PRP Records

Probable Primes Top 10000

(193013 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 (> 30000) Who ? When ?
1501555555*2^458524+1513138036Darren Bedwell08/2009
15022^458465+2^32+1138012T. D. Noe06/2007
15032^458321-113053137969Enzo Doria07/2014
15042^458298+79459137962Enzo Doria06/2016
15052^458248-21815137947Enzo Doria07/2013
15062^458194+1876549137931Enzo Doria07/2016
1507(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
15082^457937+57137853Lelio R Paula09/2017
15092^457822+105137819Donovan Johnson06/2006
15102^457754-113711137798Enzo Doria09/2014
151111^132315-360137792Enzo Doria09/2012
15122^457347-37137676Lelio R Paula09/2017
15132^457322-2786393137668Enzo Doria10/2015
1514gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
15152^457240-59939137643Enzo Doria10/2015
15162^457120-21575137607Enzo Doria07/2013
1517(11*2^456978+1)/15137564Lelio R Paula07/2015
1518(7*25^98399+10613)/12137556Curtis Bright05/2015
15192^456796-113513137510Enzo Doria08/2014
1520(7*2^456655+1)/39137467Lelio R Paula07/2015
15212^456503-114361137422Enzo Doria01/2015
1522(11*2^456387+1)/19137386Lelio R Paula07/2015
1523(71*10^137250+1)/9137251Serge Batalov05/2010
15242^455922+76249137247Enzo Doria05/2016
152514^119741-119741^14137239Serge Batalov04/2016
1526(19*2^455760+1)/3455137196Lelio R Paula07/2015
1527124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
15282^455689+72677137177Enzo Doria04/2016
1529(17948!)^2+Prime(17948)137118Robert Price08/2014
1530(37^87421-1)/36137093Robert Price03/2012
15312^455323-57137066Lelio R Paula09/2017
1532(73*17^111333-9)/16136991Curtis Bright05/2015
15332^455025-112723136977Enzo Doria06/2014
15342^454675-1777136871Yves Minet10/2011
1535(6092*28^94536-143)/9136812Curtis Bright05/2015
15362^454348-53136773Lelio R Paula09/2017
153731^91680-2136729Lelio R Paula05/2017
15382^454199-113697136728Enzo Doria09/2014
15392^453935-2791357136649Enzo Doria01/2016
15402^453906-69131136640Enzo Doria11/2015
15412^453791+1873913136605Enzo Doria06/2016
1542(21*2^453740-1)/2735136588Lelio R Paula07/2015
15432^453503-2788297136519Enzo Doria11/2015
15442^453267-113827136447Enzo Doria09/2014
15452^453102+1877629136398Enzo Doria08/2016
1546L(651821)136223Henri Lifchitz09/2008
15472^452460+77701136205Enzo Doria05/2016
15482^452440-114755136199Enzo Doria04/2015
1549(2^451956-5)/181136051Lelio R Paula07/2015
15502^451947-22165136050Enzo Doria07/2013
15512^451787-21805136002Enzo Doria07/2013
15522^451734-112817135986Enzo Doria06/2014
1553(11*2^451714+1)/75135979Lelio R Paula07/2015
15542^451705-21879135977Enzo Doria07/2013
15552^451560-112349135934Enzo Doria06/2014
15562^451530+45135925Lelio R Paula08/2017
15572^451450-21743135900Enzo Doria07/2013
15582^450805+65135706Lelio R Paula08/2017
1559(13725^32768+1)/131074135573Lelio R Paula03/2012
1560(5^193939+1)/6135557Paul Bourdelais12/2008
15612^449944-113247135447Enzo Doria07/2014
15622^449770-113247135395Enzo Doria07/2014
15632^449637-21471135355Enzo Doria07/2013
15642^449571-75135335Lelio R Paula08/2017
1565(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
15662^449330-35135262Lelio R Paula08/2017
1567(19*2^449325+1)/9135261Lelio R Paula07/2015
15682^449049-115309135178Enzo Doria07/2015
15692^449030-15135172Lelio R Paula08/2017
1570(27*2^448936-1)/11135144Lelio R Paula07/2015
15712^448762-351401135091Enzo Doria07/2015
1572(10^135011+719)/9135011Serge Batalov12/2014
15732^448386-2786261134978Enzo Doria03/2016
15742^448113-113949134896Enzo Doria11/2014
15752^447888-2786639134828Enzo Doria03/2016
15762^447870-396765134823Enzo Doria07/2013
15772^447766-21791134791Enzo Doria07/2013
1578(23*2^447647+1)/155134755Lelio R Paula07/2015
15792^447552-1019134727Yves Minet02/2014
15802^447437-113569134692Enzo Doria08/2014
15812^447426-65134689Lelio R Paula08/2017
15822^447357-2797573134668Enzo Doria04/2016
15832^447278+93134645Lelio R Paula08/2017
15842^447094-113193134589Enzo Doria07/2014
15853^282041-9934134568Enzo Doria05/2014
15862^447019-109039134567Enzo Doria04/2014
15872^446990-22041134558Enzo Doria07/2013
15882^446782-39701134495Enzo Doria09/2015
15892^446494-16485134409Enzo Doria04/2013
159029504^30069-30069^29504134405Norbert Schneider12/2014
15912^446441+65134393Lelio R Paula08/2017
1592(10^134385+719)/9134385Serge Batalov12/2014
1593(13*2^446187-1)/661134314Lelio R Paula07/2015
1594(2^446022-7)/339134264Lelio R Paula07/2015
159563^74568+2134174Lelio R Paula06/2017
15962^445671-22071134161Enzo Doria07/2013
1597(28*10^134122-1)/9134123Serge Batalov10/2014
15982^445515-113859134114Enzo Doria10/2014
15992^445328-216917134058Enzo Doria05/2014
16002^445202+1874899134020Enzo Doria06/2016
1601(13*2^445102+1)/17133989Lelio R Paula07/2015
16022^444964-113639133948Enzo Doria08/2014
160328118^30097-30097^28118133902Norbert Schneider01/2015
16042^444784-113859133894Enzo Doria10/2014
1605(89*10^133580+1)/9133581Serge Batalov05/2010
160662^74521-61^74521133571Robert Price05/2013
16072^443198-1867301133416Enzo Doria03/2016
1608(71^72043-1)/70133369Paul Bourdelais09/2017
16092^442799+1874633133296Enzo Doria06/2016
1610L(637751)133283Henri Lifchitz09/2008
1611109^65410-2133269Lelio R Paula10/2017
16122^442688-113489133263Enzo Doria08/2014
1613(7*2^442640-1)/783133246Lelio R Paula07/2015
1614(9*2^442463+1)/17441133192Lelio R Paula07/2015
16152^442437-1849993133187Enzo Doria08/2015
16162^442430-2791721133185Enzo Doria03/2016
1617(13*2^442428-1)/309133183Lelio R Paula07/2015
1618(25*2^442379-1)/71133169Lelio R Paula07/2015
1619(2^441799+78557)/5132995Lelio R Paula07/2015
16202^441781-2787883132990Enzo Doria03/2016
1621(3*2^441685+1)/749132959Lelio R Paula07/2015
16222^441618+37132941Lelio R Paula08/2017
16232^441521-113575132912Enzo Doria08/2014
16242^441396-65132874Lelio R Paula08/2017
16252^441330+1871959132854Enzo Doria05/2016
16262^441063+383132774Lelio R Paula06/2012
16272^440846+1870909132708Enzo Doria05/2016
16282^440656-113489132651Enzo Doria08/2014
1629numbpart(14180123587)132646Serge Batalov04/2017
1630(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
1631(38^83891+1)/39132529Robert Price09/2013
16322^439931-21132433Lelio R Paula08/2017
163347^79201-46^79201132432Robert Price10/2012
16342^439897-113653132423Enzo Doria08/2014
1635(5*2^439822+1)/9132400Lelio R Paula06/2015
1636(112*10^132337-1)/3132339Serge Batalov12/2014
16372^439576-113247132326Enzo Doria07/2014
16382^439497-29143132302Enzo Doria07/2015
16392^439409-114193132276Enzo Doria12/2014
16409*10^132148-7132149Robert Price09/2015
16412^438845+1870217132106Enzo Doria05/2016
16422^438789+87855132089Lelio R Paula01/2016
16432^438774-2786411132085Enzo Doria03/2016
16442^438755-1848205132079Enzo Doria07/2015
16452^438739-112087132074Enzo Doria06/2014
164613907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
1647L(631181)131910Henri Lifchitz09/2008
1648(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
16492^438079-1863877131875Enzo Doria03/2016
1650(2^438067+5)/329131869Lelio R Paula06/2015
16512^437908-113855131824Enzo Doria09/2014
16522^437884-286349131817Enzo Doria07/2015
16533^276062-112292131716Enzo Doria07/2014
16542^437343+75953131654Enzo Doria04/2016
165535^85243-34^85243131621Robert Price05/2012
1656(68^71713+1)/69131413Paul Bourdelais09/2017
16572^436451+1884713131385Enzo Doria03/2017
16582^436365+35131359Robert Price11/2015
16592^436300+1866871131340Enzo Doria03/2016
1660(23*2^435891-1)/699131215Lelio R Paula07/2015
1661(11*2^435879+1)/3337131211Lelio R Paula06/2015
1663(2^435808+1)/641/6700417131182Lelio R Paula02/2012
1662(2^435808+1)/4294967297131182Serge Batalov12/2016
16642^435773+1875557131181Enzo Doria06/2016
16652^435612-2789939131133Enzo Doria12/2015
166666^72047-65^72047131093Robert Price09/2013
16672^435468+75631131089Enzo Doria04/2016
166837^83588-2131083Lelio R Paula08/2015
1669(4^217720+11)/3131081Robert Price02/2017
16702^435202-113193131009Enzo Doria07/2014
1671floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
16722^434835-111937130899Enzo Doria05/2014
16732^434685+72257130854Enzo Doria04/2016
16742^434539-29317130810Enzo Doria07/2015
16752^434469-114259130789Enzo Doria01/2015
16762^434246+33130722Robert Price11/2015
16772^433911-91130621Lelio R Paula06/2017
16782^433744-114419130570Enzo Doria02/2015
16792^433708+1869451130560Enzo Doria05/2016
16802^433710+93130560Lelio R Paula06/2017
1681(29*2^433547-1)/27130511Lelio R Paula06/2015
16824*10^130480+9130481Robert Price05/2015
1683(23*2^433449-1)/75130481Lelio R Paula06/2015
1684(23*2^433334-1)/3731130445Lelio R Paula06/2015
16852^433023-113497130353Enzo Doria08/2014
16862^433002+1179379130347Enzo Doria06/2016
16872^432974+19130339Robert Price08/2015
1688(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
16892^432217+41130111Lelio R Paula06/2017
1690(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
1691((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
169297^65480-2130094Lelio R Paula05/2017
16932^432117-113215130081Enzo Doria07/2014
16942^431804+72511129986Enzo Doria04/2016
1695(3^272141-3^136071+1)/7129844Serge Batalov03/2014
1696(9*2^431141+1)/17129787Lelio R Paula06/2015
1697(29*2^430881-1)/21129709Lelio R Paula06/2015
16982^430807+1869563129686Enzo Doria05/2016
16992^430721-21429129660Enzo Doria07/2013
17002^430415-276271129568Enzo Doria07/2015
17012^430142-2791721129486Enzo Doria03/2016
17022^429568-21017129313Enzo Doria07/2013
17032^429194-112685129201Enzo Doria06/2014
17042^429145-2780449129186Enzo Doria04/2016
17052^428892-113453129110Enzo Doria07/2014
1706(11*2^428881-7)/15129106Renaud Lifchitz03/2011
17072^428727-113959129060Enzo Doria10/2014
1708(7*2^428725-1)/13129059Lelio R Paula05/2014
1709(10^129051-31)/3129051Serge Batalov12/2014
17102^428564+71161129011Enzo Doria04/2016
17112^428502-113285128992Enzo Doria07/2014
17122^428421-21373128968Enzo Doria06/2013
1713L(616787)128901Henri Lifchitz09/2008
171491^65772-2128851Lelio R Paula05/2017
17152^428022+43128848Lelio R Paula05/2017
17162^427999-459397128841Enzo Doria05/2015
17172^427993+76847128839Enzo Doria05/2016
17182^427824-1851507128788Enzo Doria08/2015
17192^427807-21469128783Enzo Doria07/2013
172011^123594-240128710Enzo Doria09/2012
17212^427504-21503128692Enzo Doria07/2013
17222^427420+91128667Lelio R Paula05/2017
17232^427269-113635128621Enzo Doria08/2014
17242^427130+1877569128579Enzo Doria08/2016
17252^427016-115349128545Enzo Doria07/2015
17262^426889-112879128507Enzo Doria06/2014
17272^426804+1869931128481Enzo Doria05/2016
17282^426750+77635128465Enzo Doria05/2016
17292^426425-91128367Lelio R Paula05/2017
1730(15*2^426398-1)/11128359Lelio R Paula05/2014
17312^426352+74971128345Enzo Doria04/2016
17322^426300-1863689128330Enzo Doria03/2016
17332^426293+1881017128327Enzo Doria11/2016
17342^426043+35128252Robert Price11/2015
17352^425808-459959128181Enzo Doria06/2015
17362^425627-113605128127Enzo Doria08/2014
173718565^30002-30002^18565128070Norbert Schneider01/2015
1738(2^425287-9)/2737128021Lelio R Paula05/2015
1739(3*2^425233-1)/25128007Lelio R Paula05/2014
17402^425205+4911128000Marek Hubal02/2017
17412^425118-113663127974Enzo Doria08/2014
17422^425061+1869761127957Enzo Doria05/2016
17432^424918-21141127914Enzo Doria07/2013
17442^424864-29489127897Enzo Doria08/2015
1745(97*10^127858-1)/3127860Serge Batalov12/2014
17462^424632-2786639127827Enzo Doria03/2016
17472^424577-113755127811Enzo Doria09/2014
1748(7*2^424512-1)/3127792Lelio R Paula05/2014
174911^122629-720127705Enzo Doria11/2012
17502^423696-21429127546Enzo Doria07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 09 2017 09:21 (Time in France)

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