PRP Records

Probable Primes Top 10000

(202622 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 ?
600120^55908-4172738Lelio R Paula01/2015
6002(73*10^72735+53)/972736Robert Price10/2015
600310^72730+22401172731Patrick De Geest05/2013
600410^72730-9972730Robert Price05/2011
60053*10^72723+6772724Robert Price11/2017
6006(11^69833+3^69833)/1472723Robert Price03/2013
6007(10^72723-79)/372723Robert Price10/2017
6008(88*10^72711-43)/972712Robert Price11/2015
60093^152379+28072704Lelio R Paula01/2015
6010(25*10^72703-241)/972704Robert Price01/2017
6011(47*10^72696+133)/972697Robert Price04/2017
601217^59077-9072692Lelio R Paula01/2015
601365^40096+5872691Lelio R Paula01/2016
6014(29*2^241446-1)/24572682Lelio R Paula01/2014
601611^69783-3840000072672Enzo Doria01/2013
60152^241409-11290372672Enzo Doria06/2014
6017(3^152287+1)/472659Paul Bourdelais04/2008
60183^152249-5672642Lelio R Paula01/2015
601910^72631+3772632Robert Price01/2011
602010^72631-881372631Patrick De Geest05/2013
6021(19*2^241254+1)/10172624Lelio R Paula08/2012
6022(9^76103+8^76103)/1772620Robert Price12/2012
60232^241220-11233772615Enzo Doria06/2014
6024(82*10^72612+449)/972613Robert Price02/2017
60252^241169-1579372600Enzo Doria04/2013
60269*10^72595+1172596Robert Kinser01/2017
6027(25*2^241048+1)/8972563Lelio R Paula08/2012
6028(22*10^72560+17)/372561Robert Price09/2015
60292^241032-2372558Lelio R Paula02/2012
603034485*10^72550+2^241004-372555Gilbert Mozzo12/2012
60312^241004-372550M. Frind & P. Underwood07/2002
603297*10^72522-372524Robert Price01/2017
6033(68*10^72516+7)/372518Robert Price03/2016
6034(78557*2^240844+1)/6372505Lelio R Paula06/2014
603567^39701-6672497Norbert Schneider11/2014
6036(185*10^72484+7)/372486Robert Price02/2017
6038(293*27^50631-1736)/1372473Curtis Bright05/2015
6037103^36005-10272473Norbert Schneider10/2016
603915^61616+8872467Lelio R Paula01/2015
604045^43831+272462Lelio R Paula05/2013
60412^240692-49238972456Paul Bourdelais03/2013
6042(646*10^72446-7)/972448Robert Price07/2016
60439*6^93083+772434Lelio R Paula10/2014
60442^240617-364572433Lelio R Paula05/2013
604511^69531-2400072410Enzo Doria12/2012
6046(22699*2^240396+1)/5572370Lelio R Paula06/2014
60476^92995+1372365Lelio R Paula01/2015
6048(11*10^72362-149)/372363Robert Price01/2017
6049(2^240381+3)/5165572358Lelio R Paula05/2012
60506^92974-5572348Lelio R Paula01/2015
60512^240295+1172337Lelio R Paula02/2012
6052(14*10^72326-53)/372327Robert Price12/2016
605315^61493-4672322Lelio R Paula01/2015
6054lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
60555*10^72302+972303Dmitry Domanov11/2010
6056(9787*2^240179-1)/26572303Lelio R Paula04/2015
605711^69419-312072293Enzo Doria12/2012
60584*10^72274-8372275Robert Price10/2017
605910^72267+3372268Robert Price01/2011
606010^72267-55394772267Patrick De Geest05/2013
606111^69389-138072262Enzo Doria12/2012
6062(16^60013-5^60013)/1172262Robert Price07/2013
60637^85507-3072262Lelio R Paula08/2014
6064(19*2^240026-1)/1572256Lelio R Paula02/2014
6065(3^151426-2)/66133772243Lelio R Paula06/2012
6066gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
60672^239863-11226772206Enzo Doria06/2014
60682^239853-11485372203Enzo Doria05/2015
6069(4*10^72174+149)/972174Robert Price03/2017
6071(2^239671+9)/29613172143Lelio R Paula05/2012
60702^239651-11066572143Enzo Doria05/2014
6072(29*2^239650-1)/330572140Lelio R Paula01/2014
6073241^30280+30280^24172128Norbert Schneider11/2014
6074(68*10^72120-23)/972121Robert Price10/2015
6075(9^75571+8^75571)/1772112Robert Price12/2012
6076(15*2^239530-1)/17372105Lelio R Paula01/2014
60772^239513-11251972101Enzo Doria06/2014
6078(10^72097+149)/372097Serge Batalov12/2014
60792^239442-655572080Lelio R Paula05/2012
60802*5^103106+372069Lelio R Paula10/2014
60812^239402-19772068Lelio R Paula02/2012
60822^239356-11187572054Enzo Doria05/2014
6083(38*10^72050-119)/972051Robert Price11/2016
60842^239339+1501572049Lelio R Paula01/2013
6085159^32728+272048Lelio R Paula05/2013
608615^61259-3872047Lelio R Paula01/2015
608792^36683-91^3668372038Robert Price08/2015
60882^239280+5461572031Lelio R Paula05/2012
6089(47*2^239267+1)/7772027Lelio R Paula04/2015
6090(85*10^72025-1)/372027Robert Price07/2017
60912^239236-9730572018Lelio R Paula05/2012
60922^239169+5971998Lelio R Paula02/2012
6093lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6094(15*2^239171-1)/10630171994Lelio R Paula01/2014
6095(29^49211-1)/2871965Robert Price04/2012
6096(299*10^71963+1)/371965Robert Price11/2017
6098L(344293)71953Renaud Lifchitz09/2003
6097V(344293)71953Serge Batalov03/2015
60996*10^71951+771952Dmitry Domanov11/2010
61003^150798+4071949Lelio R Paula01/2015
61012^238961+9571935Lelio R Paula02/2012
61022^238936-40771927Yves Minet02/2012
61032^238923-2863571923Lelio R Paula05/2012
610410^71910+2511971911Patrick De Geest05/2016
610510^71910-80171910Robert Price04/2016
61062^238845-11265171900Enzo Doria06/2014
61072^238792-11124571884Enzo Doria05/2014
61086*7^85059+571884Lelio R Paula10/2014
61092^238752-11058971872Enzo Doria05/2014
611012^66581+771853Lelio R Paula07/2014
6111(7*2^238691+1)/4122971850Lelio R Paula06/2012
61124*3^150568-571840Lelio R Paula04/2014
61136^92301+6771825Lelio R Paula01/2015
61142^238568+9876533171817Jason Earls01/2009
61152^238541-11272371808Enzo Doria06/2014
61162^238529-1594971805Enzo Doria04/2013
61179*5^102721-871800Lelio R Paula10/2014
61182^238494-16571794Lelio R Paula02/2012
61192^238389-11090571763Enzo Doria05/2014
6120(145*10^71760-1)/971762Serge Batalov12/2014
61217^84913+506271760Mike Oakes02/2010
6122(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
61232^238268-9730571726Lelio R Paula05/2012
6124gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
61252^238235-11324771716Enzo Doria07/2014
61262*12^66450-5^6645071712Mike Oakes11/2010
6127(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
61282^238199-11181771706Enzo Doria05/2014
6129lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
61302^238144+9876533171689Jason Earls01/2009
613118^57102-426571679Enzo Doria03/2013
6132(73*10^71670-1)/971671Robert Price01/2015
61332^238081+1155*23808171670Henri Lifchitz02/2005
61342^238067-11192571666Enzo Doria05/2014
613536^46030+3571637Norbert Schneider04/2014
6136(74*10^71621+313)/971622Robert Price11/2017
61372^237905-9171617Lelio R Paula02/2012
6138(31*2^237902-1)/12371616Lelio R Paula01/2014
6139(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6140(24737*2^237841+1)/2571601Lelio R Paula06/2014
61412^237846+129971599Lelio R Paula05/2012
61426^92004+19980171594Mike Oakes02/2011
6143159^32516+271581Lelio R Paula05/2013
61442^237781+85571580Lelio R Paula05/2012
61452^237720-407971561Yves Minet06/2011
61462^237698-11094571555Enzo Doria05/2014
61472^237695-11323971554Enzo Doria07/2014
61488*5^102362-971549Lelio R Paula10/2014
6149(4*10^71546-31)/971546Erik Branger05/2011
61502^237650+3771540Lelio R Paula02/2012
615118^56977-439171522Enzo Doria03/2013
6152(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6153((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
6154(26*10^71503+7)/371504Erik Branger11/2013
6155(4*10^71498+173)/371499Robert Price01/2017
61563^149848+11071496Lelio R Paula11/2014
61572^237498+51371495Lelio R Paula05/2012
61582^237485+10771491Lelio R Paula02/2012
6159(2^237465+9)/241971481Lelio R Paula05/2012
61602^237439-11223771477Enzo Doria06/2014
61612^237407-978771467Lelio R Paula11/2009
61622^237383+7295371460Enzo Doria04/2016
616382^37337-81^3733771457Robert Price01/2015
6164(1017*2^237313-1)/1971441Lelio R Paula04/2015
61652^237311+19171438Lelio R Paula02/2012
61662^237280-5971429Lelio R Paula02/2012
616711^68564-9871403Lelio R Paula01/2015
61682^237173+7480171397Enzo Doria04/2016
616915^60697+5671386Lelio R Paula01/2015
61702^237118+17771380Lelio R Paula02/2012
61712^237110+6971378Lelio R Paula02/2012
617215^60690-5871377Lelio R Paula01/2015
6173(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6174(3^149567+2)/53971359Lelio R Paula06/2012
6175(5*10^71357-143)/371358Robert Price04/2016
61762^237039-11462171356Enzo Doria05/2015
617712^66116-3771352Lelio R Paula02/2015
6178(3^149497+2^149497)/571328Jean-Louis Charton10/2010
61792^236941-6694571327Lelio R Paula05/2012
61802^236911-114771318Yves Minet10/2009
618165^39337+4271315Lelio R Paula01/2016
61826*10^71299+771300Dmitry Domanov11/2010
6183(25*2^236843+1)/375371295Lelio R Paula06/2012
618410^71291+1518771292Patrick De Geest03/2016
618610^71291-558730911971291Robert Price03/2015
618510^71291-27358171291Patrick De Geest03/2016
6187-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
6188(2^236738+9)/1371265Lelio R Paula05/2012
61895^101949+4271260Lelio R Paula07/2014
61905*10^71237+971238Dmitry Domanov11/2010
61912^236634-1602571234Enzo Doria04/2013
619271^38478+7071233Norbert Schneider12/2014
61939*7^84280+871226Lelio R Paula10/2014
6194(10^71223+59)/371223Serge Batalov12/2014
6195(15185*2^236569-1)/45371216Lelio R Paula04/2015
619651829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
61972^236528-17371203Lelio R Paula02/2012
61983*2^236511-571198Lelio R Paula04/2014
61992^236477-9971187Lelio R Paula02/2012
620011^68356-213071186Enzo Doria12/2012
620111^68355-312071185Enzo Doria12/2012
620236^45737-35^4573771181Robert Price10/2012
6203(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
62042^236432+2571174Lelio R Paula02/2012
62055^101818-1280671168Enzo Doria02/2013
6206(7*10^71166-457)/971166Robert Price09/2017
620765^39253+6271163Lelio R Paula01/2016
620839^44718+3871150Norbert Schneider05/2014
62092^236296-40771133Yves Minet02/2012
62102^236286-11771130Lelio R Paula02/2012
62112^236257-11119371121Enzo Doria05/2014
62127^84149-3671115Lelio R Paula08/2014
62132^236209-11212371106Enzo Doria06/2014
621418^56644-498571104Enzo Doria03/2013
6215(46*10^71077+521)/971078Robert Price08/2017
621621^53753+271074Ray Chandler08/2011
6217(86*10^71068-311)/971069Robert Price10/2017
62182^236081-11092371068Enzo Doria05/2014
6219(293*27^49642-1736)/1371058Curtis Bright05/2015
622065^39192+2271052Lelio R Paula01/2016
6221(439#+1)^397-439#^39771038Mike Oakes11/2010
62227^84050-271031Lelio R Paula09/2013
622320^54558-2370982Lelio R Paula01/2015
62242^235793-11255570981Enzo Doria06/2014
622549936!3-3^4993670981Robert Price08/2015
62262^235787-7879570979Lelio R Paula05/2012
6227Perrin(581132)70970Eric W. Weisstein02/2011
622814^61913-9770961Lelio R Paula01/2015
62292^235720+1632170959Yves Minet03/2010
62302^235718+1609570959Lelio R Paula05/2012
6231163841#+34993370957Nicolas PALAU11/2016
62322^235710+770956Lelio R Paula02/2012
6233(175^31627+1)/17670939Eric Chen10/2017
62342^235635-11208770934Enzo Doria06/2014
62362^235575-196570916Lelio R Paula05/2012
62356^91133+10170916Lelio R Paula01/2015
6237(21181*2^235505+1)/370898Lelio R Paula06/2014
6238(14*10^70896+211)/970897Robert Price11/2017
62395^101425+8470894Lelio R Paula07/2014
6240177^31536+270893Lelio R Paula05/2013
624143*71^38292+470891Serge Batalov03/2016
6242(29*2^235506-1)/11202978570888Lelio R Paula01/2014
624311^68045-153070862Enzo Doria12/2012
62445*10^70858+2170859Robert Price01/2017
62452^235326+370841Donovan Johnson02/2006
624634523!2+470841Robert Price02/2015
6247(31*2^235307+1)/370836Lelio R Paula06/2012
62482^235308+13570835Lelio R Paula02/2012
6249r(35414,90)*1000+91170831Patrick De Geest07/2004
62502^235274+15970825Lelio R Paula02/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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