PRP Records

Probable Primes Top 10000

(252675 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 ?
2001(29*2^433547-1)/27130511Lelio R Paula06/2015
20024*10^130480+9130481Robert Price05/2015
2003(23*2^433449-1)/75130481Lelio R Paula06/2015
2004(23*2^433334-1)/3731130445Lelio R Paula06/2015
20052^433023-113497130353Enzo Doria08/2014
20062^433002+1179379130347Enzo Doria06/2016
20072^432974+19130339Robert Price08/2015
2008(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
20092^432217+41130111Lelio R Paula06/2017
2010(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
2011((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
201297^65480-2130094Lelio R Paula05/2017
20134*10^130088-89130089Robert Price11/2018
20142^432117-113215130081Enzo Doria07/2014
20152^431804+72511129986Enzo Doria04/2016
2016(3^272141-3^136071+1)/7129844Serge Batalov03/2014
2017(9*2^431141+1)/17129787Lelio R Paula06/2015
2018(29*2^430881-1)/21129709Lelio R Paula06/2015
20192^430807+1869563129686Enzo Doria05/2016
20202^430721-21429129660Enzo Doria07/2013
20212^430415-276271129568Enzo Doria07/2015
20222^430142-2791721129486Enzo Doria03/2016
2023(7*10^129472-13)/3129473Robert Price07/2018
20242^429568-21017129313Enzo Doria07/2013
2025(11*10^129239-179)/3129240Robert Price09/2018
20262^429194-112685129201Enzo Doria06/2014
20272^429145-2780449129186Enzo Doria04/2016
20282^428892-113453129110Enzo Doria07/2014
2029(11*2^428881-7)/15129106Renaud Lifchitz03/2011
20302^428727-113959129060Enzo Doria10/2014
2031(7*2^428725-1)/13129059Lelio R Paula05/2014
2032(10^129051-31)/3129051Serge Batalov12/2014
20332^428564+71161129011Enzo Doria04/2016
20342^428502-113285128992Enzo Doria07/2014
20352^428421-21373128968Enzo Doria06/2013
2036L(616787)128901Henri Lifchitz09/2008
203791^65772-2128851Lelio R Paula05/2017
20382^428022+43128848Lelio R Paula05/2017
20392^427999-459397128841Enzo Doria05/2015
20402^427993+76847128839Enzo Doria05/2016
20412^427824-1851507128788Enzo Doria08/2015
20422^427807-21469128783Enzo Doria07/2013
204311^123594-240128710Enzo Doria09/2012
20442^427504-21503128692Enzo Doria07/2013
20452^427420+91128667Lelio R Paula05/2017
20462^427269-113635128621Enzo Doria08/2014
20472^427130+1877569128579Enzo Doria08/2016
20482^427016-115349128545Enzo Doria07/2015
2049(4*10^128510+137)/3128511Robert Price03/2018
20502^426889-112879128507Enzo Doria06/2014
20512^426804+1869931128481Enzo Doria05/2016
20522^426750+77635128465Enzo Doria05/2016
20532^426425-91128367Lelio R Paula05/2017
2054(15*2^426398-1)/11128359Lelio R Paula05/2014
20552^426352+74971128345Enzo Doria04/2016
20564*10^128343-21128344Robert Price09/2018
20572^426300-1863689128330Enzo Doria03/2016
20582^426293+1881017128327Enzo Doria11/2016
20592^426043+35128252Robert Price11/2015
2060(4*10^128244-19)/3128245Robert Price03/2018
20612^425808-459959128181Enzo Doria06/2015
20622^425627-113605128127Enzo Doria08/2014
206318565^30002-30002^18565128070Norbert Schneider01/2015
2064(2^425287-9)/2737128021Lelio R Paula05/2015
2065(3*2^425233-1)/25128007Lelio R Paula05/2014
20662^425205+4911128000Marek Hubal02/2017
20672^425118-113663127974Enzo Doria08/2014
20682^425061+1869761127957Enzo Doria05/2016
20692^424918-21141127914Enzo Doria07/2013
20702^424864-29489127897Enzo Doria08/2015
2071(97*10^127858-1)/3127860Serge Batalov12/2014
20722^424632-2786639127827Enzo Doria03/2016
20732^424577-113755127811Enzo Doria09/2014
2074(7*2^424512-1)/3127792Lelio R Paula05/2014
207511^122629-720127705Enzo Doria11/2012
20762^423696-21429127546Enzo Doria07/2013
20772^423664-1864559127536Enzo Doria03/2016
20783^267267-4127519Henri Lifchitz10/2014
2079(19^99689+5^99689)/24127477Robert Price09/2013
2080(21*2^423372+1)/101127447Lelio R Paula05/2014
20812^423328-21537127435Enzo Doria07/2013
2082(2^423165-7)/25127384Lelio R Paula05/2015
2083(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
2084(16*10^127259+197)/3127260Robert Price04/2019
2085(234483*27^88884-145)/26127230Curtis Bright05/2015
20862^422515-114997127190Enzo Doria06/2015
20875*10^127179-3127180Robert Price07/2015
2088(44*10^127169-233)/9127170Robert Price01/2019
20895*10^127153+77127154Robert Price12/2018
2090-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
2091(78^67141-1)/77127036Paul Bourdelais09/2017
20922^421860-113285126993Enzo Doria07/2014
2093(2^421827-7)/11126982Lelio R Paula05/2015
209411^121910-840126957Enzo Doria12/2012
2095(71^68539+1)/72126882Paul Bourdelais09/2017
2096(5*10^126871-119)/3126872Robert Price03/2018
2097331^50339-10004126846Enzo Doria07/2012
20982^421363-2790757126843Enzo Doria03/2016
2099(106*10^126839-1)/3126841Serge Batalov12/2014
2100(7*2^421243+1)/39126807Lelio R Paula05/2014
2101(14*10^126784-83)/3126785Robert Price12/2018
21022^421161-286183126783Enzo Doria06/2015
21032^420939-113935126716Enzo Doria10/2014
2104177^56363-2126703Lelio R Paula10/2017
21052^420741-113659126656Enzo Doria08/2014
21062^420694-21126642Lelio R Paula05/2017
2107(13*10^126638+437)/9126639Robert Price04/2018
21084*10^126625+87126626Robert Price08/2018
2109(31*2^420556+1)/7126601Lelio R Paula05/2014
21102^420424-59189126561Enzo Doria10/2015
21112^420126+71893126471Enzo Doria04/2016
2112(43*10^126441+47)/9126442Robert Price12/2018
21132^419866+1877059126393Enzo Doria07/2016
2114F(604711)126377Henri Lifchitz02/2005
21152^419757+72707126360Enzo Doria04/2016
21162^419720-21569126349Enzo Doria07/2013
21172^419637+29126324Henri Lifchitz02/2006
21182^419612+1876741126316Enzo Doria07/2016
21192^419520+2793271126289Enzo Doria03/2016
2120(2^419447-5)/369126264Lelio R Paula05/2014
21212^419328-1859939126231Enzo Doria03/2016
21222^419282-1851507126217Enzo Doria08/2015
21232^419251+1866143126208Enzo Doria03/2016
212411^121185+2126202Robert Price05/2014
2125(23*2^419036-1)/1393126141Lelio R Paula05/2014
21262^418851+23126087Robert Price09/2015
2127(2^418849-9)/2681126083Lelio R Paula05/2014
21282^418829+167126081Lelio R Paula01/2012
2129(31*2^418782-1)/75891126063Lelio R Paula05/2014
2130(19*2^418754-1)/15126058Lelio R Paula05/2014
21312^418319-109501125927Enzo Doria04/2014
21322^418316-112373125926Enzo Doria06/2014
2133(8*10^125894-29)/3125895Robert Price07/2018
2134(26*10^125886-413)/9125887Robert Price05/2018
21352^417968+1869811125821Enzo Doria06/2016
21362^417902+63125802Lelio R Paula09/2015
2137(10^125792-91)/9125792Serge Batalov12/2014
2138(35*10^125754-593)/9125755Robert Price07/2018
2139(32*10^125751-77)/9125752Robert Price06/2018
21402^417704+77011125742Enzo Doria05/2016
2141(10^125706+149)/3125706Serge Batalov12/2014
21422^417419-115309125656Enzo Doria07/2015
21432^417300+77281125620Enzo Doria05/2016
21442^417095-1657125559Yves Minet07/2014
21452^416773-25125462Lelio R Paula09/2015
2146(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2147(11*2^416691+1)/43125436Lelio R Paula05/2014
21482^416641-2*416641+1125422Robert Price05/2018
2149(21*2^416566-1)/17125399Lelio R Paula05/2014
21502^416530+1870429125389Enzo Doria05/2016
21512^416490+1875109125376Enzo Doria09/2016
21522^416416-114929125354Enzo Doria05/2015
2153(172*10^125292-1)/9125294Serge Batalov12/2014
21542^416134+1865899125269Enzo Doria03/2016
2155153^57337-152125264Norbert Schneider12/2018
2156(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2157(23^91943-1)/22125201Robert Price01/2012
215843125^27010-106125185Enzo Doria08/2012
2159(38*10^125166+349)/9125167Robert Price10/2018
21602^415765-112603125158Enzo Doria06/2014
21612^415290-113591125015Enzo Doria08/2014
21622^415276-460919125011Enzo Doria06/2015
21632^415259+77243125006Enzo Doria05/2016
21642^415144-3683124971Yves Minet10/2011
21652^414874+79124890Lelio R Paula01/2015
2166(2^414765+7)/1389124854Lelio R Paula05/2014
21672^414618+79459124813Enzo Doria06/2016
21682^414432-1846709124757Enzo Doria07/2015
21692*10^124751-51124752Robert Price04/2018
2170(13*2^414274-1)/153124708Lelio R Paula05/2014
2171(7*10^124648+197)/3124649Robert Price07/2018
21722^414032-5124637Henri Lifchitz07/2006
21732^414032+1872331124637Enzo Doria05/2016
217414120^30009-30009^14120124533Norbert Schneider02/2015
217564^68909-63^68909124463Robert Price07/2013
21762^413387+76253124442Enzo Doria04/2016
21772^413352+524287124432Paul Underwood09/2018
2178287117#+391613124424Nicolas PALAU01/2017
2179(4*10^124420+83)/3124421Robert Price02/2018
2180(27*2^413207-1)/108335124385Lelio R Paula05/2014
2181(41*10^124335-383)/9124336Robert Price11/2018
21822^412868-120599124286Paul Bourdelais02/2012
218345^75145-2124231Lelio R Paula08/2015
21842^412645-112213124219Enzo Doria06/2014
21852^412248+74611124100Enzo Doria04/2016
2186(22*10^124096-13)/9124097Robert Price06/2018
21872^412192-3329124083Yves Minet12/2014
2188(25*2^412191-1)/23124082Lelio R Paula05/2014
2189F(593689)124074Henri Lifchitz01/2005
2190(11*2^412161+1)/19124073Lelio R Paula05/2014
21912^411884-113279123990Enzo Doria07/2014
2192(2^411832+1)/257123972Lelio R Paula05/2014
2193(26*10^123970-89)/9123971Robert Price06/2018
21942^411790-1853531123962Enzo Doria08/2015
2195(5^177337+1)/6123953Paul Bourdelais11/2008
21962^411711-113257123938Enzo Doria07/2014
2197(23*2^411675-1)/3123928Lelio R Paula05/2014
2198(11*10^123899-179)/3123900Robert Price09/2018
21992^411325-351103123822Enzo Doria06/2015
22002^411052+1872481123739Enzo Doria05/2016
22012^410997+39123723Lelio R Paula05/2014
2202155^56438+154123618Norbert Schneider01/2019
22032^410596-39123602Lelio R Paula05/2014
22042^410540-115079123585Enzo Doria06/2015
2205(7*10^123563+107)/3123564Robert Price02/2018
2206(3*2^410392-1)/9229123537Lelio R Paula05/2014
22072^410206-113081123485Enzo Doria07/2014
2208(25*2^410192+1)/10397123478Lelio R Paula04/2014
22092^409909-189123395Enzo Doria05/2014
22102^409896-109043123391Enzo Doria04/2014
22112^409890+75409123390Enzo Doria04/2016
2212133^58076-2123345Lelio R Paula10/2017
2213F(590041)123311Henri Lifchitz01/2005
22142^409566-113501123292Enzo Doria08/2014
22152^409533+77747123282Enzo Doria05/2016
22162^409436-112799123253Enzo Doria06/2014
22172^409225+1873787123189Enzo Doria06/2016
22182^409174+73009123174Enzo Doria04/2016
22192^409058-112685123139Enzo Doria06/2014
2220(13*10^123137-61)/3123138Robert Price11/2018
22214*10^123113+21123114Robert Price12/2018
22222^408778+77689123055Enzo Doria05/2016
22232^408690-75123028Lelio R Paula11/2013
2224(29*10^122996+673)/9122997Robert Price12/2018
22252^408574-2787341122994Enzo Doria03/2016
22263*10^122977+37122978Robert Price08/2018
2227Phi(157825,10)122961Maksym Voznyy06/2015
2228(13*2^408283+1)/1665122904Lelio R Paula05/2014
2229(16*10^122871+77)/3122872Robert Price03/2019
2230(11*2^408100-1)/35122850Lelio R Paula04/2014
2231(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2232(32*10^122733-77)/9122734Robert Price06/2018
2233(21*2^407604-1)/215122701Lelio R Paula04/2014
2234(21*2^407433-1)/13122650Lelio R Paula04/2014
2235(73*10^122592-1)/9122593Robert Price01/2015
2236(5*10^122592+91)/3122593Robert Price04/2018
22372^407179-112075122574Enzo Doria06/2014
2238(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2239(66^67349+1)/67122543Paul Bourdelais09/2017
22402^407008-1867919122522Enzo Doria04/2016
224111^117642-300122512Enzo Doria10/2012
2242(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
22432^406949+72197122504Enzo Doria04/2016
22442^406826-65122467Lelio R Paula11/2013
22452^406821-2797363122466Enzo Doria04/2016
22462^406758-17122447Lelio R Paula11/2013
2247(30^82883-1)/29122427Robert Price12/2011
2248(2^406583-1)/813167122388Jens K. Andersen02/2009
22494*10^122377+19122378Robert Price10/2018
22503*10^122345-97122346Robert Price07/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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