PRP Records

Probable Primes Top 10000

(259919 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(11*2^456978+1)/15137564Lelio R Paula07/2015
2002(7*25^98399+10613)/12137556Curtis Bright05/2015
20032^456796-113513137510Enzo Doria08/2014
2004(7*2^456655+1)/39137467Lelio R Paula07/2015
20052^456503-114361137422Enzo Doria01/2015
2006(11*2^456387+1)/19137386Lelio R Paula07/2015
2007(71*10^137250+1)/9137251Serge Batalov05/2010
20082^455922+76249137247Enzo Doria05/2016
200914^119741-119741^14137239Serge Batalov04/2016
2010(19*2^455760+1)/3455137196Lelio R Paula07/2015
2012124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
2011124^65536+57^65536137195Serge Batalov03/2018
20132^455689+72677137177Enzo Doria04/2016
2014(17948!)^2+Prime(17948)137118Robert Price08/2014
2015(37^87421-1)/36137093Robert Price03/2012
20162^455323-57137066Lelio R Paula09/2017
2017(73*17^111333-9)/16136991Curtis Bright05/2015
20182^455025-112723136977Enzo Doria06/2014
20192^454675-1777136871Yves Minet10/2011
20203*10^136829+29136830Robert Price05/2018
20214*10^136813-57136814Robert Price10/2018
2022(6092*28^94536-143)/9136812Curtis Bright05/2015
20232^454348-53136773Lelio R Paula09/2017
202431^91680-2136729Lelio R Paula05/2017
20252^454199-113697136728Enzo Doria09/2014
20267*10^136716+69136717Robert Price07/2019
2027(13*10^136687+47)/3136688Robert Price10/2018
20282^453935-2791357136649Enzo Doria01/2016
20292^453906-69131136640Enzo Doria11/2015
20302^453791+1873913136605Enzo Doria06/2016
2031(21*2^453740-1)/2735136588Lelio R Paula07/2015
2032580^49413+49413^580136550Norbert Schneider02/2019
20332^453503-2788297136519Enzo Doria11/2015
20342^453267-113827136447Enzo Doria09/2014
20352^453102+1877629136398Enzo Doria08/2016
2036(62*10^136384-791)/9136385Robert Price06/2019
2037(25*10^136303+161)/3136304Robert Price09/2019
2038(182*10^136291+1)/3136293Robert Price02/2020
203923*10^136225-7136227Robert Price02/2020
2040L(651821)136223Henri Lifchitz09/2008
20412^452460+77701136205Enzo Doria05/2016
20422^452440-114755136199Enzo Doria04/2015
2043(47*10^136141+493)/9136142Robert Price03/2019
20442*10^136057-43136058Robert Price04/2018
2045(2^451956-5)/181136051Lelio R Paula07/2015
20462^451947-22165136050Enzo Doria07/2013
20472^451787-21805136002Enzo Doria07/2013
20482^451734-112817135986Enzo Doria06/2014
2049(11*2^451714+1)/75135979Lelio R Paula07/2015
20502^451705-21879135977Enzo Doria07/2013
20512^451560-112349135934Enzo Doria06/2014
20522^451530+45135925Lelio R Paula08/2017
2053(25*10^135906-73)/3135907Robert Price09/2019
20542^451450-21743135900Enzo Doria07/2013
20552^450805+65135706Lelio R Paula08/2017
2056(13725^32768+1)/131074135573Lelio R Paula03/2012
2057(5^193939+1)/6135557Paul Bourdelais12/2008
20582^449944-113247135447Enzo Doria07/2014
20592^449770-113247135395Enzo Doria07/2014
20602^449637-21471135355Enzo Doria07/2013
20612^449571-75135335Lelio R Paula08/2017
2062(14*10^135301-53)/3135302Robert Price12/2018
2063(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
2064(13*10^135279+437)/9135280Robert Price04/2018
20652^449330-35135262Lelio R Paula08/2017
2066(19*2^449325+1)/9135261Lelio R Paula07/2015
2067(13*10^135184-43)/3135185Robert Price11/2018
20682^449049-115309135178Enzo Doria07/2015
2069(10^135174+191)/3135174Robert Price02/2018
20702^449030-15135172Lelio R Paula08/2017
2071(27*2^448936-1)/11135144Lelio R Paula07/2015
20722^448762-351401135091Enzo Doria07/2015
20732*10^135083-43135084Robert Price04/2018
20745*10^135019+77135020Robert Price12/2018
2075(10^135011+719)/9135011Serge Batalov12/2014
20762^448386-2786261134978Enzo Doria03/2016
2077(73*10^134939+143)/9134940Robert Price07/2019
20782^448113-113949134896Enzo Doria11/2014
20792^447888-2786639134828Enzo Doria03/2016
20802^447870-396765134823Enzo Doria07/2013
20812^447766-21791134791Enzo Doria07/2013
2082(19*10^134786-49)/3134787Robert Price05/2019
2083Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
2084(23*2^447647+1)/155134755Lelio R Paula07/2015
20852^447552-1019134727Yves Minet02/2014
2086(2*10^134720-41)/3134720Robert Price02/2018
20872^447437-113569134692Enzo Doria08/2014
20882^447426-65134689Lelio R Paula08/2017
20892^447357-2797573134668Enzo Doria04/2016
20902^447278+93134645Lelio R Paula08/2017
20912^447094-113193134589Enzo Doria07/2014
20923^282041-9934134568Enzo Doria05/2014
20932^447019-109039134567Enzo Doria04/2014
20942^446990-22041134558Enzo Doria07/2013
2095123^64370+122134528Karsten Bonath04/2018
20962^446782-39701134495Enzo Doria09/2015
20972^446494-16485134409Enzo Doria04/2013
209829504^30069-30069^29504134405Norbert Schneider12/2014
20992^446441+65134393Lelio R Paula08/2017
2100(10^134385+719)/9134385Serge Batalov12/2014
2101(2*10^134364+529)/9134364Robert Price01/2018
2102(13*2^446187-1)/661134314Lelio R Paula07/2015
21035^192103+3^192103+2^192103+1134275Matthias Baur12/2019
2104(2^446022-7)/339134264Lelio R Paula07/2015
210563^74568+2134174Lelio R Paula06/2017
21062^445671-22071134161Enzo Doria07/2013
2107532^49205+49205^532134129Norbert Schneider02/2019
2108(28*10^134122-1)/9134123Serge Batalov10/2014
21092^445515-113859134114Enzo Doria10/2014
2110(22*10^134111-37)/3134112Robert Price04/2019
21112^445328-216917134058Enzo Doria05/2014
21122^445202+1874899134020Enzo Doria06/2016
2113(13*2^445102+1)/17133989Lelio R Paula07/2015
2114(35*10^133979-593)/9133980Robert Price07/2018
21152*10^133955+51133956Robert Price05/2018
21162^444964-113639133948Enzo Doria08/2014
211728118^30097-30097^28118133902Norbert Schneider01/2015
21182^444784-113859133894Enzo Doria10/2014
2119(89*10^133580+1)/9133581Serge Batalov05/2010
212062^74521-61^74521133571Robert Price05/2013
2121(182*10^133543+1)/3133545Robert Price02/2020
21222^443198-1867301133416Enzo Doria03/2016
2123(19*10^133390+101)/3133391Robert Price09/2019
2124(71^72043-1)/70133369Paul Bourdelais09/2017
21252^442799+1874633133296Enzo Doria06/2016
2126L(637751)133283Henri Lifchitz09/2008
2127109^65410-2133269Lelio R Paula10/2017
21282^442688-113489133263Enzo Doria08/2014
2129(7*2^442640-1)/783133246Lelio R Paula07/2015
2130(9*2^442463+1)/17441133192Lelio R Paula07/2015
21312^442437-1849993133187Enzo Doria08/2015
21322^442430-2791721133185Enzo Doria03/2016
2133(13*2^442428-1)/309133183Lelio R Paula07/2015
2134(25*2^442379-1)/71133169Lelio R Paula07/2015
2135(2^441799+78557)/5132995Lelio R Paula07/2015
21362^441781-2787883132990Enzo Doria03/2016
2137(3*2^441685+1)/749132959Lelio R Paula07/2015
21382^441618+37132941Lelio R Paula08/2017
21392^441521-113575132912Enzo Doria08/2014
21407*10^132884-99132885Robert Price06/2019
21412^441396-65132874Lelio R Paula08/2017
21422^441330+1871959132854Enzo Doria05/2016
21432^441063+383132774Lelio R Paula06/2012
2144(22*10^132746+53)/3132747Robert Price07/2019
21452^440846+1870909132708Enzo Doria05/2016
21462^440656-113489132651Enzo Doria08/2014
2147numbpart(14180123587)132646Serge Batalov04/2017
2148(19*10^132550+191)/3132551Robert Price05/2019
2149(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
2150(38^83891+1)/39132529Robert Price09/2013
21512*10^132493-43132494Robert Price04/2018
2152(418*10^132441+23)/9132443Robert Price02/2020
21532^439931-21132433Lelio R Paula08/2017
215447^79201-46^79201132432Robert Price10/2012
21552^439897-113653132423Enzo Doria08/2014
2156(5*2^439822+1)/9132400Lelio R Paula06/2015
2157(112*10^132337-1)/3132339Serge Batalov12/2014
21582^439576-113247132326Enzo Doria07/2014
21592^439497-29143132302Enzo Doria07/2015
21602^439409-114193132276Enzo Doria12/2014
2161(44*10^132233-233)/9132234Robert Price01/2019
21629*10^132148-7132149Robert Price09/2015
2163(47*10^132125-119)/9132126Robert Price05/2019
21642^438845+1870217132106Enzo Doria05/2016
21652^438789+87855132089Lelio R Paula01/2016
21662^438774-2786411132085Enzo Doria03/2016
21672^438755-1848205132079Enzo Doria07/2015
21682^438739-112087132074Enzo Doria06/2014
216913907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
2170L(631181)131910Henri Lifchitz09/2008
2171(47*10^131886-119)/9131887Robert Price05/2019
2172(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
21732^438079-1863877131875Enzo Doria03/2016
2174(2^438067+5)/329131869Lelio R Paula06/2015
21752^437908-113855131824Enzo Doria09/2014
21762^437884-286349131817Enzo Doria07/2015
2177(11*10^131784-17)/3131785Robert Price06/2018
21783^276062-112292131716Enzo Doria07/2014
21792^437343+75953131654Enzo Doria04/2016
218035^85243-34^85243131621Robert Price05/2012
2181(203*10^131457+1)/3131459Robert Price03/2020
2182(68^71713+1)/69131413Paul Bourdelais09/2017
21832^436451+1884713131385Enzo Doria03/2017
21842^436365+35131359Robert Price11/2015
21852^436300+1866871131340Enzo Doria03/2016
2186(7*10^131339+179)/3131340Robert Price09/2018
2187(37*10^131270+341)/9131271Robert Price08/2018
2188(5*10^131223-29)/3131224Robert Price03/2018
2189(23*2^435891-1)/699131215Lelio R Paula07/2015
2190(11*2^435879+1)/3337131211Lelio R Paula06/2015
2192(2^435808+1)/641/6700417131182Lelio R Paula02/2012
2191(2^435808+1)/4294967297131182Serge Batalov12/2016
21952^435773+1875557131181Enzo Doria06/2016
2194(16*10^131180+167)/3131181Robert Price06/2019
2193(26*10^131180-77)/3131181Robert Price11/2019
2196(25*10^131144-7)/9131145Robert Price05/2018
21972^435612-2789939131133Enzo Doria12/2015
219866^72047-65^72047131093Robert Price09/2013
2199(5*10^131090+37)/3131091Robert Price03/2018
22002^435468+75631131089Enzo Doria04/2016
220137^83588-2131083Lelio R Paula08/2015
2202(4^217720+11)/3131081Robert Price02/2017
22032^435202-113193131009Enzo Doria07/2014
22049*10^130998-19130999Robert Price07/2019
2205floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
22062^434835-111937130899Enzo Doria05/2014
22072^434685+72257130854Enzo Doria04/2016
2208(7*10^130825+113)/3130826Robert Price02/2018
22092^434539-29317130810Enzo Doria07/2015
22102^434469-114259130789Enzo Doria01/2015
22112^434246+33130722Robert Price11/2015
22122^433911-91130621Lelio R Paula06/2017
22132^433744-114419130570Enzo Doria02/2015
22152^433708+1869451130560Enzo Doria05/2016
22142^433710+93130560Lelio R Paula06/2017
2216(29*2^433547-1)/27130511Lelio R Paula06/2015
22174*10^130480+9130481Robert Price05/2015
2218(23*2^433449-1)/75130481Lelio R Paula06/2015
2219(23*2^433334-1)/3731130445Lelio R Paula06/2015
22202^433023-113497130353Enzo Doria08/2014
22212^433002+1179379130347Enzo Doria06/2016
22222^432974+19130339Robert Price08/2015
2223(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
22242^432217+41130111Lelio R Paula06/2017
2225(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
2226((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
222797^65480-2130094Lelio R Paula05/2017
22284*10^130088-89130089Robert Price11/2018
22292^432117-113215130081Enzo Doria07/2014
22302^431804+72511129986Enzo Doria04/2016
2231(3^272141-3^136071+1)/7129844Serge Batalov03/2014
2232(47*10^129789-119)/9129790Robert Price05/2019
2233(9*2^431141+1)/17129787Lelio R Paula06/2015
2234(29*2^430881-1)/21129709Lelio R Paula06/2015
22352^430807+1869563129686Enzo Doria05/2016
22362^430721-21429129660Enzo Doria07/2013
22372^430415-276271129568Enzo Doria07/2015
22382^430142-2791721129486Enzo Doria03/2016
2239(7*10^129472-13)/3129473Robert Price07/2018
22402^429568-21017129313Enzo Doria07/2013
2241(11*10^129239-179)/3129240Robert Price09/2018
22422^429194-112685129201Enzo Doria06/2014
22432^429145-2780449129186Enzo Doria04/2016
22442^428892-113453129110Enzo Doria07/2014
2245(11*2^428881-7)/15129106Renaud Lifchitz03/2011
22462^428727-113959129060Enzo Doria10/2014
2247(7*2^428725-1)/13129059Lelio R Paula05/2014
2248(10^129051-31)/3129051Serge Batalov12/2014
2249(134*10^129038+7)/3129040Robert Price02/2020
22502^428564+71161129011Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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