PRP Records

Probable Primes Top 10000

(252402 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 ?
650110^72730+22401172731Patrick De Geest05/2013
650210^72730-9972730Robert Price05/2011
65033*10^72723+6772724Robert Price11/2017
6504(11^69833+3^69833)/1472723Robert Price03/2013
6505(10^72723-79)/372723Robert Price10/2017
6506(88*10^72711-43)/972712Robert Price11/2015
65073^152379+28072704Lelio R Paula01/2015
6508(25*10^72703-241)/972704Robert Price01/2017
6509(47*10^72696+133)/972697Robert Price04/2017
651017^59077-9072692Lelio R Paula01/2015
651165^40096+5872691Lelio R Paula01/2016
6512(29*2^241446-1)/24572682Lelio R Paula01/2014
651411^69783-3840000072672Enzo Doria01/2013
65132^241409-11290372672Enzo Doria06/2014
6515(3^152287+1)/472659Paul Bourdelais04/2008
65163^152249-5672642Lelio R Paula01/2015
651710^72631+3772632Robert Price01/2011
651810^72631-881372631Patrick De Geest05/2013
6519(19*2^241254+1)/10172624Lelio R Paula08/2012
6520(9^76103+8^76103)/1772620Robert Price12/2012
65212^241220-11233772615Enzo Doria06/2014
6522(82*10^72612+449)/972613Robert Price02/2017
65232^241169-1579372600Enzo Doria04/2013
65249*10^72595+1172596Robert Kinser01/2017
6525(25*2^241048+1)/8972563Lelio R Paula08/2012
6526(22*10^72560+17)/372561Robert Price09/2015
65272^241032-2372558Lelio R Paula02/2012
652834485*10^72550+2^241004-372555Gilbert Mozzo12/2012
65292^241004-372550M. Frind & P. Underwood07/2002
653097*10^72522-372524Robert Price01/2017
6531(68*10^72516+7)/372518Robert Price03/2016
6532(78557*2^240844+1)/6372505Lelio R Paula06/2014
653367^39701-6672497Norbert Schneider11/2014
6534(185*10^72484+7)/372486Robert Price02/2017
6536(293*27^50631-1736)/1372473Curtis Bright05/2015
6535103^36005-10272473Norbert Schneider10/2016
653715^61616+8872467Lelio R Paula01/2015
653845^43831+272462Lelio R Paula05/2013
65392^240692-49238972456Paul Bourdelais03/2013
6540(646*10^72446-7)/972448Robert Price07/2016
65419*6^93083+772434Lelio R Paula10/2014
65422^240617-364572433Lelio R Paula05/2013
654311^69531-2400072410Enzo Doria12/2012
6544(22699*2^240396+1)/5572370Lelio R Paula06/2014
65456^92995+1372365Lelio R Paula01/2015
6546(11*10^72362-149)/372363Robert Price01/2017
6547(2^240381+3)/5165572358Lelio R Paula05/2012
65486^92974-5572348Lelio R Paula01/2015
65492^240295+1172337Lelio R Paula02/2012
6550(14*10^72326-53)/372327Robert Price12/2016
655115^61493-4672322Lelio R Paula01/2015
6552lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
65535*10^72302+972303Dmitry Domanov11/2010
6554(9787*2^240179-1)/26572303Lelio R Paula04/2015
655511^69419-312072293Enzo Doria12/2012
65564*10^72274-8372275Robert Price10/2017
655710^72267+3372268Robert Price01/2011
655810^72267-55394772267Patrick De Geest05/2013
655911^69389-138072262Enzo Doria12/2012
6560(16^60013-5^60013)/1172262Robert Price07/2013
65617^85507-3072262Lelio R Paula08/2014
6562(19*2^240026-1)/1572256Lelio R Paula02/2014
6563(3^151426-2)/66133772243Lelio R Paula06/2012
6564gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
65652^239863-11226772206Enzo Doria06/2014
65662^239853-11485372203Enzo Doria05/2015
6567(4*10^72174+149)/972174Robert Price03/2017
6569(2^239671+9)/29613172143Lelio R Paula05/2012
65682^239651-11066572143Enzo Doria05/2014
6570(29*2^239650-1)/330572140Lelio R Paula01/2014
6571241^30280+30280^24172128Norbert Schneider11/2014
6572(68*10^72120-23)/972121Robert Price10/2015
6573(9^75571+8^75571)/1772112Robert Price12/2012
6574(15*2^239530-1)/17372105Lelio R Paula01/2014
65752^239513-11251972101Enzo Doria06/2014
6576(10^72097+149)/372097Serge Batalov12/2014
65772^239442-655572080Lelio R Paula05/2012
65782*5^103106+372069Lelio R Paula10/2014
65792^239402-19772068Lelio R Paula02/2012
65802^239356-11187572054Enzo Doria05/2014
6581(38*10^72050-119)/972051Robert Price11/2016
65822^239339+1501572049Lelio R Paula01/2013
6583159^32728+272048Lelio R Paula05/2013
658415^61259-3872047Lelio R Paula01/2015
658592^36683-91^3668372038Robert Price08/2015
65862^239280+5461572031Lelio R Paula05/2012
6587(47*2^239267+1)/7772027Lelio R Paula04/2015
6588(85*10^72025-1)/372027Robert Price07/2017
65892^239236-9730572018Lelio R Paula05/2012
6590144^33361-14372006Norbert Schneider11/2018
65912^239169+5971998Lelio R Paula02/2012
6592lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6593(15*2^239171-1)/10630171994Lelio R Paula01/2014
6594(29^49211-1)/2871965Robert Price04/2012
6595(299*10^71963+1)/371965Robert Price11/2017
6597L(344293)71953Renaud Lifchitz09/2003
6596V(344293)71953Serge Batalov03/2015
65986*10^71951+771952Dmitry Domanov11/2010
65993^150798+4071949Lelio R Paula01/2015
66002^238961+9571935Lelio R Paula02/2012
66012^238936-40771927Yves Minet02/2012
66022^238923-2863571923Lelio R Paula05/2012
660310^71910+2511971911Patrick De Geest05/2016
660410^71910-80171910Robert Price04/2016
66052^238845-11265171900Enzo Doria06/2014
66062^238792-11124571884Enzo Doria05/2014
66076*7^85059+571884Lelio R Paula10/2014
66082^238752-11058971872Enzo Doria05/2014
660912^66581+771853Lelio R Paula07/2014
6610(7*2^238691+1)/4122971850Lelio R Paula06/2012
66114*3^150568-571840Lelio R Paula04/2014
66126^92301+6771825Lelio R Paula01/2015
66132^238568+9876533171817Jason Earls01/2009
66142^238541-11272371808Enzo Doria06/2014
66152^238529-1594971805Enzo Doria04/2013
66169*5^102721-871800Lelio R Paula10/2014
66172^238494-16571794Lelio R Paula02/2012
66182^238389-11090571763Enzo Doria05/2014
6619(145*10^71760-1)/971762Serge Batalov12/2014
66207^84913+506271760Mike Oakes02/2010
6621(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
66222^238268-9730571726Lelio R Paula05/2012
6623gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
66242^238235-11324771716Enzo Doria07/2014
66252*12^66450-5^6645071712Mike Oakes11/2010
6626(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
66272^238199-11181771706Enzo Doria05/2014
6628lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
66292^238144+9876533171689Jason Earls01/2009
663018^57102-426571679Enzo Doria03/2013
6631(73*10^71670-1)/971671Robert Price01/2015
66322^238081+1155*23808171670Henri Lifchitz02/2005
66332^238067-11192571666Enzo Doria05/2014
663436^46030+3571637Norbert Schneider04/2014
6635(74*10^71621+313)/971622Robert Price11/2017
66362^237905-9171617Lelio R Paula02/2012
6637(31*2^237902-1)/12371616Lelio R Paula01/2014
6638(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6639(24737*2^237841+1)/2571601Lelio R Paula06/2014
66402^237846+129971599Lelio R Paula05/2012
66416^92004+19980171594Mike Oakes02/2011
6642159^32516+271581Lelio R Paula05/2013
66432^237781+85571580Lelio R Paula05/2012
66442^237720-407971561Yves Minet06/2011
66452^237698-11094571555Enzo Doria05/2014
66462^237695-11323971554Enzo Doria07/2014
66478*5^102362-971549Lelio R Paula10/2014
6648(4*10^71546-31)/971546Erik Branger05/2011
66492^237650+3771540Lelio R Paula02/2012
665018^56977-439171522Enzo Doria03/2013
6651(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6652((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
6653(26*10^71503+7)/371504Erik Branger11/2013
6654(4*10^71498+173)/371499Robert Price01/2017
66553^149848+11071496Lelio R Paula11/2014
66562^237498+51371495Lelio R Paula05/2012
66572^237485+10771491Lelio R Paula02/2012
6658(2^237465+9)/241971481Lelio R Paula05/2012
66592^237439-11223771477Enzo Doria06/2014
66602^237407-978771467Lelio R Paula11/2009
66612^237383+7295371460Enzo Doria04/2016
666282^37337-81^3733771457Robert Price01/2015
6663(1017*2^237313-1)/1971441Lelio R Paula04/2015
66642^237311+19171438Lelio R Paula02/2012
66652^237280-5971429Lelio R Paula02/2012
666611^68564-9871403Lelio R Paula01/2015
66672^237173+7480171397Enzo Doria04/2016
666815^60697+5671386Lelio R Paula01/2015
66692^237118+17771380Lelio R Paula02/2012
66702^237110+6971378Lelio R Paula02/2012
667115^60690-5871377Lelio R Paula01/2015
6672(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6673(3^149567+2)/53971359Lelio R Paula06/2012
6674(5*10^71357-143)/371358Robert Price04/2016
66752^237039-11462171356Enzo Doria05/2015
667612^66116-3771352Lelio R Paula02/2015
6677(3^149497+2^149497)/571328Jean-Louis Charton10/2010
66782^236941-6694571327Lelio R Paula05/2012
66792^236911-114771318Yves Minet10/2009
668065^39337+4271315Lelio R Paula01/2016
66816*10^71299+771300Dmitry Domanov11/2010
6682(25*2^236843+1)/375371295Lelio R Paula06/2012
668310^71291+1518771292Patrick De Geest03/2016
668510^71291-558730911971291Robert Price03/2015
668410^71291-27358171291Patrick De Geest03/2016
6686-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
668715105^17054+17054^1510571271Norbert Schneider08/2018
6688(2^236738+9)/1371265Lelio R Paula05/2012
66895^101949+4271260Lelio R Paula07/2014
66905*10^71237+971238Dmitry Domanov11/2010
66912^236634-1602571234Enzo Doria04/2013
669271^38478+7071233Norbert Schneider12/2014
66939*7^84280+871226Lelio R Paula10/2014
6694(10^71223+59)/371223Serge Batalov12/2014
6695(15185*2^236569-1)/45371216Lelio R Paula04/2015
669651829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
66972^236528-17371203Lelio R Paula02/2012
66983*2^236511-571198Lelio R Paula04/2014
66992^236477-9971187Lelio R Paula02/2012
670011^68356-213071186Enzo Doria12/2012
670115128^17031+17031^1512871186Norbert Schneider08/2018
670211^68355-312071185Enzo Doria12/2012
670336^45737-35^4573771181Robert Price10/2012
6704(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
67052^236432+2571174Lelio R Paula02/2012
67065^101818-1280671168Enzo Doria02/2013
6707(7*10^71166-457)/971166Robert Price09/2017
670865^39253+6271163Lelio R Paula01/2016
670939^44718+3871150Norbert Schneider05/2014
67102^236296-40771133Yves Minet02/2012
67112^236286-11771130Lelio R Paula02/2012
67122^236257-11119371121Enzo Doria05/2014
67137^84149-3671115Lelio R Paula08/2014
6714164176#-p(164176)71108Henri Lifchitz12/2018
67152^236209-11212371106Enzo Doria06/2014
671618^56644-498571104Enzo Doria03/2013
6717(46*10^71077+521)/971078Robert Price08/2017
671821^53753+271074Ray Chandler08/2011
6719(86*10^71068-311)/971069Robert Price10/2017
67202^236081-11092371068Enzo Doria05/2014
6721(293*27^49642-1736)/1371058Curtis Bright05/2015
672265^39192+2271052Lelio R Paula01/2016
6723(439#+1)^397-439#^39771038Mike Oakes11/2010
67247^84050-271031Lelio R Paula09/2013
672520^54558-2370982Lelio R Paula01/2015
67262^235793-11255570981Enzo Doria06/2014
672749936!3-3^4993670981Robert Price08/2015
67282^235787-7879570979Lelio R Paula05/2012
6729Perrin(581132)70970Eric W. Weisstein02/2011
673014^61913-9770961Lelio R Paula01/2015
67322^235720+1632170959Yves Minet03/2010
67312^235718+1609570959Lelio R Paula05/2012
6733163841#+34993370957Nicolas PALAU11/2016
67342^235710+770956Lelio R Paula02/2012
6735(175^31627+1)/17670939Eric Chen10/2017
67362^235635-11208770934Enzo Doria06/2014
6737153^32467+15270931Norbert Schneider11/2018
67392^235575-196570916Lelio R Paula05/2012
67386^91133+10170916Lelio R Paula01/2015
6740(21181*2^235505+1)/370898Lelio R Paula06/2014
6741(14*10^70896+211)/970897Robert Price11/2017
67425^101425+8470894Lelio R Paula07/2014
6743177^31536+270893Lelio R Paula05/2013
674443*71^38292+470891Serge Batalov03/2016
6745(29*2^235506-1)/11202978570888Lelio R Paula01/2014
674611^68045-153070862Enzo Doria12/2012
67475*10^70858+2170859Robert Price01/2017
67492^235326+370841Donovan Johnson02/2006
674834523!2+470841Robert Price02/2015
6750(31*2^235307+1)/370836Lelio R Paula06/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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