PRP Records

Probable Primes Top 10000

(252538 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 ?
17512^459063-345307138192Enzo Doria06/2015
17522*10^138162-43138163Robert Price04/2018
17532^458927-112747138151Enzo Doria06/2014
17542^458927-69217138151Enzo Doria11/2015
1755555555*2^458524+1513138036Darren Bedwell08/2009
17562^458465+2^32+1138012T. D. Noe06/2007
17572^458321-113053137969Enzo Doria07/2014
17582^458298+79459137962Enzo Doria06/2016
17592^458248-21815137947Enzo Doria07/2013
17602^458194+1876549137931Enzo Doria07/2016
1761(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
17622^457937+57137853Lelio R Paula09/2017
1763(8*10^137845+13)/3137846Robert Price06/2018
17642^457822+105137819Donovan Johnson06/2006
17652^457754-113711137798Enzo Doria09/2014
176611^132315-360137792Enzo Doria09/2012
17672^457347-37137676Lelio R Paula09/2017
17682^457322-2786393137668Enzo Doria10/2015
1769gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
17702^457240-59939137643Enzo Doria10/2015
17712^457120-21575137607Enzo Doria07/2013
1772(11*2^456978+1)/15137564Lelio R Paula07/2015
1773(7*25^98399+10613)/12137556Curtis Bright05/2015
17742^456796-113513137510Enzo Doria08/2014
1775(7*2^456655+1)/39137467Lelio R Paula07/2015
17762^456503-114361137422Enzo Doria01/2015
1777(11*2^456387+1)/19137386Lelio R Paula07/2015
1778(71*10^137250+1)/9137251Serge Batalov05/2010
17792^455922+76249137247Enzo Doria05/2016
178014^119741-119741^14137239Serge Batalov04/2016
1781(19*2^455760+1)/3455137196Lelio R Paula07/2015
1782124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
1783124^65536+57^65536137195Serge Batalov03/2018
17842^455689+72677137177Enzo Doria04/2016
1785(17948!)^2+Prime(17948)137118Robert Price08/2014
1786(37^87421-1)/36137093Robert Price03/2012
17872^455323-57137066Lelio R Paula09/2017
1788(73*17^111333-9)/16136991Curtis Bright05/2015
17892^455025-112723136977Enzo Doria06/2014
17902^454675-1777136871Yves Minet10/2011
17913*10^136829+29136830Robert Price05/2018
17924*10^136813-57136814Robert Price10/2018
1793(6092*28^94536-143)/9136812Curtis Bright05/2015
17942^454348-53136773Lelio R Paula09/2017
179531^91680-2136729Lelio R Paula05/2017
17962^454199-113697136728Enzo Doria09/2014
1797(13*10^136687+47)/3136688Robert Price10/2018
17982^453935-2791357136649Enzo Doria01/2016
17992^453906-69131136640Enzo Doria11/2015
18002^453791+1873913136605Enzo Doria06/2016
1801(21*2^453740-1)/2735136588Lelio R Paula07/2015
18022^453503-2788297136519Enzo Doria11/2015
18032^453267-113827136447Enzo Doria09/2014
18042^453102+1877629136398Enzo Doria08/2016
1805L(651821)136223Henri Lifchitz09/2008
18062^452460+77701136205Enzo Doria05/2016
18072^452440-114755136199Enzo Doria04/2015
18082*10^136057-43136058Robert Price04/2018
1809(2^451956-5)/181136051Lelio R Paula07/2015
18102^451947-22165136050Enzo Doria07/2013
18112^451787-21805136002Enzo Doria07/2013
18122^451734-112817135986Enzo Doria06/2014
1813(11*2^451714+1)/75135979Lelio R Paula07/2015
18142^451705-21879135977Enzo Doria07/2013
18152^451560-112349135934Enzo Doria06/2014
18162^451530+45135925Lelio R Paula08/2017
18172^451450-21743135900Enzo Doria07/2013
18182^450805+65135706Lelio R Paula08/2017
1819(13725^32768+1)/131074135573Lelio R Paula03/2012
1820(5^193939+1)/6135557Paul Bourdelais12/2008
18212^449944-113247135447Enzo Doria07/2014
18222^449770-113247135395Enzo Doria07/2014
18232^449637-21471135355Enzo Doria07/2013
18242^449571-75135335Lelio R Paula08/2017
1825(14*10^135301-53)/3135302Robert Price12/2018
1826(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
1827(13*10^135279+437)/9135280Robert Price04/2018
18282^449330-35135262Lelio R Paula08/2017
1829(19*2^449325+1)/9135261Lelio R Paula07/2015
1830(13*10^135184-43)/3135185Robert Price11/2018
18312^449049-115309135178Enzo Doria07/2015
1832(10^135174+191)/3135174Robert Price02/2018
18332^449030-15135172Lelio R Paula08/2017
1834(27*2^448936-1)/11135144Lelio R Paula07/2015
18352^448762-351401135091Enzo Doria07/2015
18362*10^135083-43135084Robert Price04/2018
18375*10^135019+77135020Robert Price12/2018
1838(10^135011+719)/9135011Serge Batalov12/2014
18392^448386-2786261134978Enzo Doria03/2016
18402^448113-113949134896Enzo Doria11/2014
18412^447888-2786639134828Enzo Doria03/2016
18422^447870-396765134823Enzo Doria07/2013
18432^447766-21791134791Enzo Doria07/2013
1844(23*2^447647+1)/155134755Lelio R Paula07/2015
18452^447552-1019134727Yves Minet02/2014
1846(2*10^134720-41)/3134720Robert Price02/2018
18472^447437-113569134692Enzo Doria08/2014
18482^447426-65134689Lelio R Paula08/2017
18492^447357-2797573134668Enzo Doria04/2016
18502^447278+93134645Lelio R Paula08/2017
18512^447094-113193134589Enzo Doria07/2014
18523^282041-9934134568Enzo Doria05/2014
18532^447019-109039134567Enzo Doria04/2014
18542^446990-22041134558Enzo Doria07/2013
1855123^64370+122134528Karsten Bonath04/2018
18562^446782-39701134495Enzo Doria09/2015
18572^446494-16485134409Enzo Doria04/2013
185829504^30069-30069^29504134405Norbert Schneider12/2014
18592^446441+65134393Lelio R Paula08/2017
1860(10^134385+719)/9134385Serge Batalov12/2014
1861(2*10^134364+529)/9134364Robert Price01/2018
1862(13*2^446187-1)/661134314Lelio R Paula07/2015
1863(2^446022-7)/339134264Lelio R Paula07/2015
186463^74568+2134174Lelio R Paula06/2017
18652^445671-22071134161Enzo Doria07/2013
1866(28*10^134122-1)/9134123Serge Batalov10/2014
18672^445515-113859134114Enzo Doria10/2014
18682^445328-216917134058Enzo Doria05/2014
18692^445202+1874899134020Enzo Doria06/2016
1870(13*2^445102+1)/17133989Lelio R Paula07/2015
1871(35*10^133979-593)/9133980Robert Price07/2018
18722*10^133955+51133956Robert Price05/2018
18732^444964-113639133948Enzo Doria08/2014
187428118^30097-30097^28118133902Norbert Schneider01/2015
18752^444784-113859133894Enzo Doria10/2014
1876(89*10^133580+1)/9133581Serge Batalov05/2010
187762^74521-61^74521133571Robert Price05/2013
18782^443198-1867301133416Enzo Doria03/2016
1879(71^72043-1)/70133369Paul Bourdelais09/2017
18802^442799+1874633133296Enzo Doria06/2016
1881L(637751)133283Henri Lifchitz09/2008
1882109^65410-2133269Lelio R Paula10/2017
18832^442688-113489133263Enzo Doria08/2014
1884(7*2^442640-1)/783133246Lelio R Paula07/2015
1885(9*2^442463+1)/17441133192Lelio R Paula07/2015
18862^442437-1849993133187Enzo Doria08/2015
18872^442430-2791721133185Enzo Doria03/2016
1888(13*2^442428-1)/309133183Lelio R Paula07/2015
1889(25*2^442379-1)/71133169Lelio R Paula07/2015
1890(2^441799+78557)/5132995Lelio R Paula07/2015
18912^441781-2787883132990Enzo Doria03/2016
1892(3*2^441685+1)/749132959Lelio R Paula07/2015
18932^441618+37132941Lelio R Paula08/2017
18942^441521-113575132912Enzo Doria08/2014
18952^441396-65132874Lelio R Paula08/2017
18962^441330+1871959132854Enzo Doria05/2016
18972^441063+383132774Lelio R Paula06/2012
18982^440846+1870909132708Enzo Doria05/2016
18992^440656-113489132651Enzo Doria08/2014
1900numbpart(14180123587)132646Serge Batalov04/2017
1901(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
1902(38^83891+1)/39132529Robert Price09/2013
19032*10^132493-43132494Robert Price04/2018
19042^439931-21132433Lelio R Paula08/2017
190547^79201-46^79201132432Robert Price10/2012
19062^439897-113653132423Enzo Doria08/2014
1907(5*2^439822+1)/9132400Lelio R Paula06/2015
1908(112*10^132337-1)/3132339Serge Batalov12/2014
19092^439576-113247132326Enzo Doria07/2014
19102^439497-29143132302Enzo Doria07/2015
19112^439409-114193132276Enzo Doria12/2014
1912(44*10^132233-233)/9132234Robert Price01/2019
19139*10^132148-7132149Robert Price09/2015
19142^438845+1870217132106Enzo Doria05/2016
19152^438789+87855132089Lelio R Paula01/2016
19162^438774-2786411132085Enzo Doria03/2016
19172^438755-1848205132079Enzo Doria07/2015
19182^438739-112087132074Enzo Doria06/2014
191913907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
1920L(631181)131910Henri Lifchitz09/2008
1921(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
19222^438079-1863877131875Enzo Doria03/2016
1923(2^438067+5)/329131869Lelio R Paula06/2015
19242^437908-113855131824Enzo Doria09/2014
19252^437884-286349131817Enzo Doria07/2015
1926(11*10^131784-17)/3131785Robert Price06/2018
19273^276062-112292131716Enzo Doria07/2014
19282^437343+75953131654Enzo Doria04/2016
192935^85243-34^85243131621Robert Price05/2012
1930(68^71713+1)/69131413Paul Bourdelais09/2017
19312^436451+1884713131385Enzo Doria03/2017
19322^436365+35131359Robert Price11/2015
19342^436300+1866871131340Enzo Doria03/2016
1933(7*10^131339+179)/3131340Robert Price09/2018
1935(37*10^131270+341)/9131271Robert Price08/2018
1936(5*10^131223-29)/3131224Robert Price03/2018
1937(23*2^435891-1)/699131215Lelio R Paula07/2015
1938(11*2^435879+1)/3337131211Lelio R Paula06/2015
1940(2^435808+1)/641/6700417131182Lelio R Paula02/2012
1939(2^435808+1)/4294967297131182Serge Batalov12/2016
19412^435773+1875557131181Enzo Doria06/2016
1942(25*10^131144-7)/9131145Robert Price05/2018
19432^435612-2789939131133Enzo Doria12/2015
194466^72047-65^72047131093Robert Price09/2013
1945(5*10^131090+37)/3131091Robert Price03/2018
19462^435468+75631131089Enzo Doria04/2016
194737^83588-2131083Lelio R Paula08/2015
1948(4^217720+11)/3131081Robert Price02/2017
19492^435202-113193131009Enzo Doria07/2014
1950floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
19512^434835-111937130899Enzo Doria05/2014
19522^434685+72257130854Enzo Doria04/2016
1953(7*10^130825+113)/3130826Robert Price02/2018
19542^434539-29317130810Enzo Doria07/2015
19552^434469-114259130789Enzo Doria01/2015
19562^434246+33130722Robert Price11/2015
19572^433911-91130621Lelio R Paula06/2017
19582^433744-114419130570Enzo Doria02/2015
19602^433708+1869451130560Enzo Doria05/2016
19592^433710+93130560Lelio R Paula06/2017
1961(29*2^433547-1)/27130511Lelio R Paula06/2015
19624*10^130480+9130481Robert Price05/2015
1963(23*2^433449-1)/75130481Lelio R Paula06/2015
1964(23*2^433334-1)/3731130445Lelio R Paula06/2015
19652^433023-113497130353Enzo Doria08/2014
19662^433002+1179379130347Enzo Doria06/2016
19672^432974+19130339Robert Price08/2015
1968(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
19692^432217+41130111Lelio R Paula06/2017
1970(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
1971((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
197297^65480-2130094Lelio R Paula05/2017
19734*10^130088-89130089Robert Price11/2018
19742^432117-113215130081Enzo Doria07/2014
19752^431804+72511129986Enzo Doria04/2016
1976(3^272141-3^136071+1)/7129844Serge Batalov03/2014
1977(9*2^431141+1)/17129787Lelio R Paula06/2015
1978(29*2^430881-1)/21129709Lelio R Paula06/2015
19792^430807+1869563129686Enzo Doria05/2016
19802^430721-21429129660Enzo Doria07/2013
19812^430415-276271129568Enzo Doria07/2015
19822^430142-2791721129486Enzo Doria03/2016
1983(7*10^129472-13)/3129473Robert Price07/2018
19842^429568-21017129313Enzo Doria07/2013
1985(11*10^129239-179)/3129240Robert Price09/2018
19862^429194-112685129201Enzo Doria06/2014
19872^429145-2780449129186Enzo Doria04/2016
19882^428892-113453129110Enzo Doria07/2014
1989(11*2^428881-7)/15129106Renaud Lifchitz03/2011
19902^428727-113959129060Enzo Doria10/2014
1991(7*2^428725-1)/13129059Lelio R Paula05/2014
1992(10^129051-31)/3129051Serge Batalov12/2014
19932^428564+71161129011Enzo Doria04/2016
19942^428502-113285128992Enzo Doria07/2014
19952^428421-21373128968Enzo Doria06/2013
1996L(616787)128901Henri Lifchitz09/2008
199791^65772-2128851Lelio R Paula05/2017
19982^428022+43128848Lelio R Paula05/2017
19992^427999-459397128841Enzo Doria05/2015
20002^427993+76847128839Enzo Doria05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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