PRP Records

Probable Primes Top 10000

(253466 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(2^441799+78557)/5132995Lelio R Paula07/2015
20022^441781-2787883132990Enzo Doria03/2016
2003(3*2^441685+1)/749132959Lelio R Paula07/2015
20042^441618+37132941Lelio R Paula08/2017
20052^441521-113575132912Enzo Doria08/2014
20067*10^132884-99132885Robert Price06/2019
20072^441396-65132874Lelio R Paula08/2017
20082^441330+1871959132854Enzo Doria05/2016
20092^441063+383132774Lelio R Paula06/2012
2010(22*10^132746+53)/3132747Robert Price07/2019
20112^440846+1870909132708Enzo Doria05/2016
20122^440656-113489132651Enzo Doria08/2014
2013numbpart(14180123587)132646Serge Batalov04/2017
2014(19*10^132550+191)/3132551Robert Price05/2019
2015(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
2016(38^83891+1)/39132529Robert Price09/2013
20172*10^132493-43132494Robert Price04/2018
20182^439931-21132433Lelio R Paula08/2017
201947^79201-46^79201132432Robert Price10/2012
20202^439897-113653132423Enzo Doria08/2014
2021(5*2^439822+1)/9132400Lelio R Paula06/2015
2022(112*10^132337-1)/3132339Serge Batalov12/2014
20232^439576-113247132326Enzo Doria07/2014
20242^439497-29143132302Enzo Doria07/2015
20252^439409-114193132276Enzo Doria12/2014
2026(44*10^132233-233)/9132234Robert Price01/2019
20279*10^132148-7132149Robert Price09/2015
2028(47*10^132125-119)/9132126Robert Price05/2019
20292^438845+1870217132106Enzo Doria05/2016
20302^438789+87855132089Lelio R Paula01/2016
20312^438774-2786411132085Enzo Doria03/2016
20322^438755-1848205132079Enzo Doria07/2015
20332^438739-112087132074Enzo Doria06/2014
203413907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
2035L(631181)131910Henri Lifchitz09/2008
2036(47*10^131886-119)/9131887Robert Price05/2019
2037(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
20382^438079-1863877131875Enzo Doria03/2016
2039(2^438067+5)/329131869Lelio R Paula06/2015
20402^437908-113855131824Enzo Doria09/2014
20412^437884-286349131817Enzo Doria07/2015
2042(11*10^131784-17)/3131785Robert Price06/2018
20433^276062-112292131716Enzo Doria07/2014
20442^437343+75953131654Enzo Doria04/2016
204535^85243-34^85243131621Robert Price05/2012
2046(68^71713+1)/69131413Paul Bourdelais09/2017
20472^436451+1884713131385Enzo Doria03/2017
20482^436365+35131359Robert Price11/2015
20502^436300+1866871131340Enzo Doria03/2016
2049(7*10^131339+179)/3131340Robert Price09/2018
2051(37*10^131270+341)/9131271Robert Price08/2018
2052(5*10^131223-29)/3131224Robert Price03/2018
2053(23*2^435891-1)/699131215Lelio R Paula07/2015
2054(11*2^435879+1)/3337131211Lelio R Paula06/2015
2055(2^435808+1)/641/6700417131182Lelio R Paula02/2012
2056(2^435808+1)/4294967297131182Serge Batalov12/2016
20572^435773+1875557131181Enzo Doria06/2016
2058(16*10^131180+167)/3131181Robert Price06/2019
2059(25*10^131144-7)/9131145Robert Price05/2018
20602^435612-2789939131133Enzo Doria12/2015
206166^72047-65^72047131093Robert Price09/2013
2062(5*10^131090+37)/3131091Robert Price03/2018
20632^435468+75631131089Enzo Doria04/2016
206437^83588-2131083Lelio R Paula08/2015
2065(4^217720+11)/3131081Robert Price02/2017
20662^435202-113193131009Enzo Doria07/2014
20679*10^130998-19130999Robert Price07/2019
2068floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
20692^434835-111937130899Enzo Doria05/2014
20702^434685+72257130854Enzo Doria04/2016
2071(7*10^130825+113)/3130826Robert Price02/2018
20722^434539-29317130810Enzo Doria07/2015
20732^434469-114259130789Enzo Doria01/2015
20742^434246+33130722Robert Price11/2015
20752^433911-91130621Lelio R Paula06/2017
20762^433744-114419130570Enzo Doria02/2015
20782^433708+1869451130560Enzo Doria05/2016
20772^433710+93130560Lelio R Paula06/2017
2079(29*2^433547-1)/27130511Lelio R Paula06/2015
20804*10^130480+9130481Robert Price05/2015
2081(23*2^433449-1)/75130481Lelio R Paula06/2015
2082(23*2^433334-1)/3731130445Lelio R Paula06/2015
20832^433023-113497130353Enzo Doria08/2014
20842^433002+1179379130347Enzo Doria06/2016
20852^432974+19130339Robert Price08/2015
2086(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
20872^432217+41130111Lelio R Paula06/2017
2088(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
2089((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
209097^65480-2130094Lelio R Paula05/2017
20914*10^130088-89130089Robert Price11/2018
20922^432117-113215130081Enzo Doria07/2014
20932^431804+72511129986Enzo Doria04/2016
2094(3^272141-3^136071+1)/7129844Serge Batalov03/2014
2095(47*10^129789-119)/9129790Robert Price05/2019
2096(9*2^431141+1)/17129787Lelio R Paula06/2015
2097(29*2^430881-1)/21129709Lelio R Paula06/2015
20982^430807+1869563129686Enzo Doria05/2016
20992^430721-21429129660Enzo Doria07/2013
21002^430415-276271129568Enzo Doria07/2015
21012^430142-2791721129486Enzo Doria03/2016
2102(7*10^129472-13)/3129473Robert Price07/2018
21032^429568-21017129313Enzo Doria07/2013
2104(11*10^129239-179)/3129240Robert Price09/2018
21052^429194-112685129201Enzo Doria06/2014
21062^429145-2780449129186Enzo Doria04/2016
21072^428892-113453129110Enzo Doria07/2014
2108(11*2^428881-7)/15129106Renaud Lifchitz03/2011
21092^428727-113959129060Enzo Doria10/2014
2110(7*2^428725-1)/13129059Lelio R Paula05/2014
2111(10^129051-31)/3129051Serge Batalov12/2014
21122^428564+71161129011Enzo Doria04/2016
21132^428502-113285128992Enzo Doria07/2014
21142^428421-21373128968Enzo Doria06/2013
2115L(616787)128901Henri Lifchitz09/2008
211691^65772-2128851Lelio R Paula05/2017
21172^428022+43128848Lelio R Paula05/2017
21182^427999-459397128841Enzo Doria05/2015
21192^427993+76847128839Enzo Doria05/2016
21202^427824-1851507128788Enzo Doria08/2015
21212^427807-21469128783Enzo Doria07/2013
212211^123594-240128710Enzo Doria09/2012
21232^427504-21503128692Enzo Doria07/2013
21242^427420+91128667Lelio R Paula05/2017
2125(68*10^128645-257)/9128646Robert Price07/2019
21262^427269-113635128621Enzo Doria08/2014
21272^427130+1877569128579Enzo Doria08/2016
21282^427016-115349128545Enzo Doria07/2015
2129(4*10^128510+137)/3128511Robert Price03/2018
21302^426889-112879128507Enzo Doria06/2014
21312^426804+1869931128481Enzo Doria05/2016
21322^426750+77635128465Enzo Doria05/2016
21332^426425-91128367Lelio R Paula05/2017
2134(15*2^426398-1)/11128359Lelio R Paula05/2014
21352^426352+74971128345Enzo Doria04/2016
21364*10^128343-21128344Robert Price09/2018
21372^426300-1863689128330Enzo Doria03/2016
21382^426293+1881017128327Enzo Doria11/2016
21392^426043+35128252Robert Price11/2015
2140(4*10^128244-19)/3128245Robert Price03/2018
21412^425808-459959128181Enzo Doria06/2015
21422^425627-113605128127Enzo Doria08/2014
2143(22*10^128094+53)/3128095Robert Price07/2019
214418565^30002-30002^18565128070Norbert Schneider01/2015
2145(2^425287-9)/2737128021Lelio R Paula05/2015
2146(3*2^425233-1)/25128007Lelio R Paula05/2014
21472^425205+4911128000Marek Hubal02/2017
21482^425118-113663127974Enzo Doria08/2014
21492^425061+1869761127957Enzo Doria05/2016
2150746^44541+44541^746127955Norbert Schneider07/2019
21512^424918-21141127914Enzo Doria07/2013
21522^424864-29489127897Enzo Doria08/2015
2153(97*10^127858-1)/3127860Serge Batalov12/2014
21542^424632-2786639127827Enzo Doria03/2016
21552^424577-113755127811Enzo Doria09/2014
2156(7*2^424512-1)/3127792Lelio R Paula05/2014
2157(56*10^127752+691)/9127753Robert Price05/2019
215811^122629-720127705Enzo Doria11/2012
21592^423696-21429127546Enzo Doria07/2013
21602^423664-1864559127536Enzo Doria03/2016
21613^267267-4127519Henri Lifchitz10/2014
2162(19^99689+5^99689)/24127477Robert Price09/2013
2163(21*2^423372+1)/101127447Lelio R Paula05/2014
21642^423328-21537127435Enzo Doria07/2013
2165(2^423165-7)/25127384Lelio R Paula05/2015
2166(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
2167(16*10^127259+197)/3127260Robert Price04/2019
2168(234483*27^88884-145)/26127230Curtis Bright05/2015
21692^422515-114997127190Enzo Doria06/2015
21705*10^127179-3127180Robert Price07/2015
2171(44*10^127169-233)/9127170Robert Price01/2019
21725*10^127153+77127154Robert Price12/2018
2173736^44335+44335^736127104Norbert Schneider07/2019
2174-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
2175(78^67141-1)/77127036Paul Bourdelais09/2017
21762^421860-113285126993Enzo Doria07/2014
2177(2^421827-7)/11126982Lelio R Paula05/2015
217811^121910-840126957Enzo Doria12/2012
2179(71^68539+1)/72126882Paul Bourdelais09/2017
2180(5*10^126871-119)/3126872Robert Price03/2018
2181331^50339-10004126846Enzo Doria07/2012
21822^421363-2790757126843Enzo Doria03/2016
2183(106*10^126839-1)/3126841Serge Batalov12/2014
2184(7*2^421243+1)/39126807Lelio R Paula05/2014
2185(14*10^126784-83)/3126785Robert Price12/2018
21862^421161-286183126783Enzo Doria06/2015
21872^420939-113935126716Enzo Doria10/2014
2188177^56363-2126703Lelio R Paula10/2017
21892^420741-113659126656Enzo Doria08/2014
21902^420694-21126642Lelio R Paula05/2017
2191(13*10^126638+437)/9126639Robert Price04/2018
21924*10^126625+87126626Robert Price08/2018
2193(31*2^420556+1)/7126601Lelio R Paula05/2014
21947*10^126600-99126601Robert Price06/2019
21952^420424-59189126561Enzo Doria10/2015
21962^420126+71893126471Enzo Doria04/2016
2197(43*10^126441+47)/9126442Robert Price12/2018
21982^419866+1877059126393Enzo Doria07/2016
2199F(604711)126377Henri Lifchitz02/2005
22002^419757+72707126360Enzo Doria04/2016
22012^419720-21569126349Enzo Doria07/2013
22022^419637+29126324Henri Lifchitz02/2006
22032^419612+1876741126316Enzo Doria07/2016
22042^419520+2793271126289Enzo Doria03/2016
2205(2^419447-5)/369126264Lelio R Paula05/2014
22062^419328-1859939126231Enzo Doria03/2016
22072^419282-1851507126217Enzo Doria08/2015
22082^419251+1866143126208Enzo Doria03/2016
220911^121185+2126202Robert Price05/2014
2210(23*2^419036-1)/1393126141Lelio R Paula05/2014
22112^418851+23126087Robert Price09/2015
2212(2^418849-9)/2681126083Lelio R Paula05/2014
22132^418829+167126081Lelio R Paula01/2012
2214(31*2^418782-1)/75891126063Lelio R Paula05/2014
2215(19*2^418754-1)/15126058Lelio R Paula05/2014
22162^418319-109501125927Enzo Doria04/2014
22172^418316-112373125926Enzo Doria06/2014
2218(8*10^125894-29)/3125895Robert Price07/2018
2219(26*10^125886-413)/9125887Robert Price05/2018
22202^417968+1869811125821Enzo Doria06/2016
22212^417902+63125802Lelio R Paula09/2015
2222(10^125792-91)/9125792Serge Batalov12/2014
2223(35*10^125754-593)/9125755Robert Price07/2018
2224(32*10^125751-77)/9125752Robert Price06/2018
22252^417704+77011125742Enzo Doria05/2016
2226(10^125706+149)/3125706Serge Batalov12/2014
22272^417419-115309125656Enzo Doria07/2015
22282^417300+77281125620Enzo Doria05/2016
22292^417095-1657125559Yves Minet07/2014
22302^416773-25125462Lelio R Paula09/2015
2231(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2232(11*2^416691+1)/43125436Lelio R Paula05/2014
2233(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
22342^416641-2*416641+1125422Robert Price05/2018
2235(21*2^416566-1)/17125399Lelio R Paula05/2014
22362^416530+1870429125389Enzo Doria05/2016
2237(56*10^125385+691)/9125386Robert Price05/2019
22382^416490+1875109125376Enzo Doria09/2016
22392^416416-114929125354Enzo Doria05/2015
2240(172*10^125292-1)/9125294Serge Batalov12/2014
22412^416134+1865899125269Enzo Doria03/2016
2242153^57337-152125264Norbert Schneider12/2018
2243(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2244(23^91943-1)/22125201Robert Price01/2012
224543125^27010-106125185Enzo Doria08/2012
2246(38*10^125166+349)/9125167Robert Price10/2018
22472^415765-112603125158Enzo Doria06/2014
22488*10^125088-13125089Robert Price08/2019
22492^415290-113591125015Enzo Doria08/2014
22502^415276-460919125011Enzo Doria06/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2019 14:10 (Time in France)

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