014
20962^405173+71237121970Enzo Doria04/2016
2097(2^405016+1)/257121920Lelio R Paula04/2014
20982^404858+71329121875Enzo Doria04/2016
20992^404813-114703121861Enzo Doria04/2015
21002^404764+77791121847Enzo Doria05/2016
2101317^48694+48694^317121787Norbert Schneider08/2015
21022^404536-115259121778Enzo Doria06/2015
21032^404501-631121767Yves Minet07/2012
210463^67620+2121672Lelio R Paula08/2015
2105(17*10^121621+1)/9121622Serge Batalov05/2010
2106(15*2^403912+1)/271121589Lelio R Paula05/2014
2107(10^121543-79)/3121543Robert Price01/2018
21082^403676+76831121519Enzo Doria05/2016
2109(7*10^121487+143)/3121488Robert Price03/2018
21102^403363-113635121425Enzo Doria08/2014
21112^403336-1861469121417Enzo Doria03/2016
2112p(24442)#/2-64121381Robert Price04/2017
211311^116555-720121380Enzo Doria11/2012
21142^403100-461267121346Enzo Doria07/2015
21152^403093-112213121344Enzo Doria06/2014
2116(316^48539+1)/317121330Eric Chen10/2017
21172^403004+1866361121317Enzo Doria03/2016
21182^402953+89121301Lelio R Paula10/2013
21192^402944-2788319121299Enzo Doria03/2016
2120(27*2^402865+1)/5121276Lelio R Paula04/2014
21212^402828-113183121264Enzo Doria07/2014
2122(17*10^121242+1)/9121243Serge Batalov05/2010
2123(15*2^402757+1)/101121242Lelio R Paula05/2014
21252^402715+1874223121230Enzo Doria06/2016
2124(35*10^121229-593)/9121230Robert Price07/2018
2126(91^61879+1)/92121222Paul Bourdelais09/2017
21277*10^121144+9121145Robert Price09/2015
21282^401725-113251120932Enzo Doria07/2014
2129(15*2^401677-1)/19120917Lelio R Paula05/2014
21302^401652+73711120910Enzo Doria04/2016
2131(2^401632+3)/79120902Lelio R Paula04/2014
21322^401406-2791331120836Enzo Doria03/2016
2133(28^83497+1)/29120832Robert Price07/2013
21342^401369+1867367120825Enzo Doria03/2016
2135(10^120782+29)/3120782Serge Batalov12/2014
21362^401215-1657120778Yves Minet07/2014
21372^401159+53120761Lelio R Paula10/2013
21382^401031-113047120723Enzo Doria07/2014
2139(29*2^400909-1)/303120685Lelio R Paula04/2014
21402^400571-15120584Lelio R Paula10/2013
2141(10^120574+359)/9120574Serge Batalov12/2014
21422^400424-216413120540Enzo Doria04/2013
2143(17*2^400200-1)/587120471Lelio R Paula05/2014
21442^400166+1874899120462Enzo Doria06/2016
2145(3*2^400045-1)/865120424Lelio R Paula04/2014
21462^399966+73759120402Enzo Doria04/2016
2147(112*10^120395-1)/3120397Serge Batalov12/2014
21482^399918-95120388Lelio R Paula04/2013
21492^399792-1849259120350Enzo Doria08/2015
21509*10^120342-7120343Robert Price09/2015
21512^399526-1861721120270Enzo Doria11/2015
2152(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
21532^399322-2798111120208Enzo Doria04/2016
215472^64693-71^64693120157Robert Price03/2014
21552^399111-28489120145Enzo Doria08/2015
21572^398877+105120074Donovan Johnson01/2006
2156(101*10^120072-87)/7120074Hans Havermann02/2015
2158(88^61751+1)/89120072Paul Bourdelais09/2017
21592^398710+57120024Lelio R Paula04/2013
21602^398691-115057120018Enzo Doria06/2015
2161L(574219)120005Renaud Lifchitz03/2004
21622^398571+60413119982Yves Minet03/2011
2163p(24179)#/2-64119949Robert Price04/2017
21642^398448+1872001119945Enzo Doria05/2016
21658*10^119930-3119931Ray Chandler04/2011
2166(10^119880+179)/9119880Serge Batalov12/2014
2167(9*2^398145+1)/73119853Lelio R Paula04/2014
2168(10^119836+77)/3119836Robert Price01/2018
21692^398029+1872527119819Enzo Doria05/2016
21702^397897-113541119779Enzo Doria08/2014
2171(21*2^397661-1)/27593119705Lelio R Paula04/2014
2172(58^67853-1)/57119653Paul Bourdelais09/2017
21732^397426+73849119638Enzo Doria04/2016
21742^396933-112723119489Enzo Doria06/2014
217511^114738-150119488Enzo Doria10/2012
2176(4*10^119474+149)/9119474Robert Price04/2018
21772^396790-21119446Lelio R Paula04/2013
2178(2^396633-7)/5119398Lelio R Paula04/2014
2179105^59050+104119352Norbert Schneider11/2016
21802^396374+73729119321Enzo Doria04/2016
21812^396258-459491119286Enzo Doria05/2015
21822^396128-396128-1119247Karsten Bonath06/2018
2183(2^395986+5)/76881119199Lelio R Paula04/2014
2184(23*2^395942-1)/91119190Lelio R Paula04/2014
2185(11*2^395548+1)/3119073Lelio R Paula04/2014
2186(30^80599+1)/31119054Robert Price07/2013
21872^395062-109121118926Enzo Doria04/2014
2188(2^394918+78557)/3118882Lelio R Paula01/2015
2189(2^394739+3)/1883118826Lelio R Paula04/2014
21902^394266+71389118686Enzo Doria04/2016
21912^394215-51261118671Tony Prest / Never Odd Or Even04/2018
2192(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
2193(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
2194(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
2195(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
2196(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
2197(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
21985^169727+2118635Lelio R Paula08/2013
21992^394034-3118617M. Frind & P. Underwood09/2002
22003^248572-6242118599Enzo Doria05/2014
2201(3*2^393964-1)/181118594Lelio R Paula04/2014
22027^140303-6118570Robert Price11/2014
22032^393427+75683118434Enzo Doria04/2016
22042^393376-114749118418Enzo Doria04/2015
22052^393180+73118359Lelio R Paula04/2013
2206p(23881)#/2+256118328Robert Price05/2017
2207(10^118324+359)/9118324Serge Batalov12/2014
2208p(23879)#/2+64118317Robert Price03/2017
2209(53*10^118216+1)/9118217Serge Batalov11/2010
2210(7*2^392697+1)/15118214Renaud Lifchitz03/2011
2211(157^53819-1)/156118179Alexander Zhirkov06/2016
2212(19*2^392551+1)/3118171Lelio R Paula04/2014
22132^392516-29219118160Enzo Doria07/2015
2214Phi(177231,10)118152Maksym Voznyy09/2015
22152^392413-112123118129Enzo Doria06/2014
2216(2^392342+5)/27118106Lelio R Paula04/2014
22172^392300-1841429118095Enzo Doria06/2015
22182^392220+75241118070Enzo Doria04/2016
221910^118009+664447118010Patrick De Geest07/2018
222010^118009-20001118009Robert Price01/2018
22212^391933+5897117984Yves Minet02/2011
22222^391912-1849259117978Enzo Doria08/2015
2223(2^391812+5)/14181117944Lelio R Paula04/2014
2224(7*2^391521+1)/285117858Lelio R Paula04/2014
22252^391324+90901117801Yves Minet02/2011
22262^391301-1859923117794Enzo Doria03/2016
22272^391261-4131117782Yves Minet02/2018
2228(2^391115-7)/11791117734Lelio R Paula04/2014
22292^390960+1880881117691Enzo Doria11/2016
22302^390897-1860553117672Enzo Doria11/2015
22312^390889-115003117670Enzo Doria06/2015
22322^390779-30337117637Paul Bourdelais02/2012
223311^112916-780117590Enzo Doria12/2012
2234(16^97613-5^97613)/11117537Robert Price07/2013
2235(17*2^390272+1)/1983117482Lelio R Paula04/2014
223631^78759-30117459Theodore Burton02/2007
22372^389998+37117402Lelio R Paula03/2013
22382^389478+43117245Lelio R Paula03/2013
2239(29*2^389351-1)/9117207Lelio R Paula04/2014
2240(2^389341-7)/3865117200Lelio R Paula03/2014
224110^117142+209223117143Patrick De Geest04/2018
224310^117142-1000000001117142Robert Price03/2018
224210^117142-966057117142Patrick De Geest04/2018
224410^117135+360577117136Patrick De Geest07/2018
224510^117135-401117135Robert Price01/2018
22464*10^117123+79117124Robert Price08/2018
22472^389033-12797413117111Enzo Doria04/2016
22482^388960-109505117089Enzo Doria04/2014
2249(2^388928-5)/569117077Lelio R Paula03/2014
22502^388888-1529117067Yves Minet01/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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