PRP Records

Probable Primes Top 10000

(225451 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 ?
20012^419520+2793271126289Enzo Doria03/2016
2002(2^419447-5)/369126264Lelio R Paula05/2014
20032^419328-1859939126231Enzo Doria03/2016
20042^419282-1851507126217Enzo Doria08/2015
20052^419251+1866143126208Enzo Doria03/2016
200611^121185+2126202Robert Price05/2014
2007(23*2^419036-1)/1393126141Lelio R Paula05/2014
20082^418851+23126087Robert Price09/2015
2009(2^418849-9)/2681126083Lelio R Paula05/2014
20102^418829+167126081Lelio R Paula01/2012
2011(31*2^418782-1)/75891126063Lelio R Paula05/2014
2012(19*2^418754-1)/15126058Lelio R Paula05/2014
20132^418319-109501125927Enzo Doria04/2014
20142^418316-112373125926Enzo Doria06/2014
2015(8*10^125894-29)/3125895Robert Price07/2018
2016(26*10^125886-413)/9125887Robert Price05/2018
20172^417968+1869811125821Enzo Doria06/2016
20182^417902+63125802Lelio R Paula09/2015
2019(10^125792-91)/9125792Serge Batalov12/2014
2020(35*10^125754-593)/9125755Robert Price07/2018
2021(32*10^125751-77)/9125752Robert Price06/2018
20222^417704+77011125742Enzo Doria05/2016
2023(10^125706+149)/3125706Serge Batalov12/2014
20242^417419-115309125656Enzo Doria07/2015
20252^417300+77281125620Enzo Doria05/2016
20262^417095-1657125559Yves Minet07/2014
20272^416773-25125462Lelio R Paula09/2015
2028(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2029(11*2^416691+1)/43125436Lelio R Paula05/2014
20302^416641-2*416641+1125422Robert Price05/2018
2031(21*2^416566-1)/17125399Lelio R Paula05/2014
20322^416530+1870429125389Enzo Doria05/2016
20332^416490+1875109125376Enzo Doria09/2016
20342^416416-114929125354Enzo Doria05/2015
2035(172*10^125292-1)/9125294Serge Batalov12/2014
20362^416134+1865899125269Enzo Doria03/2016
2037(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2038(23^91943-1)/22125201Robert Price01/2012
203943125^27010-106125185Enzo Doria08/2012
2040(38*10^125166+349)/9125167Robert Price10/2018
20412^415765-112603125158Enzo Doria06/2014
20422^415290-113591125015Enzo Doria08/2014
20432^415276-460919125011Enzo Doria06/2015
20442^415259+77243125006Enzo Doria05/2016
20452^415144-3683124971Yves Minet10/2011
20462^414874+79124890Lelio R Paula01/2015
2047(2^414765+7)/1389124854Lelio R Paula05/2014
20482^414618+79459124813Enzo Doria06/2016
20492^414432-1846709124757Enzo Doria07/2015
20502*10^124751-51124752Robert Price04/2018
2051(13*2^414274-1)/153124708Lelio R Paula05/2014
2052(7*10^124648+197)/3124649Robert Price07/2018
20542^414032-5124637Henri Lifchitz07/2006
20532^414032+1872331124637Enzo Doria05/2016
205514120^30009-30009^14120124533Norbert Schneider02/2015
205664^68909-63^68909124463Robert Price07/2013
20572^413387+76253124442Enzo Doria04/2016
20582^413352+524287124432Paul Underwood09/2018
2059287117#+391613124424Nicolas PALAU01/2017
2060(4*10^124420+83)/3124421Robert Price02/2018
2061(27*2^413207-1)/108335124385Lelio R Paula05/2014
20622^412868-120599124286Paul Bourdelais02/2012
206345^75145-2124231Lelio R Paula08/2015
20642^412645-112213124219Enzo Doria06/2014
20652^412248+74611124100Enzo Doria04/2016
2066(22*10^124096-13)/9124097Robert Price06/2018
20672^412192-3329124083Yves Minet12/2014
2068(25*2^412191-1)/23124082Lelio R Paula05/2014
2069F(593689)124074Henri Lifchitz01/2005
2070(11*2^412161+1)/19124073Lelio R Paula05/2014
20712^411884-113279123990Enzo Doria07/2014
2072(2^411832+1)/257123972Lelio R Paula05/2014
2073(26*10^123970-89)/9123971Robert Price06/2018
20742^411790-1853531123962Enzo Doria08/2015
2075(5^177337+1)/6123953Paul Bourdelais11/2008
20762^411711-113257123938Enzo Doria07/2014
2077(23*2^411675-1)/3123928Lelio R Paula05/2014
2078(11*10^123899-179)/3123900Robert Price09/2018
20792^411325-351103123822Enzo Doria06/2015
20802^411052+1872481123739Enzo Doria05/2016
20812^410997+39123723Lelio R Paula05/2014
20822^410596-39123602Lelio R Paula05/2014
20832^410540-115079123585Enzo Doria06/2015
2084(7*10^123563+107)/3123564Robert Price02/2018
2085(3*2^410392-1)/9229123537Lelio R Paula05/2014
20862^410206-113081123485Enzo Doria07/2014
2087(25*2^410192+1)/10397123478Lelio R Paula04/2014
20882^409909-189123395Enzo Doria05/2014
20892^409896-109043123391Enzo Doria04/2014
20902^409890+75409123390Enzo Doria04/2016
2091133^58076-2123345Lelio R Paula10/2017
2092F(590041)123311Henri Lifchitz01/2005
20932^409566-113501123292Enzo Doria08/2014
20942^409533+77747123282Enzo Doria05/2016
20952^409436-112799123253Enzo Doria06/2014
20962^409225+1873787123189Enzo Doria06/2016
20972^409174+73009123174Enzo Doria04/2016
20982^409058-112685123139Enzo Doria06/2014
20992^408778+77689123055Enzo Doria05/2016
21002^408690-75123028Lelio R Paula11/2013
21012^408574-2787341122994Enzo Doria03/2016
21023*10^122977+37122978Robert Price08/2018
2103Phi(157825,10)122961Maksym Voznyy06/2015
2104(13*2^408283+1)/1665122904Lelio R Paula05/2014
2105(11*2^408100-1)/35122850Lelio R Paula04/2014
2106(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2107(32*10^122733-77)/9122734Robert Price06/2018
2108(21*2^407604-1)/215122701Lelio R Paula04/2014
2109(21*2^407433-1)/13122650Lelio R Paula04/2014
2110(73*10^122592-1)/9122593Robert Price01/2015
2111(5*10^122592+91)/3122593Robert Price04/2018
21122^407179-112075122574Enzo Doria06/2014
2113(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2114(66^67349+1)/67122543Paul Bourdelais09/2017
21152^407008-1867919122522Enzo Doria04/2016
211611^117642-300122512Enzo Doria10/2012
2117(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
21182^406949+72197122504Enzo Doria04/2016
21192^406826-65122467Lelio R Paula11/2013
21202^406821-2797363122466Enzo Doria04/2016
21212^406758-17122447Lelio R Paula11/2013
2122(30^82883-1)/29122427Robert Price12/2011
2123(2^406583-1)/813167122388Jens K. Andersen02/2009
21243*10^122345-97122346Robert Price07/2018
212597^61575-2122336Lelio R Paula12/2014
21262^406298+2799109122308Enzo Doria04/2016
2127(27*2^406241-1)/10277122289Lelio R Paula04/2014
21282^406229-1849993122288Enzo Doria08/2015
21293*10^122274+7122275Robert Price07/2015
21302^406117+1876577122254Enzo Doria07/2016
21313^256199-2^256199122238Mike Oakes06/2005
21322^405992-78557122216Jorge Menendez03/2018
2133(8*10^122203+43)/3122204Robert Price06/2018
21342^405774+179149122151Enzo Doria06/2016
21352^405514-3311122072Yves Minet12/2014
21362^405514-115511122072Enzo Doria07/2015
21372^405422-113261122045Enzo Doria07/2014
21382^405173+71237121970Enzo Doria04/2016
2139(2^405016+1)/257121920Lelio R Paula04/2014
21402^404858+71329121875Enzo Doria04/2016
21412^404813-114703121861Enzo Doria04/2015
21422^404764+77791121847Enzo Doria05/2016
2143317^48694+48694^317121787Norbert Schneider08/2015
21442^404536-115259121778Enzo Doria06/2015
21452^404501-631121767Yves Minet07/2012
214663^67620+2121672Lelio R Paula08/2015
2147(17*10^121621+1)/9121622Serge Batalov05/2010
2148(15*2^403912+1)/271121589Lelio R Paula05/2014
2149(10^121543-79)/3121543Robert Price01/2018
21502^403676+76831121519Enzo Doria05/2016
2151(7*10^121487+143)/3121488Robert Price03/2018
21522^403363-113635121425Enzo Doria08/2014
21532^403336-1861469121417Enzo Doria03/2016
2154p(24442)#/2-64121381Robert Price04/2017
215511^116555-720121380Enzo Doria11/2012
21562^403100-461267121346Enzo Doria07/2015
21572^403093-112213121344Enzo Doria06/2014
2158(316^48539+1)/317121330Eric Chen10/2017
21592^403004+1866361121317Enzo Doria03/2016
21602^402953+89121301Lelio R Paula10/2013
21612^402944-2788319121299Enzo Doria03/2016
2162(27*2^402865+1)/5121276Lelio R Paula04/2014
21632^402828-113183121264Enzo Doria07/2014
2164(17*10^121242+1)/9121243Serge Batalov05/2010
2165(15*2^402757+1)/101121242Lelio R Paula05/2014
21672^402715+1874223121230Enzo Doria06/2016
2166(35*10^121229-593)/9121230Robert Price07/2018
2168(91^61879+1)/92121222Paul Bourdelais09/2017
21697*10^121144+9121145Robert Price09/2015
21702^401725-113251120932Enzo Doria07/2014
2171(15*2^401677-1)/19120917Lelio R Paula05/2014
21722^401652+73711120910Enzo Doria04/2016
2173(2^401632+3)/79120902Lelio R Paula04/2014
21742^401406-2791331120836Enzo Doria03/2016
2175(28^83497+1)/29120832Robert Price07/2013
21762^401369+1867367120825Enzo Doria03/2016
2177(10^120782+29)/3120782Serge Batalov12/2014
21782^401215-1657120778Yves Minet07/2014
21792^401159+53120761Lelio R Paula10/2013
21802^401031-113047120723Enzo Doria07/2014
2181(29*2^400909-1)/303120685Lelio R Paula04/2014
21822^400571-15120584Lelio R Paula10/2013
2183(10^120574+359)/9120574Serge Batalov12/2014
21842^400424-216413120540Enzo Doria04/2013
2185(17*2^400200-1)/587120471Lelio R Paula05/2014
21862^400166+1874899120462Enzo Doria06/2016
2187(3*2^400045-1)/865120424Lelio R Paula04/2014
21882^399966+73759120402Enzo Doria04/2016
2189(112*10^120395-1)/3120397Serge Batalov12/2014
21902^399918-95120388Lelio R Paula04/2013
21912^399792-1849259120350Enzo Doria08/2015
21929*10^120342-7120343Robert Price09/2015
21932^399526-1861721120270Enzo Doria11/2015
2194(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
21952^399322-2798111120208Enzo Doria04/2016
219672^64693-71^64693120157Robert Price03/2014
21972^399111-28489120145Enzo Doria08/2015
21992^398877+105120074Donovan Johnson01/2006
2198(101*10^120072-87)/7120074Hans Havermann02/2015
2200(88^61751+1)/89120072Paul Bourdelais09/2017
22012^398710+57120024Lelio R Paula04/2013
22022^398691-115057120018Enzo Doria06/2015
2203L(574219)120005Renaud Lifchitz03/2004
22042^398571+60413119982Yves Minet03/2011
2205p(24179)#/2-64119949Robert Price04/2017
22062^398448+1872001119945Enzo Doria05/2016
22078*10^119930-3119931Ray Chandler04/2011
2208(10^119880+179)/9119880Serge Batalov12/2014
2209(9*2^398145+1)/73119853Lelio R Paula04/2014
2210(10^119836+77)/3119836Robert Price01/2018
22112^398029+1872527119819Enzo Doria05/2016
22122^397897-113541119779Enzo Doria08/2014
2213(21*2^397661-1)/27593119705Lelio R Paula04/2014
2214(58^67853-1)/57119653Paul Bourdelais09/2017
22152^397426+73849119638Enzo Doria04/2016
22162^396933-112723119489Enzo Doria06/2014
221711^114738-150119488Enzo Doria10/2012
2218(4*10^119474+149)/9119474Robert Price04/2018
22192^396790-21119446Lelio R Paula04/2013
2220(2^396633-7)/5119398Lelio R Paula04/2014
2221105^59050+104119352Norbert Schneider11/2016
22222^396374+73729119321Enzo Doria04/2016
22232^396258-459491119286Enzo Doria05/2015
22242^396128-396128-1119247Karsten Bonath06/2018
2225(2^395986+5)/76881119199Lelio R Paula04/2014
2226(23*2^395942-1)/91119190Lelio R Paula04/2014
2227(11*2^395548+1)/3119073Lelio R Paula04/2014
2228(30^80599+1)/31119054Robert Price07/2013
22292^395062-109121118926Enzo Doria04/2014
2230(2^394918+78557)/3118882Lelio R Paula01/2015
2231(2^394739+3)/1883118826Lelio R Paula04/2014
22322^394266+71389118686Enzo Doria04/2016
22332^394215-51261118671Tony Prest / Never Odd Or Even04/2018
2234(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
2235(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
2236(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
2237(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
2238(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
2239(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
22405^169727+2118635Lelio R Paula08/2013
22412^394034-3118617M. Frind & P. Underwood09/2002
2242(7*10^118607+179)/3118608Robert Price09/2018
22433^248572-6242118599Enzo Doria05/2014
2244(3*2^393964-1)/181118594Lelio R Paula04/2014
22457^140303-6118570Robert Price11/2014
22462^393427+75683118434Enzo Doria04/2016
22472^393376-114749118418Enzo Doria04/2015
22482^393180+73118359Lelio R Paula04/2013
2249p(23881)#/2+256118328Robert Price05/2017
2250(10^118324+359)/9118324Serge Batalov12/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 20 2018 23:15 (Time in France)

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