PRP Records

Probable Primes Top 10000

(252538 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 (> 50000) Who ? When ?
20012^427824-1851507128788Enzo Doria08/2015
20022^427807-21469128783Enzo Doria07/2013
200311^123594-240128710Enzo Doria09/2012
20042^427504-21503128692Enzo Doria07/2013
20052^427420+91128667Lelio R Paula05/2017
20062^427269-113635128621Enzo Doria08/2014
20072^427130+1877569128579Enzo Doria08/2016
20082^427016-115349128545Enzo Doria07/2015
2009(4*10^128510+137)/3128511Robert Price03/2018
20102^426889-112879128507Enzo Doria06/2014
20112^426804+1869931128481Enzo Doria05/2016
20122^426750+77635128465Enzo Doria05/2016
20132^426425-91128367Lelio R Paula05/2017
2014(15*2^426398-1)/11128359Lelio R Paula05/2014
20152^426352+74971128345Enzo Doria04/2016
20164*10^128343-21128344Robert Price09/2018
20172^426300-1863689128330Enzo Doria03/2016
20182^426293+1881017128327Enzo Doria11/2016
20192^426043+35128252Robert Price11/2015
2020(4*10^128244-19)/3128245Robert Price03/2018
20212^425808-459959128181Enzo Doria06/2015
20222^425627-113605128127Enzo Doria08/2014
202318565^30002-30002^18565128070Norbert Schneider01/2015
2024(2^425287-9)/2737128021Lelio R Paula05/2015
2025(3*2^425233-1)/25128007Lelio R Paula05/2014
20262^425205+4911128000Marek Hubal02/2017
20272^425118-113663127974Enzo Doria08/2014
20282^425061+1869761127957Enzo Doria05/2016
20292^424918-21141127914Enzo Doria07/2013
20302^424864-29489127897Enzo Doria08/2015
2031(97*10^127858-1)/3127860Serge Batalov12/2014
20322^424632-2786639127827Enzo Doria03/2016
20332^424577-113755127811Enzo Doria09/2014
2034(7*2^424512-1)/3127792Lelio R Paula05/2014
203511^122629-720127705Enzo Doria11/2012
20362^423696-21429127546Enzo Doria07/2013
20372^423664-1864559127536Enzo Doria03/2016
20383^267267-4127519Henri Lifchitz10/2014
2039(19^99689+5^99689)/24127477Robert Price09/2013
2040(21*2^423372+1)/101127447Lelio R Paula05/2014
20412^423328-21537127435Enzo Doria07/2013
2042(2^423165-7)/25127384Lelio R Paula05/2015
2043(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
2044(234483*27^88884-145)/26127230Curtis Bright05/2015
20452^422515-114997127190Enzo Doria06/2015
20465*10^127179-3127180Robert Price07/2015
2047(44*10^127169-233)/9127170Robert Price01/2019
20485*10^127153+77127154Robert Price12/2018
2049-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
2050(78^67141-1)/77127036Paul Bourdelais09/2017
20512^421860-113285126993Enzo Doria07/2014
2052(2^421827-7)/11126982Lelio R Paula05/2015
205311^121910-840126957Enzo Doria12/2012
2054(71^68539+1)/72126882Paul Bourdelais09/2017
2055(5*10^126871-119)/3126872Robert Price03/2018
2056331^50339-10004126846Enzo Doria07/2012
20572^421363-2790757126843Enzo Doria03/2016
2058(106*10^126839-1)/3126841Serge Batalov12/2014
2059(7*2^421243+1)/39126807Lelio R Paula05/2014
2060(14*10^126784-83)/3126785Robert Price12/2018
20612^421161-286183126783Enzo Doria06/2015
20622^420939-113935126716Enzo Doria10/2014
2063177^56363-2126703Lelio R Paula10/2017
20642^420741-113659126656Enzo Doria08/2014
20652^420694-21126642Lelio R Paula05/2017
2066(13*10^126638+437)/9126639Robert Price04/2018
20674*10^126625+87126626Robert Price08/2018
2068(31*2^420556+1)/7126601Lelio R Paula05/2014
20692^420424-59189126561Enzo Doria10/2015
20702^420126+71893126471Enzo Doria04/2016
2071(43*10^126441+47)/9126442Robert Price12/2018
20722^419866+1877059126393Enzo Doria07/2016
2073F(604711)126377Henri Lifchitz02/2005
20742^419757+72707126360Enzo Doria04/2016
20752^419720-21569126349Enzo Doria07/2013
20762^419637+29126324Henri Lifchitz02/2006
20772^419612+1876741126316Enzo Doria07/2016
20782^419520+2793271126289Enzo Doria03/2016
2079(2^419447-5)/369126264Lelio R Paula05/2014
20802^419328-1859939126231Enzo Doria03/2016
20812^419282-1851507126217Enzo Doria08/2015
20822^419251+1866143126208Enzo Doria03/2016
208311^121185+2126202Robert Price05/2014
2084(23*2^419036-1)/1393126141Lelio R Paula05/2014
20852^418851+23126087Robert Price09/2015
2086(2^418849-9)/2681126083Lelio R Paula05/2014
20872^418829+167126081Lelio R Paula01/2012
2088(31*2^418782-1)/75891126063Lelio R Paula05/2014
2089(19*2^418754-1)/15126058Lelio R Paula05/2014
20902^418319-109501125927Enzo Doria04/2014
20912^418316-112373125926Enzo Doria06/2014
2092(8*10^125894-29)/3125895Robert Price07/2018
2093(26*10^125886-413)/9125887Robert Price05/2018
20942^417968+1869811125821Enzo Doria06/2016
20952^417902+63125802Lelio R Paula09/2015
2096(10^125792-91)/9125792Serge Batalov12/2014
2097(35*10^125754-593)/9125755Robert Price07/2018
2098(32*10^125751-77)/9125752Robert Price06/2018
20992^417704+77011125742Enzo Doria05/2016
2100(10^125706+149)/3125706Serge Batalov12/2014
21012^417419-115309125656Enzo Doria07/2015
21022^417300+77281125620Enzo Doria05/2016
21032^417095-1657125559Yves Minet07/2014
21042^416773-25125462Lelio R Paula09/2015
2105(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2106(11*2^416691+1)/43125436Lelio R Paula05/2014
21072^416641-2*416641+1125422Robert Price05/2018
2108(21*2^416566-1)/17125399Lelio R Paula05/2014
21092^416530+1870429125389Enzo Doria05/2016
21102^416490+1875109125376Enzo Doria09/2016
21112^416416-114929125354Enzo Doria05/2015
2112(172*10^125292-1)/9125294Serge Batalov12/2014
21132^416134+1865899125269Enzo Doria03/2016
2114153^57337-152125264Norbert Schneider12/2018
2115(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2116(23^91943-1)/22125201Robert Price01/2012
211743125^27010-106125185Enzo Doria08/2012
2118(38*10^125166+349)/9125167Robert Price10/2018
21192^415765-112603125158Enzo Doria06/2014
21202^415290-113591125015Enzo Doria08/2014
21212^415276-460919125011Enzo Doria06/2015
21222^415259+77243125006Enzo Doria05/2016
21232^415144-3683124971Yves Minet10/2011
21242^414874+79124890Lelio R Paula01/2015
2125(2^414765+7)/1389124854Lelio R Paula05/2014
21262^414618+79459124813Enzo Doria06/2016
21272^414432-1846709124757Enzo Doria07/2015
21282*10^124751-51124752Robert Price04/2018
2129(13*2^414274-1)/153124708Lelio R Paula05/2014
2130(7*10^124648+197)/3124649Robert Price07/2018
21312^414032-5124637Henri Lifchitz07/2006
21322^414032+1872331124637Enzo Doria05/2016
213314120^30009-30009^14120124533Norbert Schneider02/2015
213464^68909-63^68909124463Robert Price07/2013
21352^413387+76253124442Enzo Doria04/2016
21362^413352+524287124432Paul Underwood09/2018
2137287117#+391613124424Nicolas PALAU01/2017
2138(4*10^124420+83)/3124421Robert Price02/2018
2139(27*2^413207-1)/108335124385Lelio R Paula05/2014
2140(41*10^124335-383)/9124336Robert Price11/2018
21412^412868-120599124286Paul Bourdelais02/2012
214245^75145-2124231Lelio R Paula08/2015
21432^412645-112213124219Enzo Doria06/2014
21442^412248+74611124100Enzo Doria04/2016
2145(22*10^124096-13)/9124097Robert Price06/2018
21462^412192-3329124083Yves Minet12/2014
2147(25*2^412191-1)/23124082Lelio R Paula05/2014
2148F(593689)124074Henri Lifchitz01/2005
2149(11*2^412161+1)/19124073Lelio R Paula05/2014
21502^411884-113279123990Enzo Doria07/2014
2151(2^411832+1)/257123972Lelio R Paula05/2014
2152(26*10^123970-89)/9123971Robert Price06/2018
21532^411790-1853531123962Enzo Doria08/2015
2154(5^177337+1)/6123953Paul Bourdelais11/2008
21552^411711-113257123938Enzo Doria07/2014
2156(23*2^411675-1)/3123928Lelio R Paula05/2014
2157(11*10^123899-179)/3123900Robert Price09/2018
21582^411325-351103123822Enzo Doria06/2015
21592^411052+1872481123739Enzo Doria05/2016
21602^410997+39123723Lelio R Paula05/2014
2161155^56438+154123618Norbert Schneider01/2019
21622^410596-39123602Lelio R Paula05/2014
21632^410540-115079123585Enzo Doria06/2015
2164(7*10^123563+107)/3123564Robert Price02/2018
2165(3*2^410392-1)/9229123537Lelio R Paula05/2014
21662^410206-113081123485Enzo Doria07/2014
2167(25*2^410192+1)/10397123478Lelio R Paula04/2014
21682^409909-189123395Enzo Doria05/2014
21692^409896-109043123391Enzo Doria04/2014
21702^409890+75409123390Enzo Doria04/2016
2171133^58076-2123345Lelio R Paula10/2017
2172F(590041)123311Henri Lifchitz01/2005
21732^409566-113501123292Enzo Doria08/2014
21742^409533+77747123282Enzo Doria05/2016
21752^409436-112799123253Enzo Doria06/2014
21762^409225+1873787123189Enzo Doria06/2016
21772^409174+73009123174Enzo Doria04/2016
21782^409058-112685123139Enzo Doria06/2014
2179(13*10^123137-61)/3123138Robert Price11/2018
21804*10^123113+21123114Robert Price12/2018
21812^408778+77689123055Enzo Doria05/2016
21822^408690-75123028Lelio R Paula11/2013
2183(29*10^122996+673)/9122997Robert Price12/2018
21842^408574-2787341122994Enzo Doria03/2016
21853*10^122977+37122978Robert Price08/2018
2186Phi(157825,10)122961Maksym Voznyy06/2015
2187(13*2^408283+1)/1665122904Lelio R Paula05/2014
2188(11*2^408100-1)/35122850Lelio R Paula04/2014
2189(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2190(32*10^122733-77)/9122734Robert Price06/2018
2191(21*2^407604-1)/215122701Lelio R Paula04/2014
2192(21*2^407433-1)/13122650Lelio R Paula04/2014
2193(73*10^122592-1)/9122593Robert Price01/2015
2194(5*10^122592+91)/3122593Robert Price04/2018
21952^407179-112075122574Enzo Doria06/2014
2196(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2197(66^67349+1)/67122543Paul Bourdelais09/2017
21982^407008-1867919122522Enzo Doria04/2016
219911^117642-300122512Enzo Doria10/2012
2200(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
22012^406949+72197122504Enzo Doria04/2016
22022^406826-65122467Lelio R Paula11/2013
22032^406821-2797363122466Enzo Doria04/2016
22042^406758-17122447Lelio R Paula11/2013
2205(30^82883-1)/29122427Robert Price12/2011
2206(2^406583-1)/813167122388Jens K. Andersen02/2009
22074*10^122377+19122378Robert Price10/2018
22083*10^122345-97122346Robert Price07/2018
220997^61575-2122336Lelio R Paula12/2014
22102^406298+2799109122308Enzo Doria04/2016
2211(27*2^406241-1)/10277122289Lelio R Paula04/2014
22122^406229-1849993122288Enzo Doria08/2015
22133*10^122274+7122275Robert Price07/2015
22142^406117+1876577122254Enzo Doria07/2016
22153^256199-2^256199122238Mike Oakes06/2005
22162^405992-78557122216Jorge Menendez03/2018
2217(8*10^122203+43)/3122204Robert Price06/2018
22182^405774+179149122151Enzo Doria06/2016
22192^405514-3311122072Yves Minet12/2014
22202^405514-115511122072Enzo Doria07/2015
22212^405422-113261122045Enzo Doria07/2014
22222^405173+71237121970Enzo Doria04/2016
2223(2^405016+1)/257121920Lelio R Paula04/2014
22242^404858+71329121875Enzo Doria04/2016
22252^404813-114703121861Enzo Doria04/2015
22262^404764+77791121847Enzo Doria05/2016
2227317^48694+48694^317121787Norbert Schneider08/2015
22282^404536-115259121778Enzo Doria06/2015
22292^404501-631121767Yves Minet07/2012
223063^67620+2121672Lelio R Paula08/2015
2231(17*10^121621+1)/9121622Serge Batalov05/2010
2232(15*2^403912+1)/271121589Lelio R Paula05/2014
2233(10^121543-79)/3121543Robert Price01/2018
22342^403676+76831121519Enzo Doria05/2016
2235(7*10^121487+143)/3121488Robert Price03/2018
22362^403363-113635121425Enzo Doria08/2014
22372^403336-1861469121417Enzo Doria03/2016
2238p(24442)#/2-64121381Robert Price04/2017
223911^116555-720121380Enzo Doria11/2012
22402^403100-461267121346Enzo Doria07/2015
22412^403093-112213121344Enzo Doria06/2014
2242(316^48539+1)/317121330Eric Chen10/2017
22432^403004+1866361121317Enzo Doria03/2016
22442^402953+89121301Lelio R Paula10/2013
22452^402944-2788319121299Enzo Doria03/2016
2246(44*10^121297-719)/9121298Robert Price12/2018
2247(27*2^402865+1)/5121276Lelio R Paula04/2014
22482^402828-113183121264Enzo Doria07/2014
2249(17*10^121242+1)/9121243Serge Batalov05/2010
2250(15*2^402757+1)/101121242Lelio R Paula05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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