PRP Records

Probable Primes Top 10000

(247113 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 ?
6501(29*2^241446-1)/24572682Lelio R Paula01/2014
650311^69783-3840000072672Enzo Doria01/2013
65022^241409-11290372672Enzo Doria06/2014
6504(3^152287+1)/472659Paul Bourdelais04/2008
65053^152249-5672642Lelio R Paula01/2015
650610^72631+3772632Robert Price01/2011
650710^72631-881372631Patrick De Geest05/2013
6508(19*2^241254+1)/10172624Lelio R Paula08/2012
6509(9^76103+8^76103)/1772620Robert Price12/2012
65102^241220-11233772615Enzo Doria06/2014
6511(82*10^72612+449)/972613Robert Price02/2017
65122^241169-1579372600Enzo Doria04/2013
65139*10^72595+1172596Robert Kinser01/2017
6514(25*2^241048+1)/8972563Lelio R Paula08/2012
6515(22*10^72560+17)/372561Robert Price09/2015
65162^241032-2372558Lelio R Paula02/2012
651734485*10^72550+2^241004-372555Gilbert Mozzo12/2012
65182^241004-372550M. Frind & P. Underwood07/2002
651997*10^72522-372524Robert Price01/2017
6520(68*10^72516+7)/372518Robert Price03/2016
6521(78557*2^240844+1)/6372505Lelio R Paula06/2014
652267^39701-6672497Norbert Schneider11/2014
6523(185*10^72484+7)/372486Robert Price02/2017
6525(293*27^50631-1736)/1372473Curtis Bright05/2015
6524103^36005-10272473Norbert Schneider10/2016
652615^61616+8872467Lelio R Paula01/2015
652745^43831+272462Lelio R Paula05/2013
65282^240692-49238972456Paul Bourdelais03/2013
6529(646*10^72446-7)/972448Robert Price07/2016
65309*6^93083+772434Lelio R Paula10/2014
65312^240617-364572433Lelio R Paula05/2013
653211^69531-2400072410Enzo Doria12/2012
6533(22699*2^240396+1)/5572370Lelio R Paula06/2014
65346^92995+1372365Lelio R Paula01/2015
6535(11*10^72362-149)/372363Robert Price01/2017
6536(2^240381+3)/5165572358Lelio R Paula05/2012
65376^92974-5572348Lelio R Paula01/2015
65382^240295+1172337Lelio R Paula02/2012
6539(14*10^72326-53)/372327Robert Price12/2016
654015^61493-4672322Lelio R Paula01/2015
6541lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
65425*10^72302+972303Dmitry Domanov11/2010
6543(9787*2^240179-1)/26572303Lelio R Paula04/2015
654411^69419-312072293Enzo Doria12/2012
65454*10^72274-8372275Robert Price10/2017
654610^72267+3372268Robert Price01/2011
654710^72267-55394772267Patrick De Geest05/2013
654811^69389-138072262Enzo Doria12/2012
6549(16^60013-5^60013)/1172262Robert Price07/2013
65507^85507-3072262Lelio R Paula08/2014
6551(19*2^240026-1)/1572256Lelio R Paula02/2014
6552(3^151426-2)/66133772243Lelio R Paula06/2012
6553gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
65542^239863-11226772206Enzo Doria06/2014
65552^239853-11485372203Enzo Doria05/2015
6556(4*10^72174+149)/972174Robert Price03/2017
6558(2^239671+9)/29613172143Lelio R Paula05/2012
65572^239651-11066572143Enzo Doria05/2014
6559(29*2^239650-1)/330572140Lelio R Paula01/2014
6560241^30280+30280^24172128Norbert Schneider11/2014
6561(68*10^72120-23)/972121Robert Price10/2015
6562(9^75571+8^75571)/1772112Robert Price12/2012
6563(15*2^239530-1)/17372105Lelio R Paula01/2014
65642^239513-11251972101Enzo Doria06/2014
6565(10^72097+149)/372097Serge Batalov12/2014
65662^239442-655572080Lelio R Paula05/2012
65672*5^103106+372069Lelio R Paula10/2014
65682^239402-19772068Lelio R Paula02/2012
65692^239356-11187572054Enzo Doria05/2014
6570(38*10^72050-119)/972051Robert Price11/2016
65712^239339+1501572049Lelio R Paula01/2013
6572159^32728+272048Lelio R Paula05/2013
657315^61259-3872047Lelio R Paula01/2015
657492^36683-91^3668372038Robert Price08/2015
65752^239280+5461572031Lelio R Paula05/2012
6576(47*2^239267+1)/7772027Lelio R Paula04/2015
6577(85*10^72025-1)/372027Robert Price07/2017
65782^239236-9730572018Lelio R Paula05/2012
6579144^33361-14372006Norbert Schneider11/2018
65802^239169+5971998Lelio R Paula02/2012
6581lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6582(15*2^239171-1)/10630171994Lelio R Paula01/2014
6583(29^49211-1)/2871965Robert Price04/2012
6584(299*10^71963+1)/371965Robert Price11/2017
6586L(344293)71953Renaud Lifchitz09/2003
6585V(344293)71953Serge Batalov03/2015
65876*10^71951+771952Dmitry Domanov11/2010
65883^150798+4071949Lelio R Paula01/2015
65892^238961+9571935Lelio R Paula02/2012
65902^238936-40771927Yves Minet02/2012
65912^238923-2863571923Lelio R Paula05/2012
659210^71910+2511971911Patrick De Geest05/2016
659310^71910-80171910Robert Price04/2016
65942^238845-11265171900Enzo Doria06/2014
65952^238792-11124571884Enzo Doria05/2014
65966*7^85059+571884Lelio R Paula10/2014
65972^238752-11058971872Enzo Doria05/2014
659812^66581+771853Lelio R Paula07/2014
6599(7*2^238691+1)/4122971850Lelio R Paula06/2012
66004*3^150568-571840Lelio R Paula04/2014
66016^92301+6771825Lelio R Paula01/2015
66022^238568+9876533171817Jason Earls01/2009
66032^238541-11272371808Enzo Doria06/2014
66042^238529-1594971805Enzo Doria04/2013
66059*5^102721-871800Lelio R Paula10/2014
66062^238494-16571794Lelio R Paula02/2012
66072^238389-11090571763Enzo Doria05/2014
6608(145*10^71760-1)/971762Serge Batalov12/2014
66097^84913+506271760Mike Oakes02/2010
6610(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
66112^238268-9730571726Lelio R Paula05/2012
6612gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
66132^238235-11324771716Enzo Doria07/2014
66142*12^66450-5^6645071712Mike Oakes11/2010
6615(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
66162^238199-11181771706Enzo Doria05/2014
6617lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
66182^238144+9876533171689Jason Earls01/2009
661918^57102-426571679Enzo Doria03/2013
6620(73*10^71670-1)/971671Robert Price01/2015
66212^238081+1155*23808171670Henri Lifchitz02/2005
66222^238067-11192571666Enzo Doria05/2014
662336^46030+3571637Norbert Schneider04/2014
6624(74*10^71621+313)/971622Robert Price11/2017
66252^237905-9171617Lelio R Paula02/2012
6626(31*2^237902-1)/12371616Lelio R Paula01/2014
6627(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6628(24737*2^237841+1)/2571601Lelio R Paula06/2014
66292^237846+129971599Lelio R Paula05/2012
66306^92004+19980171594Mike Oakes02/2011
6631159^32516+271581Lelio R Paula05/2013
66322^237781+85571580Lelio R Paula05/2012
66332^237720-407971561Yves Minet06/2011
66342^237698-11094571555Enzo Doria05/2014
66352^237695-11323971554Enzo Doria07/2014
66368*5^102362-971549Lelio R Paula10/2014
6637(4*10^71546-31)/971546Erik Branger05/2011
66382^237650+3771540Lelio R Paula02/2012
663918^56977-439171522Enzo Doria03/2013
6640(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6641((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
6642(26*10^71503+7)/371504Erik Branger11/2013
6643(4*10^71498+173)/371499Robert Price01/2017
66443^149848+11071496Lelio R Paula11/2014
66452^237498+51371495Lelio R Paula05/2012
66462^237485+10771491Lelio R Paula02/2012
6647(2^237465+9)/241971481Lelio R Paula05/2012
66482^237439-11223771477Enzo Doria06/2014
66492^237407-978771467Lelio R Paula11/2009
66502^237383+7295371460Enzo Doria04/2016
665182^37337-81^3733771457Robert Price01/2015
6652(1017*2^237313-1)/1971441Lelio R Paula04/2015
66532^237311+19171438Lelio R Paula02/2012
66542^237280-5971429Lelio R Paula02/2012
665511^68564-9871403Lelio R Paula01/2015
66562^237173+7480171397Enzo Doria04/2016
665715^60697+5671386Lelio R Paula01/2015
66582^237118+17771380Lelio R Paula02/2012
66592^237110+6971378Lelio R Paula02/2012
666015^60690-5871377Lelio R Paula01/2015
6661(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6662(3^149567+2)/53971359Lelio R Paula06/2012
6663(5*10^71357-143)/371358Robert Price04/2016
66642^237039-11462171356Enzo Doria05/2015
666512^66116-3771352Lelio R Paula02/2015
6666(3^149497+2^149497)/571328Jean-Louis Charton10/2010
66672^236941-6694571327Lelio R Paula05/2012
66682^236911-114771318Yves Minet10/2009
666965^39337+4271315Lelio R Paula01/2016
66706*10^71299+771300Dmitry Domanov11/2010
6671(25*2^236843+1)/375371295Lelio R Paula06/2012
667210^71291+1518771292Patrick De Geest03/2016
667410^71291-558730911971291Robert Price03/2015
667310^71291-27358171291Patrick De Geest03/2016
6675-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
667615105^17054+17054^1510571271Norbert Schneider08/2018
6677(2^236738+9)/1371265Lelio R Paula05/2012
66785^101949+4271260Lelio R Paula07/2014
66795*10^71237+971238Dmitry Domanov11/2010
66802^236634-1602571234Enzo Doria04/2013
668171^38478+7071233Norbert Schneider12/2014
66829*7^84280+871226Lelio R Paula10/2014
6683(10^71223+59)/371223Serge Batalov12/2014
6684(15185*2^236569-1)/45371216Lelio R Paula04/2015
668551829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
66862^236528-17371203Lelio R Paula02/2012
66873*2^236511-571198Lelio R Paula04/2014
66882^236477-9971187Lelio R Paula02/2012
668911^68356-213071186Enzo Doria12/2012
669015128^17031+17031^1512871186Norbert Schneider08/2018
669111^68355-312071185Enzo Doria12/2012
669236^45737-35^4573771181Robert Price10/2012
6693(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
66942^236432+2571174Lelio R Paula02/2012
66955^101818-1280671168Enzo Doria02/2013
6696(7*10^71166-457)/971166Robert Price09/2017
669765^39253+6271163Lelio R Paula01/2016
669839^44718+3871150Norbert Schneider05/2014
66992^236296-40771133Yves Minet02/2012
67002^236286-11771130Lelio R Paula02/2012
67012^236257-11119371121Enzo Doria05/2014
67027^84149-3671115Lelio R Paula08/2014
67032^236209-11212371106Enzo Doria06/2014
670418^56644-498571104Enzo Doria03/2013
6705(46*10^71077+521)/971078Robert Price08/2017
670621^53753+271074Ray Chandler08/2011
6707(86*10^71068-311)/971069Robert Price10/2017
67082^236081-11092371068Enzo Doria05/2014
6709(293*27^49642-1736)/1371058Curtis Bright05/2015
671065^39192+2271052Lelio R Paula01/2016
6711(439#+1)^397-439#^39771038Mike Oakes11/2010
67127^84050-271031Lelio R Paula09/2013
671320^54558-2370982Lelio R Paula01/2015
67142^235793-11255570981Enzo Doria06/2014
671549936!3-3^4993670981Robert Price08/2015
67162^235787-7879570979Lelio R Paula05/2012
6717Perrin(581132)70970Eric W. Weisstein02/2011
671814^61913-9770961Lelio R Paula01/2015
67192^235720+1632170959Yves Minet03/2010
67202^235718+1609570959Lelio R Paula05/2012
6721163841#+34993370957Nicolas PALAU11/2016
67222^235710+770956Lelio R Paula02/2012
6723(175^31627+1)/17670939Eric Chen10/2017
67242^235635-11208770934Enzo Doria06/2014
6725153^32467+15270931Norbert Schneider11/2018
67272^235575-196570916Lelio R Paula05/2012
67266^91133+10170916Lelio R Paula01/2015
6728(21181*2^235505+1)/370898Lelio R Paula06/2014
6729(14*10^70896+211)/970897Robert Price11/2017
67305^101425+8470894Lelio R Paula07/2014
6731177^31536+270893Lelio R Paula05/2013
673243*71^38292+470891Serge Batalov03/2016
6733(29*2^235506-1)/11202978570888Lelio R Paula01/2014
673411^68045-153070862Enzo Doria12/2012
67355*10^70858+2170859Robert Price01/2017
67372^235326+370841Donovan Johnson02/2006
673634523!2+470841Robert Price02/2015
6738(31*2^235307+1)/370836Lelio R Paula06/2012
67392^235308+13570835Lelio R Paula02/2012
6740r(35414,90)*1000+91170831Patrick De Geest07/2004
67412^235274+15970825Lelio R Paula02/2012
67423^148409+7070810Lelio R Paula11/2014
6743(19*10^70794+17)/970795Robert Price03/2015
67442^235108-23270970775Paul Bourdelais03/2013
6745(2^235099-2^117550+1)/57077211/2006
674619^55325-670748Lelio R Paula08/2014
6747257^29356+29356^25770746Norbert Schneider10/2014
674822*10^70729+370731Robert Price10/2017
67492^234956+1171570729Lelio R Paula05/2012
6750(7*10^70727-43)/970727Robert Price10/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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