PRP Records

Probable Primes Top 10000

(255169 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 ?
20015*10^135019+77135020Robert Price12/2018
2002(10^135011+719)/9135011Serge Batalov12/2014
20032^448386-2786261134978Enzo Doria03/2016
2004(73*10^134939+143)/9134940Robert Price07/2019
20052^448113-113949134896Enzo Doria11/2014
20062^447888-2786639134828Enzo Doria03/2016
20072^447870-396765134823Enzo Doria07/2013
20082^447766-21791134791Enzo Doria07/2013
2009(19*10^134786-49)/3134787Robert Price05/2019
2010Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
2011(23*2^447647+1)/155134755Lelio R Paula07/2015
20122^447552-1019134727Yves Minet02/2014
2013(2*10^134720-41)/3134720Robert Price02/2018
20142^447437-113569134692Enzo Doria08/2014
20152^447426-65134689Lelio R Paula08/2017
20162^447357-2797573134668Enzo Doria04/2016
20172^447278+93134645Lelio R Paula08/2017
20182^447094-113193134589Enzo Doria07/2014
20193^282041-9934134568Enzo Doria05/2014
20202^447019-109039134567Enzo Doria04/2014
20212^446990-22041134558Enzo Doria07/2013
2022123^64370+122134528Karsten Bonath04/2018
20232^446782-39701134495Enzo Doria09/2015
20242^446494-16485134409Enzo Doria04/2013
202529504^30069-30069^29504134405Norbert Schneider12/2014
20262^446441+65134393Lelio R Paula08/2017
2027(10^134385+719)/9134385Serge Batalov12/2014
2028(2*10^134364+529)/9134364Robert Price01/2018
2029(13*2^446187-1)/661134314Lelio R Paula07/2015
2030(2^446022-7)/339134264Lelio R Paula07/2015
203163^74568+2134174Lelio R Paula06/2017
20322^445671-22071134161Enzo Doria07/2013
2033532^49205+49205^532134129Norbert Schneider02/2019
2034(28*10^134122-1)/9134123Serge Batalov10/2014
20352^445515-113859134114Enzo Doria10/2014
2036(22*10^134111-37)/3134112Robert Price04/2019
20372^445328-216917134058Enzo Doria05/2014
20382^445202+1874899134020Enzo Doria06/2016
2039(13*2^445102+1)/17133989Lelio R Paula07/2015
2040(35*10^133979-593)/9133980Robert Price07/2018
20412*10^133955+51133956Robert Price05/2018
20422^444964-113639133948Enzo Doria08/2014
204328118^30097-30097^28118133902Norbert Schneider01/2015
20442^444784-113859133894Enzo Doria10/2014
2045(89*10^133580+1)/9133581Serge Batalov05/2010
204662^74521-61^74521133571Robert Price05/2013
20472^443198-1867301133416Enzo Doria03/2016
2048(19*10^133390+101)/3133391Robert Price09/2019
2049(71^72043-1)/70133369Paul Bourdelais09/2017
20502^442799+1874633133296Enzo Doria06/2016
2051L(637751)133283Henri Lifchitz09/2008
2052109^65410-2133269Lelio R Paula10/2017
20532^442688-113489133263Enzo Doria08/2014
2054(7*2^442640-1)/783133246Lelio R Paula07/2015
2055(9*2^442463+1)/17441133192Lelio R Paula07/2015
20562^442437-1849993133187Enzo Doria08/2015
20572^442430-2791721133185Enzo Doria03/2016
2058(13*2^442428-1)/309133183Lelio R Paula07/2015
2059(25*2^442379-1)/71133169Lelio R Paula07/2015
2060(2^441799+78557)/5132995Lelio R Paula07/2015
20612^441781-2787883132990Enzo Doria03/2016
2062(3*2^441685+1)/749132959Lelio R Paula07/2015
20632^441618+37132941Lelio R Paula08/2017
20642^441521-113575132912Enzo Doria08/2014
20657*10^132884-99132885Robert Price06/2019
20662^441396-65132874Lelio R Paula08/2017
20672^441330+1871959132854Enzo Doria05/2016
20682^441063+383132774Lelio R Paula06/2012
2069(22*10^132746+53)/3132747Robert Price07/2019
20702^440846+1870909132708Enzo Doria05/2016
20712^440656-113489132651Enzo Doria08/2014
2072numbpart(14180123587)132646Serge Batalov04/2017
2073(19*10^132550+191)/3132551Robert Price05/2019
2074(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
2075(38^83891+1)/39132529Robert Price09/2013
20762*10^132493-43132494Robert Price04/2018
20772^439931-21132433Lelio R Paula08/2017
207847^79201-46^79201132432Robert Price10/2012
20792^439897-113653132423Enzo Doria08/2014
2080(5*2^439822+1)/9132400Lelio R Paula06/2015
2081(112*10^132337-1)/3132339Serge Batalov12/2014
20822^439576-113247132326Enzo Doria07/2014
20832^439497-29143132302Enzo Doria07/2015
20842^439409-114193132276Enzo Doria12/2014
2085(44*10^132233-233)/9132234Robert Price01/2019
20869*10^132148-7132149Robert Price09/2015
2087(47*10^132125-119)/9132126Robert Price05/2019
20882^438845+1870217132106Enzo Doria05/2016
20892^438789+87855132089Lelio R Paula01/2016
20902^438774-2786411132085Enzo Doria03/2016
20912^438755-1848205132079Enzo Doria07/2015
20922^438739-112087132074Enzo Doria06/2014
209313907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
2094L(631181)131910Henri Lifchitz09/2008
2095(47*10^131886-119)/9131887Robert Price05/2019
2096(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
20972^438079-1863877131875Enzo Doria03/2016
2098(2^438067+5)/329131869Lelio R Paula06/2015
20992^437908-113855131824Enzo Doria09/2014
21002^437884-286349131817Enzo Doria07/2015
2101(11*10^131784-17)/3131785Robert Price06/2018
21023^276062-112292131716Enzo Doria07/2014
21032^437343+75953131654Enzo Doria04/2016
210435^85243-34^85243131621Robert Price05/2012
2105(68^71713+1)/69131413Paul Bourdelais09/2017
21062^436451+1884713131385Enzo Doria03/2017
21072^436365+35131359Robert Price11/2015
21082^436300+1866871131340Enzo Doria03/2016
2109(7*10^131339+179)/3131340Robert Price09/2018
2110(37*10^131270+341)/9131271Robert Price08/2018
2111(5*10^131223-29)/3131224Robert Price03/2018
2112(23*2^435891-1)/699131215Lelio R Paula07/2015
2113(11*2^435879+1)/3337131211Lelio R Paula06/2015
2115(2^435808+1)/641/6700417131182Lelio R Paula02/2012
2114(2^435808+1)/4294967297131182Serge Batalov12/2016
21162^435773+1875557131181Enzo Doria06/2016
2117(16*10^131180+167)/3131181Robert Price06/2019
2118(25*10^131144-7)/9131145Robert Price05/2018
21192^435612-2789939131133Enzo Doria12/2015
212066^72047-65^72047131093Robert Price09/2013
2121(5*10^131090+37)/3131091Robert Price03/2018
21222^435468+75631131089Enzo Doria04/2016
212337^83588-2131083Lelio R Paula08/2015
2124(4^217720+11)/3131081Robert Price02/2017
21252^435202-113193131009Enzo Doria07/2014
21269*10^130998-19130999Robert Price07/2019
2127floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
21282^434835-111937130899Enzo Doria05/2014
21292^434685+72257130854Enzo Doria04/2016
2130(7*10^130825+113)/3130826Robert Price02/2018
21312^434539-29317130810Enzo Doria07/2015
21322^434469-114259130789Enzo Doria01/2015
21332^434246+33130722Robert Price11/2015
21342^433911-91130621Lelio R Paula06/2017
21352^433744-114419130570Enzo Doria02/2015
21372^433708+1869451130560Enzo Doria05/2016
21362^433710+93130560Lelio R Paula06/2017
2138(29*2^433547-1)/27130511Lelio R Paula06/2015
21394*10^130480+9130481Robert Price05/2015
2140(23*2^433449-1)/75130481Lelio R Paula06/2015
2141(23*2^433334-1)/3731130445Lelio R Paula06/2015
21422^433023-113497130353Enzo Doria08/2014
21432^433002+1179379130347Enzo Doria06/2016
21442^432974+19130339Robert Price08/2015
2145(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
21462^432217+41130111Lelio R Paula06/2017
2147(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
2148((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
214997^65480-2130094Lelio R Paula05/2017
21504*10^130088-89130089Robert Price11/2018
21512^432117-113215130081Enzo Doria07/2014
21522^431804+72511129986Enzo Doria04/2016
2153(3^272141-3^136071+1)/7129844Serge Batalov03/2014
2154(47*10^129789-119)/9129790Robert Price05/2019
2155(9*2^431141+1)/17129787Lelio R Paula06/2015
2156(29*2^430881-1)/21129709Lelio R Paula06/2015
21572^430807+1869563129686Enzo Doria05/2016
21582^430721-21429129660Enzo Doria07/2013
21592^430415-276271129568Enzo Doria07/2015
21602^430142-2791721129486Enzo Doria03/2016
2161(7*10^129472-13)/3129473Robert Price07/2018
21622^429568-21017129313Enzo Doria07/2013
2163(11*10^129239-179)/3129240Robert Price09/2018
21642^429194-112685129201Enzo Doria06/2014
21652^429145-2780449129186Enzo Doria04/2016
21662^428892-113453129110Enzo Doria07/2014
2167(11*2^428881-7)/15129106Renaud Lifchitz03/2011
21682^428727-113959129060Enzo Doria10/2014
2169(7*2^428725-1)/13129059Lelio R Paula05/2014
2170(10^129051-31)/3129051Serge Batalov12/2014
21712^428564+71161129011Enzo Doria04/2016
21722^428502-113285128992Enzo Doria07/2014
21732^428421-21373128968Enzo Doria06/2013
2174L(616787)128901Henri Lifchitz09/2008
217591^65772-2128851Lelio R Paula05/2017
21762^428022+43128848Lelio R Paula05/2017
21772^427999-459397128841Enzo Doria05/2015
21782^427993+76847128839Enzo Doria05/2016
21792^427824-1851507128788Enzo Doria08/2015
21802^427807-21469128783Enzo Doria07/2013
218111^123594-240128710Enzo Doria09/2012
21822^427504-21503128692Enzo Doria07/2013
21832^427420+91128667Lelio R Paula05/2017
2184(68*10^128645-257)/9128646Robert Price07/2019
21852^427269-113635128621Enzo Doria08/2014
21862^427130+1877569128579Enzo Doria08/2016
21872^427016-115349128545Enzo Doria07/2015
2188(4*10^128510+137)/3128511Robert Price03/2018
21892^426889-112879128507Enzo Doria06/2014
21902^426804+1869931128481Enzo Doria05/2016
21912^426750+77635128465Enzo Doria05/2016
21922^426425-91128367Lelio R Paula05/2017
2193(15*2^426398-1)/11128359Lelio R Paula05/2014
21942^426352+74971128345Enzo Doria04/2016
21954*10^128343-21128344Robert Price09/2018
21962^426300-1863689128330Enzo Doria03/2016
21972^426293+1881017128327Enzo Doria11/2016
21982^426043+35128252Robert Price11/2015
2199(4*10^128244-19)/3128245Robert Price03/2018
22002^425808-459959128181Enzo Doria06/2015
22012^425627-113605128127Enzo Doria08/2014
2202(22*10^128094+53)/3128095Robert Price07/2019
2203(86*10^128086-221)/9128087Robert Price09/2019
220418565^30002-30002^18565128070Norbert Schneider01/2015
2205(2^425287-9)/2737128021Lelio R Paula05/2015
2206(3*2^425233-1)/25128007Lelio R Paula05/2014
22072^425205+4911128000Marek Hubal02/2017
22082^425118-113663127974Enzo Doria08/2014
22092^425061+1869761127957Enzo Doria05/2016
2210746^44541+44541^746127955Norbert Schneider07/2019
22112^424918-21141127914Enzo Doria07/2013
22122^424864-29489127897Enzo Doria08/2015
2213(97*10^127858-1)/3127860Serge Batalov12/2014
22142^424632-2786639127827Enzo Doria03/2016
22152^424577-113755127811Enzo Doria09/2014
2216(7*2^424512-1)/3127792Lelio R Paula05/2014
2217(56*10^127752+691)/9127753Robert Price05/2019
221811^122629-720127705Enzo Doria11/2012
22192^423696-21429127546Enzo Doria07/2013
22202^423664-1864559127536Enzo Doria03/2016
22213^267267-4127519Henri Lifchitz10/2014
2222(19^99689+5^99689)/24127477Robert Price09/2013
2223(21*2^423372+1)/101127447Lelio R Paula05/2014
22242^423328-21537127435Enzo Doria07/2013
2225(2^423165-7)/25127384Lelio R Paula05/2015
2226(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
2227(16*10^127259+197)/3127260Robert Price04/2019
2228(234483*27^88884-145)/26127230Curtis Bright05/2015
22292^422515-114997127190Enzo Doria06/2015
22305*10^127179-3127180Robert Price07/2015
2231(44*10^127169-233)/9127170Robert Price01/2019
22325*10^127153+77127154Robert Price12/2018
2233736^44335+44335^736127104Norbert Schneider07/2019
2234-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
2235(78^67141-1)/77127036Paul Bourdelais09/2017
22362^421860-113285126993Enzo Doria07/2014
2237(2^421827-7)/11126982Lelio R Paula05/2015
223811^121910-840126957Enzo Doria12/2012
2239(71^68539+1)/72126882Paul Bourdelais09/2017
2240(5*10^126871-119)/3126872Robert Price03/2018
2241331^50339-10004126846Enzo Doria07/2012
22422^421363-2790757126843Enzo Doria03/2016
2243(106*10^126839-1)/3126841Serge Batalov12/2014
2244(7*2^421243+1)/39126807Lelio R Paula05/2014
2245(14*10^126784-83)/3126785Robert Price12/2018
22462^421161-286183126783Enzo Doria06/2015
22472^420939-113935126716Enzo Doria10/2014
2248177^56363-2126703Lelio R Paula10/2017
22492^420741-113659126656Enzo Doria08/2014
22502^420694-21126642Lelio R Paula05/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 13 2019 10:51 (Time in France)

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