PRP Records

Probable Primes Top 10000

(255312 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(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
2002(13*10^135279+437)/9135280Robert Price04/2018
20032^449330-35135262Lelio R Paula08/2017
2004(19*2^449325+1)/9135261Lelio R Paula07/2015
2005(13*10^135184-43)/3135185Robert Price11/2018
20062^449049-115309135178Enzo Doria07/2015
2007(10^135174+191)/3135174Robert Price02/2018
20082^449030-15135172Lelio R Paula08/2017
2009(27*2^448936-1)/11135144Lelio R Paula07/2015
20102^448762-351401135091Enzo Doria07/2015
20112*10^135083-43135084Robert Price04/2018
20125*10^135019+77135020Robert Price12/2018
2013(10^135011+719)/9135011Serge Batalov12/2014
20142^448386-2786261134978Enzo Doria03/2016
2015(73*10^134939+143)/9134940Robert Price07/2019
20162^448113-113949134896Enzo Doria11/2014
20172^447888-2786639134828Enzo Doria03/2016
20182^447870-396765134823Enzo Doria07/2013
20192^447766-21791134791Enzo Doria07/2013
2020(19*10^134786-49)/3134787Robert Price05/2019
2021Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
2022(23*2^447647+1)/155134755Lelio R Paula07/2015
20232^447552-1019134727Yves Minet02/2014
2024(2*10^134720-41)/3134720Robert Price02/2018
20252^447437-113569134692Enzo Doria08/2014
20262^447426-65134689Lelio R Paula08/2017
20272^447357-2797573134668Enzo Doria04/2016
20282^447278+93134645Lelio R Paula08/2017
20292^447094-113193134589Enzo Doria07/2014
20303^282041-9934134568Enzo Doria05/2014
20312^447019-109039134567Enzo Doria04/2014
20322^446990-22041134558Enzo Doria07/2013
2033123^64370+122134528Karsten Bonath04/2018
20342^446782-39701134495Enzo Doria09/2015
20352^446494-16485134409Enzo Doria04/2013
203629504^30069-30069^29504134405Norbert Schneider12/2014
20372^446441+65134393Lelio R Paula08/2017
2038(10^134385+719)/9134385Serge Batalov12/2014
2039(2*10^134364+529)/9134364Robert Price01/2018
2040(13*2^446187-1)/661134314Lelio R Paula07/2015
2041(2^446022-7)/339134264Lelio R Paula07/2015
204263^74568+2134174Lelio R Paula06/2017
20432^445671-22071134161Enzo Doria07/2013
2044532^49205+49205^532134129Norbert Schneider02/2019
2045(28*10^134122-1)/9134123Serge Batalov10/2014
20462^445515-113859134114Enzo Doria10/2014
2047(22*10^134111-37)/3134112Robert Price04/2019
20482^445328-216917134058Enzo Doria05/2014
20492^445202+1874899134020Enzo Doria06/2016
2050(13*2^445102+1)/17133989Lelio R Paula07/2015
2051(35*10^133979-593)/9133980Robert Price07/2018
20522*10^133955+51133956Robert Price05/2018
20532^444964-113639133948Enzo Doria08/2014
205428118^30097-30097^28118133902Norbert Schneider01/2015
20552^444784-113859133894Enzo Doria10/2014
2056(89*10^133580+1)/9133581Serge Batalov05/2010
205762^74521-61^74521133571Robert Price05/2013
20582^443198-1867301133416Enzo Doria03/2016
2059(19*10^133390+101)/3133391Robert Price09/2019
2060(71^72043-1)/70133369Paul Bourdelais09/2017
20612^442799+1874633133296Enzo Doria06/2016
2062L(637751)133283Henri Lifchitz09/2008
2063109^65410-2133269Lelio R Paula10/2017
20642^442688-113489133263Enzo Doria08/2014
2065(7*2^442640-1)/783133246Lelio R Paula07/2015
2066(9*2^442463+1)/17441133192Lelio R Paula07/2015
20672^442437-1849993133187Enzo Doria08/2015
20682^442430-2791721133185Enzo Doria03/2016
2069(13*2^442428-1)/309133183Lelio R Paula07/2015
2070(25*2^442379-1)/71133169Lelio R Paula07/2015
2071(2^441799+78557)/5132995Lelio R Paula07/2015
20722^441781-2787883132990Enzo Doria03/2016
2073(3*2^441685+1)/749132959Lelio R Paula07/2015
20742^441618+37132941Lelio R Paula08/2017
20752^441521-113575132912Enzo Doria08/2014
20767*10^132884-99132885Robert Price06/2019
20772^441396-65132874Lelio R Paula08/2017
20782^441330+1871959132854Enzo Doria05/2016
20792^441063+383132774Lelio R Paula06/2012
2080(22*10^132746+53)/3132747Robert Price07/2019
20812^440846+1870909132708Enzo Doria05/2016
20822^440656-113489132651Enzo Doria08/2014
2083numbpart(14180123587)132646Serge Batalov04/2017
2084(19*10^132550+191)/3132551Robert Price05/2019
2085(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
2086(38^83891+1)/39132529Robert Price09/2013
20872*10^132493-43132494Robert Price04/2018
20882^439931-21132433Lelio R Paula08/2017
208947^79201-46^79201132432Robert Price10/2012
20902^439897-113653132423Enzo Doria08/2014
2091(5*2^439822+1)/9132400Lelio R Paula06/2015
2092(112*10^132337-1)/3132339Serge Batalov12/2014
20932^439576-113247132326Enzo Doria07/2014
20942^439497-29143132302Enzo Doria07/2015
20952^439409-114193132276Enzo Doria12/2014
2096(44*10^132233-233)/9132234Robert Price01/2019
20979*10^132148-7132149Robert Price09/2015
2098(47*10^132125-119)/9132126Robert Price05/2019
20992^438845+1870217132106Enzo Doria05/2016
21002^438789+87855132089Lelio R Paula01/2016
21012^438774-2786411132085Enzo Doria03/2016
21022^438755-1848205132079Enzo Doria07/2015
21032^438739-112087132074Enzo Doria06/2014
210413907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
2105L(631181)131910Henri Lifchitz09/2008
2106(47*10^131886-119)/9131887Robert Price05/2019
2107(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
21082^438079-1863877131875Enzo Doria03/2016
2109(2^438067+5)/329131869Lelio R Paula06/2015
21102^437908-113855131824Enzo Doria09/2014
21112^437884-286349131817Enzo Doria07/2015
2112(11*10^131784-17)/3131785Robert Price06/2018
21133^276062-112292131716Enzo Doria07/2014
21142^437343+75953131654Enzo Doria04/2016
211535^85243-34^85243131621Robert Price05/2012
2116(68^71713+1)/69131413Paul Bourdelais09/2017
21172^436451+1884713131385Enzo Doria03/2017
21182^436365+35131359Robert Price11/2015
21192^436300+1866871131340Enzo Doria03/2016
2120(7*10^131339+179)/3131340Robert Price09/2018
2121(37*10^131270+341)/9131271Robert Price08/2018
2122(5*10^131223-29)/3131224Robert Price03/2018
2123(23*2^435891-1)/699131215Lelio R Paula07/2015
2124(11*2^435879+1)/3337131211Lelio R Paula06/2015
2126(2^435808+1)/641/6700417131182Lelio R Paula02/2012
2125(2^435808+1)/4294967297131182Serge Batalov12/2016
21292^435773+1875557131181Enzo Doria06/2016
2128(16*10^131180+167)/3131181Robert Price06/2019
2127(26*10^131180-77)/3131181Robert Price11/2019
2130(25*10^131144-7)/9131145Robert Price05/2018
21312^435612-2789939131133Enzo Doria12/2015
213266^72047-65^72047131093Robert Price09/2013
2133(5*10^131090+37)/3131091Robert Price03/2018
21342^435468+75631131089Enzo Doria04/2016
213537^83588-2131083Lelio R Paula08/2015
2136(4^217720+11)/3131081Robert Price02/2017
21372^435202-113193131009Enzo Doria07/2014
21389*10^130998-19130999Robert Price07/2019
2139floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
21402^434835-111937130899Enzo Doria05/2014
21412^434685+72257130854Enzo Doria04/2016
2142(7*10^130825+113)/3130826Robert Price02/2018
21432^434539-29317130810Enzo Doria07/2015
21442^434469-114259130789Enzo Doria01/2015
21452^434246+33130722Robert Price11/2015
21462^433911-91130621Lelio R Paula06/2017
21472^433744-114419130570Enzo Doria02/2015
21492^433708+1869451130560Enzo Doria05/2016
21482^433710+93130560Lelio R Paula06/2017
2150(29*2^433547-1)/27130511Lelio R Paula06/2015
21514*10^130480+9130481Robert Price05/2015
2152(23*2^433449-1)/75130481Lelio R Paula06/2015
2153(23*2^433334-1)/3731130445Lelio R Paula06/2015
21542^433023-113497130353Enzo Doria08/2014
21552^433002+1179379130347Enzo Doria06/2016
21562^432974+19130339Robert Price08/2015
2157(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
21582^432217+41130111Lelio R Paula06/2017
2159(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
2160((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
216197^65480-2130094Lelio R Paula05/2017
21624*10^130088-89130089Robert Price11/2018
21632^432117-113215130081Enzo Doria07/2014
21642^431804+72511129986Enzo Doria04/2016
2165(3^272141-3^136071+1)/7129844Serge Batalov03/2014
2166(47*10^129789-119)/9129790Robert Price05/2019
2167(9*2^431141+1)/17129787Lelio R Paula06/2015
2168(29*2^430881-1)/21129709Lelio R Paula06/2015
21692^430807+1869563129686Enzo Doria05/2016
21702^430721-21429129660Enzo Doria07/2013
21712^430415-276271129568Enzo Doria07/2015
21722^430142-2791721129486Enzo Doria03/2016
2173(7*10^129472-13)/3129473Robert Price07/2018
21742^429568-21017129313Enzo Doria07/2013
2175(11*10^129239-179)/3129240Robert Price09/2018
21762^429194-112685129201Enzo Doria06/2014
21772^429145-2780449129186Enzo Doria04/2016
21782^428892-113453129110Enzo Doria07/2014
2179(11*2^428881-7)/15129106Renaud Lifchitz03/2011
21802^428727-113959129060Enzo Doria10/2014
2181(7*2^428725-1)/13129059Lelio R Paula05/2014
2182(10^129051-31)/3129051Serge Batalov12/2014
21832^428564+71161129011Enzo Doria04/2016
21842^428502-113285128992Enzo Doria07/2014
21852^428421-21373128968Enzo Doria06/2013
2186L(616787)128901Henri Lifchitz09/2008
218791^65772-2128851Lelio R Paula05/2017
21882^428022+43128848Lelio R Paula05/2017
21892^427999-459397128841Enzo Doria05/2015
21902^427993+76847128839Enzo Doria05/2016
21912^427824-1851507128788Enzo Doria08/2015
21922^427807-21469128783Enzo Doria07/2013
219311^123594-240128710Enzo Doria09/2012
21942^427504-21503128692Enzo Doria07/2013
21952^427420+91128667Lelio R Paula05/2017
2196(68*10^128645-257)/9128646Robert Price07/2019
21972^427269-113635128621Enzo Doria08/2014
21982^427130+1877569128579Enzo Doria08/2016
21992^427016-115349128545Enzo Doria07/2015
2200(4*10^128510+137)/3128511Robert Price03/2018
22012^426889-112879128507Enzo Doria06/2014
22022^426804+1869931128481Enzo Doria05/2016
22032^426750+77635128465Enzo Doria05/2016
22042^426425-91128367Lelio R Paula05/2017
2205(15*2^426398-1)/11128359Lelio R Paula05/2014
22062^426352+74971128345Enzo Doria04/2016
22074*10^128343-21128344Robert Price09/2018
22082^426300-1863689128330Enzo Doria03/2016
22092^426293+1881017128327Enzo Doria11/2016
22102^426043+35128252Robert Price11/2015
2211(4*10^128244-19)/3128245Robert Price03/2018
22122^425808-459959128181Enzo Doria06/2015
22132^425627-113605128127Enzo Doria08/2014
2214(22*10^128094+53)/3128095Robert Price07/2019
2215(86*10^128086-221)/9128087Robert Price09/2019
221618565^30002-30002^18565128070Norbert Schneider01/2015
2217(2^425287-9)/2737128021Lelio R Paula05/2015
2218(3*2^425233-1)/25128007Lelio R Paula05/2014
22192^425205+4911128000Marek Hubal02/2017
22202^425118-113663127974Enzo Doria08/2014
22212^425061+1869761127957Enzo Doria05/2016
2222746^44541+44541^746127955Norbert Schneider07/2019
22232^424918-21141127914Enzo Doria07/2013
22242^424864-29489127897Enzo Doria08/2015
2225(97*10^127858-1)/3127860Serge Batalov12/2014
22262^424632-2786639127827Enzo Doria03/2016
22272^424577-113755127811Enzo Doria09/2014
2228(7*2^424512-1)/3127792Lelio R Paula05/2014
2229(56*10^127752+691)/9127753Robert Price05/2019
223011^122629-720127705Enzo Doria11/2012
22312^423696-21429127546Enzo Doria07/2013
22322^423664-1864559127536Enzo Doria03/2016
22333^267267-4127519Henri Lifchitz10/2014
2234(19^99689+5^99689)/24127477Robert Price09/2013
2235(21*2^423372+1)/101127447Lelio R Paula05/2014
22362^423328-21537127435Enzo Doria07/2013
2237(2^423165-7)/25127384Lelio R Paula05/2015
2238(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
2239(16*10^127259+197)/3127260Robert Price04/2019
2240(26*10^127240+61)/3127241Robert Price10/2019
2241(234483*27^88884-145)/26127230Curtis Bright05/2015
22422^422515-114997127190Enzo Doria06/2015
22435*10^127179-3127180Robert Price07/2015
2244(44*10^127169-233)/9127170Robert Price01/2019
22455*10^127153+77127154Robert Price12/2018
2246736^44335+44335^736127104Norbert Schneider07/2019
2247-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
2248(78^67141-1)/77127036Paul Bourdelais09/2017
22492^421860-113285126993Enzo Doria07/2014
2250(2^421827-7)/11126982Lelio R Paula05/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 14 2019 11:13 (Time in France)

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