PRP Records

Probable Primes Top 10000

(252675 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 ?
6752(293*27^50631-1736)/1372473Curtis Bright05/2015
6751103^36005-10272473Norbert Schneider10/2016
675315^61616+8872467Lelio R Paula01/2015
675445^43831+272462Lelio R Paula05/2013
67552^240692-49238972456Paul Bourdelais03/2013
6756(646*10^72446-7)/972448Robert Price07/2016
67579*6^93083+772434Lelio R Paula10/2014
67582^240617-364572433Lelio R Paula05/2013
675911^69531-2400072410Enzo Doria12/2012
6760(22699*2^240396+1)/5572370Lelio R Paula06/2014
67616^92995+1372365Lelio R Paula01/2015
6762(11*10^72362-149)/372363Robert Price01/2017
6763(2^240381+3)/5165572358Lelio R Paula05/2012
67646^92974-5572348Lelio R Paula01/2015
67652^240295+1172337Lelio R Paula02/2012
6766(14*10^72326-53)/372327Robert Price12/2016
676715^61493-4672322Lelio R Paula01/2015
6768lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
67695*10^72302+972303Dmitry Domanov11/2010
6770(9787*2^240179-1)/26572303Lelio R Paula04/2015
677111^69419-312072293Enzo Doria12/2012
67724*10^72274-8372275Robert Price10/2017
677310^72267+3372268Robert Price01/2011
677410^72267-55394772267Patrick De Geest05/2013
677511^69389-138072262Enzo Doria12/2012
6776(16^60013-5^60013)/1172262Robert Price07/2013
67777^85507-3072262Lelio R Paula08/2014
6778(19*2^240026-1)/1572256Lelio R Paula02/2014
6779(3^151426-2)/66133772243Lelio R Paula06/2012
6780gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
67812^239863-11226772206Enzo Doria06/2014
67822^239853-11485372203Enzo Doria05/2015
6783(4*10^72174+149)/972174Robert Price03/2017
6784(2^239671+9)/29613172143Lelio R Paula05/2012
67852^239651-11066572143Enzo Doria05/2014
6786(29*2^239650-1)/330572140Lelio R Paula01/2014
6787241^30280+30280^24172128Norbert Schneider11/2014
6788(68*10^72120-23)/972121Robert Price10/2015
6789(9^75571+8^75571)/1772112Robert Price12/2012
6790(15*2^239530-1)/17372105Lelio R Paula01/2014
67912^239513-11251972101Enzo Doria06/2014
6792(10^72097+149)/372097Serge Batalov12/2014
67932^239442-655572080Lelio R Paula05/2012
67942*5^103106+372069Lelio R Paula10/2014
67952^239402-19772068Lelio R Paula02/2012
67962^239356-11187572054Enzo Doria05/2014
6797(38*10^72050-119)/972051Robert Price11/2016
67982^239339+1501572049Lelio R Paula01/2013
6799159^32728+272048Lelio R Paula05/2013
680015^61259-3872047Lelio R Paula01/2015
680192^36683-91^3668372038Robert Price08/2015
68022^239280+5461572031Lelio R Paula05/2012
6804(47*2^239267+1)/7772027Lelio R Paula04/2015
6803(85*10^72025-1)/372027Robert Price07/2017
68052^239236-9730572018Lelio R Paula05/2012
6806144^33361-14372006Norbert Schneider11/2018
68072^239169+5971998Lelio R Paula02/2012
6809lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6808(15*2^239171-1)/10630171994Lelio R Paula01/2014
6811(29^49211-1)/2871965Robert Price04/2012
6810(299*10^71963+1)/371965Robert Price11/2017
6813L(344293)71953Renaud Lifchitz09/2003
6812V(344293)71953Serge Batalov03/2015
68146*10^71951+771952Dmitry Domanov11/2010
68153^150798+4071949Lelio R Paula01/2015
68162^238961+9571935Lelio R Paula02/2012
68172^238936-40771927Yves Minet02/2012
68182^238923-2863571923Lelio R Paula05/2012
681910^71910+2511971911Patrick De Geest05/2016
682010^71910-80171910Robert Price04/2016
68212^238845-11265171900Enzo Doria06/2014
68222^238792-11124571884Enzo Doria05/2014
68236*7^85059+571884Lelio R Paula10/2014
68242^238752-11058971872Enzo Doria05/2014
682512^66581+771853Lelio R Paula07/2014
6826(7*2^238691+1)/4122971850Lelio R Paula06/2012
68274*3^150568-571840Lelio R Paula04/2014
68286^92301+6771825Lelio R Paula01/2015
68292^238568+9876533171817Jason Earls01/2009
68302^238541-11272371808Enzo Doria06/2014
68312^238529-1594971805Enzo Doria04/2013
68329*5^102721-871800Lelio R Paula10/2014
68332^238494-16571794Lelio R Paula02/2012
68342^238389-11090571763Enzo Doria05/2014
6835(145*10^71760-1)/971762Serge Batalov12/2014
68367^84913+506271760Mike Oakes02/2010
6837(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
68382^238268-9730571726Lelio R Paula05/2012
6839gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
68402^238235-11324771716Enzo Doria07/2014
68412*12^66450-5^6645071712Mike Oakes11/2010
6842(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
68432^238199-11181771706Enzo Doria05/2014
6844lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
68452^238144+9876533171689Jason Earls01/2009
684618^57102-426571679Enzo Doria03/2013
6847(73*10^71670-1)/971671Robert Price01/2015
68482^238081+1155*23808171670Henri Lifchitz02/2005
68492^238067-11192571666Enzo Doria05/2014
685036^46030+3571637Norbert Schneider04/2014
6851(74*10^71621+313)/971622Robert Price11/2017
68522^237905-9171617Lelio R Paula02/2012
6853(31*2^237902-1)/12371616Lelio R Paula01/2014
6854(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6855(24737*2^237841+1)/2571601Lelio R Paula06/2014
68562^237846+129971599Lelio R Paula05/2012
68576^92004+19980171594Mike Oakes02/2011
6858159^32516+271581Lelio R Paula05/2013
68592^237781+85571580Lelio R Paula05/2012
68602^237720-407971561Yves Minet06/2011
68612^237698-11094571555Enzo Doria05/2014
68622^237695-11323971554Enzo Doria07/2014
68638*5^102362-971549Lelio R Paula10/2014
6864(4*10^71546-31)/971546Erik Branger05/2011
68652^237650+3771540Lelio R Paula02/2012
686618^56977-439171522Enzo Doria03/2013
6867(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6868((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
6869(26*10^71503+7)/371504Erik Branger11/2013
6870(4*10^71498+173)/371499Robert Price01/2017
68713^149848+11071496Lelio R Paula11/2014
68722^237498+51371495Lelio R Paula05/2012
68732^237485+10771491Lelio R Paula02/2012
6874(2^237465+9)/241971481Lelio R Paula05/2012
68752^237439-11223771477Enzo Doria06/2014
68762^237407-978771467Lelio R Paula11/2009
68772^237383+7295371460Enzo Doria04/2016
687882^37337-81^3733771457Robert Price01/2015
6879(1017*2^237313-1)/1971441Lelio R Paula04/2015
68802^237311+19171438Lelio R Paula02/2012
68812^237280-5971429Lelio R Paula02/2012
688211^68564-9871403Lelio R Paula01/2015
68832^237173+7480171397Enzo Doria04/2016
688415^60697+5671386Lelio R Paula01/2015
68852^237118+17771380Lelio R Paula02/2012
68862^237110+6971378Lelio R Paula02/2012
688715^60690-5871377Lelio R Paula01/2015
6888(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6889(3^149567+2)/53971359Lelio R Paula06/2012
6890(5*10^71357-143)/371358Robert Price04/2016
68912^237039-11462171356Enzo Doria05/2015
689212^66116-3771352Lelio R Paula02/2015
6893(3^149497+2^149497)/571328Jean-Louis Charton10/2010
68942^236941-6694571327Lelio R Paula05/2012
68952^236911-114771318Yves Minet10/2009
689665^39337+4271315Lelio R Paula01/2016
68976*10^71299+771300Dmitry Domanov11/2010
6898(25*2^236843+1)/375371295Lelio R Paula06/2012
689910^71291+1518771292Patrick De Geest03/2016
690110^71291-558730911971291Robert Price03/2015
690010^71291-27358171291Patrick De Geest03/2016
6902-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
690315105^17054+17054^1510571271Norbert Schneider08/2018
6904(2^236738+9)/1371265Lelio R Paula05/2012
69055^101949+4271260Lelio R Paula07/2014
69065*10^71237+971238Dmitry Domanov11/2010
69072^236634-1602571234Enzo Doria04/2013
690871^38478+7071233Norbert Schneider12/2014
69099*7^84280+871226Lelio R Paula10/2014
6910(10^71223+59)/371223Serge Batalov12/2014
6911(15185*2^236569-1)/45371216Lelio R Paula04/2015
691251829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
69132^236528-17371203Lelio R Paula02/2012
69143*2^236511-571198Lelio R Paula04/2014
69152^236477-9971187Lelio R Paula02/2012
691611^68356-213071186Enzo Doria12/2012
691715128^17031+17031^1512871186Norbert Schneider08/2018
691811^68355-312071185Enzo Doria12/2012
691936^45737-35^4573771181Robert Price10/2012
6920(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
69212^236432+2571174Lelio R Paula02/2012
69225^101818-1280671168Enzo Doria02/2013
6923(7*10^71166-457)/971166Robert Price09/2017
692465^39253+6271163Lelio R Paula01/2016
692539^44718+3871150Norbert Schneider05/2014
69262^236296-40771133Yves Minet02/2012
69272^236286-11771130Lelio R Paula02/2012
69282^236257-11119371121Enzo Doria05/2014
69297^84149-3671115Lelio R Paula08/2014
6930164176#-p(164176)71108Henri Lifchitz12/2018
69312^236209-11212371106Enzo Doria06/2014
693218^56644-498571104Enzo Doria03/2013
6933(46*10^71077+521)/971078Robert Price08/2017
693421^53753+271074Ray Chandler08/2011
6935(86*10^71068-311)/971069Robert Price10/2017
69362^236081-11092371068Enzo Doria05/2014
6937(293*27^49642-1736)/1371058Curtis Bright05/2015
693865^39192+2271052Lelio R Paula01/2016
6939(439#+1)^397-439#^39771038Mike Oakes11/2010
69407^84050-271031Lelio R Paula09/2013
694120^54558-2370982Lelio R Paula01/2015
69422^235793-11255570981Enzo Doria06/2014
694349936!3-3^4993670981Robert Price08/2015
69442^235787-7879570979Lelio R Paula05/2012
6945Perrin(581132)70970Eric W. Weisstein02/2011
694614^61913-9770961Lelio R Paula01/2015
69472^235720+1632170959Yves Minet03/2010
69482^235718+1609570959Lelio R Paula05/2012
6949163841#+34993370957Nicolas PALAU11/2016
69502^235710+770956Lelio R Paula02/2012
6951(175^31627+1)/17670939Eric Chen10/2017
69522^235635-11208770934Enzo Doria06/2014
6953153^32467+15270931Norbert Schneider11/2018
69552^235575-196570916Lelio R Paula05/2012
69546^91133+10170916Lelio R Paula01/2015
6956(21181*2^235505+1)/370898Lelio R Paula06/2014
6957(14*10^70896+211)/970897Robert Price11/2017
69585^101425+8470894Lelio R Paula07/2014
6959177^31536+270893Lelio R Paula05/2013
696043*71^38292+470891Serge Batalov03/2016
6961(29*2^235506-1)/11202978570888Lelio R Paula01/2014
696211^68045-153070862Enzo Doria12/2012
69635*10^70858+2170859Robert Price01/2017
69652^235326+370841Donovan Johnson02/2006
696434523!2+470841Robert Price02/2015
6966(31*2^235307+1)/370836Lelio R Paula06/2012
69672^235308+13570835Lelio R Paula02/2012
6968r(35414,90)*1000+91170831Patrick De Geest07/2004
69692^235274+15970825Lelio R Paula02/2012
69703^148409+7070810Lelio R Paula11/2014
6971(19*10^70794+17)/970795Robert Price03/2015
69722^235108-23270970775Paul Bourdelais03/2013
6973(2^235099-2^117550+1)/57077211/2006
697419^55325-670748Lelio R Paula08/2014
6975257^29356+29356^25770746Norbert Schneider10/2014
697622*10^70729+370731Robert Price10/2017
69772^234956+1171570729Lelio R Paula05/2012
6978(7*10^70727-43)/970727Robert Price10/2014
69792^234890-3034170709Enzo Doria11/2012
698017^57461+1470703Lelio R Paula01/2015
6981(9179*2^234834-1)/570696Lelio R Paula04/2015
69822*10^70688+5170689Robert Price10/2017
6983123^33822-12270685Norbert Schneider01/2015
69847*10^70680-9970681Robert Price11/2017
6985(21*2^234772-1)/209570672Lelio R Paula01/2014
6986(29*2^234686-1)/2114570645Lelio R Paula01/2014
6987(15*2^234688-1)/527814170643Lelio R Paula01/2014
69892^234655-6770639Lelio R Paula02/2012
6988(79*10^70638-61)/970639Robert Price10/2015
69902^234652-17370638Lelio R Paula02/2012
69912^234618-364570628Lelio R Paula05/2012
6992(2^234610-5)/1970624Lelio R Paula05/2012
69934*5^101038+970624Lelio R Paula10/2014
69942^234603+7196370623Enzo Doria04/2016
69952^234600-11312970622Enzo Doria07/2014
69972^234586+970618Lelio R Paula02/2012
69963^148008+2670618Robert Price11/2013
6998(7*10^70616-151)/970616Robert Price09/2017
699965^38947+3270608Lelio R Paula01/2016
7000(2^234488-3)/1170587Lelio R Paula05/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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