PRP Records

Probable Primes Top 10000

(212140 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 ?
2001(25*2^410192+1)/10397123478Lelio R Paula04/2014
20022^409909-189123395Enzo Doria05/2014
20032^409896-109043123391Enzo Doria04/2014
20042^409890+75409123390Enzo Doria04/2016
2005133^58076-2123345Lelio R Paula10/2017
2006F(590041)123311Henri Lifchitz01/2005
20072^409566-113501123292Enzo Doria08/2014
20082^409533+77747123282Enzo Doria05/2016
20092^409436-112799123253Enzo Doria06/2014
20102^409225+1873787123189Enzo Doria06/2016
20112^409174+73009123174Enzo Doria04/2016
20122^409058-112685123139Enzo Doria06/2014
20132^408778+77689123055Enzo Doria05/2016
20142^408690-75123028Lelio R Paula11/2013
20152^408574-2787341122994Enzo Doria03/2016
2016Phi(157825,10)122961Maksym Voznyy06/2015
2017(13*2^408283+1)/1665122904Lelio R Paula05/2014
2018(11*2^408100-1)/35122850Lelio R Paula04/2014
2019(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2020(32*10^122733-77)/9122734Robert Price06/2018
2021(21*2^407604-1)/215122701Lelio R Paula04/2014
2022(21*2^407433-1)/13122650Lelio R Paula04/2014
2023(73*10^122592-1)/9122593Robert Price01/2015
2024(5*10^122592+91)/3122593Robert Price04/2018
20252^407179-112075122574Enzo Doria06/2014
2026(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2027(66^67349+1)/67122543Paul Bourdelais09/2017
20282^407008-1867919122522Enzo Doria04/2016
202911^117642-300122512Enzo Doria10/2012
2030(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
20312^406949+72197122504Enzo Doria04/2016
20322^406826-65122467Lelio R Paula11/2013
20332^406821-2797363122466Enzo Doria04/2016
20342^406758-17122447Lelio R Paula11/2013
2035(30^82883-1)/29122427Robert Price12/2011
2036(2^406583-1)/813167122388Jens K. Andersen02/2009
203797^61575-2122336Lelio R Paula12/2014
20382^406298+2799109122308Enzo Doria04/2016
2039(27*2^406241-1)/10277122289Lelio R Paula04/2014
20402^406229-1849993122288Enzo Doria08/2015
20413*10^122274+7122275Robert Price07/2015
20422^406117+1876577122254Enzo Doria07/2016
20433^256199-2^256199122238Mike Oakes06/2005
20442^405992-78557122216Jorge Menendez03/2018
2045(8*10^122203+43)/3122204Robert Price06/2018
20462^405774+179149122151Enzo Doria06/2016
20472^405514-3311122072Yves Minet12/2014
20482^405514-115511122072Enzo Doria07/2015
20492^405422-113261122045Enzo Doria07/2014
20502^405173+71237121970Enzo Doria04/2016
2051(2^405016+1)/257121920Lelio R Paula04/2014
20522^404858+71329121875Enzo Doria04/2016
20532^404813-114703121861Enzo Doria04/2015
20542^404764+77791121847Enzo Doria05/2016
2055317^48694+48694^317121787Norbert Schneider08/2015
20562^404536-115259121778Enzo Doria06/2015
20572^404501-631121767Yves Minet07/2012
205863^67620+2121672Lelio R Paula08/2015
2059(17*10^121621+1)/9121622Serge Batalov05/2010
2060(15*2^403912+1)/271121589Lelio R Paula05/2014
2061(10^121543-79)/3121543Robert Price01/2018
20622^403676+76831121519Enzo Doria05/2016
2063(7*10^121487+143)/3121488Robert Price03/2018
20642^403363-113635121425Enzo Doria08/2014
20652^403336-1861469121417Enzo Doria03/2016
2066p(24442)#/2-64121381Robert Price04/2017
206711^116555-720121380Enzo Doria11/2012
20682^403100-461267121346Enzo Doria07/2015
20692^403093-112213121344Enzo Doria06/2014
2070(316^48539+1)/317121330Eric Chen10/2017
20712^403004+1866361121317Enzo Doria03/2016
20722^402953+89121301Lelio R Paula10/2013
20732^402944-2788319121299Enzo Doria03/2016
2074(27*2^402865+1)/5121276Lelio R Paula04/2014
20752^402828-113183121264Enzo Doria07/2014
2076(17*10^121242+1)/9121243Serge Batalov05/2010
2077(15*2^402757+1)/101121242Lelio R Paula05/2014
20782^402715+1874223121230Enzo Doria06/2016
2079(91^61879+1)/92121222Paul Bourdelais09/2017
20807*10^121144+9121145Robert Price09/2015
20812^401725-113251120932Enzo Doria07/2014
2082(15*2^401677-1)/19120917Lelio R Paula05/2014
20832^401652+73711120910Enzo Doria04/2016
2084(2^401632+3)/79120902Lelio R Paula04/2014
20852^401406-2791331120836Enzo Doria03/2016
2086(28^83497+1)/29120832Robert Price07/2013
20872^401369+1867367120825Enzo Doria03/2016
2088(10^120782+29)/3120782Serge Batalov12/2014
20892^401215-1657120778Yves Minet07/2014
20902^401159+53120761Lelio R Paula10/2013
20912^401031-113047120723Enzo Doria07/2014
2092(29*2^400909-1)/303120685Lelio R Paula04/2014
20932^400571-15120584Lelio R Paula10/2013
2094(10^120574+359)/9120574Serge Batalov12/2014
20952^400424-216413120540Enzo Doria04/2013
2096(17*2^400200-1)/587120471Lelio R Paula05/2014
20972^400166+1874899120462Enzo Doria06/2016
2098(3*2^400045-1)/865120424Lelio R Paula04/2014
20992^399966+73759120402Enzo Doria04/2016
2100(112*10^120395-1)/3120397Serge Batalov12/2014
21012^399918-95120388Lelio R Paula04/2013
21022^399792-1849259120350Enzo Doria08/2015
21039*10^120342-7120343Robert Price09/2015
21042^399526-1861721120270Enzo Doria11/2015
2105(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
21062^399322-2798111120208Enzo Doria04/2016
210772^64693-71^64693120157Robert Price03/2014
21082^399111-28489120145Enzo Doria08/2015
21102^398877+105120074Donovan Johnson01/2006
2109(101*10^120072-87)/7120074Hans Havermann02/2015
2111(88^61751+1)/89120072Paul Bourdelais09/2017
21122^398710+57120024Lelio R Paula04/2013
21132^398691-115057120018Enzo Doria06/2015
2114L(574219)120005Renaud Lifchitz03/2004
21152^398571+60413119982Yves Minet03/2011
2116p(24179)#/2-64119949Robert Price04/2017
21172^398448+1872001119945Enzo Doria05/2016
21188*10^119930-3119931Ray Chandler04/2011
2119(10^119880+179)/9119880Serge Batalov12/2014
2120(9*2^398145+1)/73119853Lelio R Paula04/2014
2121(10^119836+77)/3119836Robert Price01/2018
21222^398029+1872527119819Enzo Doria05/2016
21232^397897-113541119779Enzo Doria08/2014
2124(21*2^397661-1)/27593119705Lelio R Paula04/2014
2125(58^67853-1)/57119653Paul Bourdelais09/2017
21262^397426+73849119638Enzo Doria04/2016
21272^396933-112723119489Enzo Doria06/2014
212811^114738-150119488Enzo Doria10/2012
2129(4*10^119474+149)/9119474Robert Price04/2018
21302^396790-21119446Lelio R Paula04/2013
2131(2^396633-7)/5119398Lelio R Paula04/2014
2132105^59050+104119352Norbert Schneider11/2016
21332^396374+73729119321Enzo Doria04/2016
21342^396258-459491119286Enzo Doria05/2015
21352^396128-396128-1119247Karsten Bonath06/2018
2136(2^395986+5)/76881119199Lelio R Paula04/2014
2137(23*2^395942-1)/91119190Lelio R Paula04/2014
2138(11*2^395548+1)/3119073Lelio R Paula04/2014
2139(30^80599+1)/31119054Robert Price07/2013
21402^395062-109121118926Enzo Doria04/2014
2141(2^394918+78557)/3118882Lelio R Paula01/2015
2142(2^394739+3)/1883118826Lelio R Paula04/2014
21432^394266+71389118686Enzo Doria04/2016
21442^394215-51261118671Tony Prest / Never Odd Or Even04/2018
2145(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
2146(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
2147(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
2148(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
2149(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
2150(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
21515^169727+2118635Lelio R Paula08/2013
21522^394034-3118617M. Frind & P. Underwood09/2002
21533^248572-6242118599Enzo Doria05/2014
2154(3*2^393964-1)/181118594Lelio R Paula04/2014
21557^140303-6118570Robert Price11/2014
21562^393427+75683118434Enzo Doria04/2016
21572^393376-114749118418Enzo Doria04/2015
21582^393180+73118359Lelio R Paula04/2013
2159p(23881)#/2+256118328Robert Price05/2017
2160(10^118324+359)/9118324Serge Batalov12/2014
2161p(23879)#/2+64118317Robert Price03/2017
2162(53*10^118216+1)/9118217Serge Batalov11/2010
2163(7*2^392697+1)/15118214Renaud Lifchitz03/2011
2164(157^53819-1)/156118179Alexander Zhirkov06/2016
2165(19*2^392551+1)/3118171Lelio R Paula04/2014
21662^392516-29219118160Enzo Doria07/2015
2167Phi(177231,10)118152Maksym Voznyy09/2015
21682^392413-112123118129Enzo Doria06/2014
2169(2^392342+5)/27118106Lelio R Paula04/2014
21702^392300-1841429118095Enzo Doria06/2015
21712^392220+75241118070Enzo Doria04/2016
217210^118009-20001118009Robert Price01/2018
21732^391933+5897117984Yves Minet02/2011
21742^391912-1849259117978Enzo Doria08/2015
2175(2^391812+5)/14181117944Lelio R Paula04/2014
2176(7*2^391521+1)/285117858Lelio R Paula04/2014
21772^391324+90901117801Yves Minet02/2011
21782^391301-1859923117794Enzo Doria03/2016
21792^391261-4131117782Yves Minet02/2018
2180(2^391115-7)/11791117734Lelio R Paula04/2014
21812^390960+1880881117691Enzo Doria11/2016
21822^390897-1860553117672Enzo Doria11/2015
21832^390889-115003117670Enzo Doria06/2015
21842^390779-30337117637Paul Bourdelais02/2012
218511^112916-780117590Enzo Doria12/2012
2186(16^97613-5^97613)/11117537Robert Price07/2013
2187(17*2^390272+1)/1983117482Lelio R Paula04/2014
218831^78759-30117459Theodore Burton02/2007
21892^389998+37117402Lelio R Paula03/2013
21902^389478+43117245Lelio R Paula03/2013
2191(29*2^389351-1)/9117207Lelio R Paula04/2014
2192(2^389341-7)/3865117200Lelio R Paula03/2014
219310^117142+209223117143Patrick De Geest04/2018
219510^117142-1000000001117142Robert Price03/2018
219410^117142-966057117142Patrick De Geest04/2018
219610^117135-401117135Robert Price01/2018
21972^389033-12797413117111Enzo Doria04/2016
21982^388960-109505117089Enzo Doria04/2014
2199(2^388928-5)/569117077Lelio R Paula03/2014
22002^388888-1529117067Yves Minet01/2013
220110^117059+28879117060Patrick De Geest05/2016
2202(10^117059-71)/1117059Serge Batalov12/2014
22033^245154-6256116969Enzo Doria05/2014
22042^388536-113495116961Enzo Doria08/2014
22052^388469-43116941Lelio R Paula03/2013
2206(7*2^388372-1)/111116911Lelio R Paula04/2014
2207(7*2^388335-1)/25116900Lelio R Paula04/2014
22082^388180+93116854Donovan Johnson07/2008
2209(2^388081+7)/1179116821Lelio R Paula03/2014
22102^387946-113261116784Enzo Doria07/2014
22112^387745+75557116723Enzo Doria04/2016
22122^387554+71455116666Enzo Doria04/2016
2213(2^387447+78557)/365116631Lelio R Paula12/2014
2214(145*10^116610-1)/9116612Serge Batalov12/2014
2215(17*2^387284-1)/59116584Lelio R Paula04/2014
2216(31*2^386968+1)/7116490Lelio R Paula03/2014
22172^386947+1869143116483Enzo Doria05/2016
2218(30^78857-1)/29116480Robert Price12/2011
2219(2^386903-3)/5116469Lelio R Paula03/2014
22202^386389-1864783116315Enzo Doria03/2016
2221(31*2^386231-1)/1711116266Lelio R Paula03/2014
2222(2^386087-5)/40959116220Lelio R Paula03/2014
22232^385969-823116189Yves Minet05/2012
222457^66162+2116173Lelio R Paula08/2013
22252^385854+75049116154Enzo Doria04/2016
22262^385775-109587116130Enzo Doria04/2014
22272^385622+71839116084Enzo Doria04/2016
22282^385564+781116067Lelio R Paula01/2012
22292^385410+71893116020Enzo Doria04/2016
2230(25*2^385091+1)/27115924Lelio R Paula04/2014
22312^384953-111943115883Paul Bourdelais02/2012
223243^70942-2115882Lelio R Paula04/2014
22337*10^115863+3115864Robert Price08/2015
22342^384834+93115847Donovan Johnson07/2008
22352^384809+71297115840Enzo Doria04/2016
2236(7*2^384759-1)/5115825Lelio R Paula04/2014
2237(71*10^115810-17)/9115811Ray Chandler08/2011
2238(97*10^115794-1)/3115796Serge Batalov12/2014
22392*10^115784-27115785Robert Price05/2018
224010^115773+126739115774Patrick De Geest04/2018
224210^115773-1000000001115773Robert Price03/2018
224110^115773-396221115773Patrick De Geest04/2018
22432^384530+1874305115756Enzo Doria06/2016
2244(3*2^384524-1)/7631115750Lelio R Paula03/2014
22452^384312+81091115690Yves Minet02/2010
2246(4*10^115668-79)/3115669Robert Price02/2018
2247(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
22483^242337-4042115625Enzo Doria05/2014
2249(11*2^383859-13)/15115553Renaud Lifchitz03/2011
22502^383780-3149115530Yves Minet10/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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