PRP Records

Probable Primes Top 10000

(218736 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 ?
6251(8*10^72759+67)/372760Robert Price01/2017
62522^241670+14572750Lelio R Paula03/2012
62535^104074+5272745Lelio R Paula08/2014
6254(3^152466-5)/72472742Lelio R Paula06/2012
625520^55908-4172738Lelio R Paula01/2015
6256(73*10^72735+53)/972736Robert Price10/2015
625710^72730+22401172731Patrick De Geest05/2013
625810^72730-9972730Robert Price05/2011
62593*10^72723+6772724Robert Price11/2017
6260(11^69833+3^69833)/1472723Robert Price03/2013
6261(10^72723-79)/372723Robert Price10/2017
6262(88*10^72711-43)/972712Robert Price11/2015
62633^152379+28072704Lelio R Paula01/2015
6264(25*10^72703-241)/972704Robert Price01/2017
6265(47*10^72696+133)/972697Robert Price04/2017
626617^59077-9072692Lelio R Paula01/2015
626765^40096+5872691Lelio R Paula01/2016
6268(29*2^241446-1)/24572682Lelio R Paula01/2014
627011^69783-3840000072672Enzo Doria01/2013
62692^241409-11290372672Enzo Doria06/2014
6271(3^152287+1)/472659Paul Bourdelais04/2008
62723^152249-5672642Lelio R Paula01/2015
627310^72631+3772632Robert Price01/2011
627410^72631-881372631Patrick De Geest05/2013
6275(19*2^241254+1)/10172624Lelio R Paula08/2012
6276(9^76103+8^76103)/1772620Robert Price12/2012
62772^241220-11233772615Enzo Doria06/2014
6278(82*10^72612+449)/972613Robert Price02/2017
62792^241169-1579372600Enzo Doria04/2013
62809*10^72595+1172596Robert Kinser01/2017
6281(25*2^241048+1)/8972563Lelio R Paula08/2012
6282(22*10^72560+17)/372561Robert Price09/2015
62832^241032-2372558Lelio R Paula02/2012
628434485*10^72550+2^241004-372555Gilbert Mozzo12/2012
62852^241004-372550M. Frind & P. Underwood07/2002
628697*10^72522-372524Robert Price01/2017
6287(68*10^72516+7)/372518Robert Price03/2016
6288(78557*2^240844+1)/6372505Lelio R Paula06/2014
628967^39701-6672497Norbert Schneider11/2014
6290(185*10^72484+7)/372486Robert Price02/2017
6292(293*27^50631-1736)/1372473Curtis Bright05/2015
6291103^36005-10272473Norbert Schneider10/2016
629315^61616+8872467Lelio R Paula01/2015
629445^43831+272462Lelio R Paula05/2013
62952^240692-49238972456Paul Bourdelais03/2013
6296(646*10^72446-7)/972448Robert Price07/2016
62979*6^93083+772434Lelio R Paula10/2014
62982^240617-364572433Lelio R Paula05/2013
629911^69531-2400072410Enzo Doria12/2012
6300(22699*2^240396+1)/5572370Lelio R Paula06/2014
63016^92995+1372365Lelio R Paula01/2015
6302(11*10^72362-149)/372363Robert Price01/2017
6303(2^240381+3)/5165572358Lelio R Paula05/2012
63046^92974-5572348Lelio R Paula01/2015
63052^240295+1172337Lelio R Paula02/2012
6306(14*10^72326-53)/372327Robert Price12/2016
630715^61493-4672322Lelio R Paula01/2015
6308lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
63095*10^72302+972303Dmitry Domanov11/2010
6310(9787*2^240179-1)/26572303Lelio R Paula04/2015
631111^69419-312072293Enzo Doria12/2012
63124*10^72274-8372275Robert Price10/2017
631310^72267+3372268Robert Price01/2011
631410^72267-55394772267Patrick De Geest05/2013
631511^69389-138072262Enzo Doria12/2012
6316(16^60013-5^60013)/1172262Robert Price07/2013
63177^85507-3072262Lelio R Paula08/2014
6318(19*2^240026-1)/1572256Lelio R Paula02/2014
6319(3^151426-2)/66133772243Lelio R Paula06/2012
6320gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
63212^239863-11226772206Enzo Doria06/2014
63222^239853-11485372203Enzo Doria05/2015
6323(4*10^72174+149)/972174Robert Price03/2017
6325(2^239671+9)/29613172143Lelio R Paula05/2012
63242^239651-11066572143Enzo Doria05/2014
6326(29*2^239650-1)/330572140Lelio R Paula01/2014
6327241^30280+30280^24172128Norbert Schneider11/2014
6328(68*10^72120-23)/972121Robert Price10/2015
6329(9^75571+8^75571)/1772112Robert Price12/2012
6330(15*2^239530-1)/17372105Lelio R Paula01/2014
63312^239513-11251972101Enzo Doria06/2014
6332(10^72097+149)/372097Serge Batalov12/2014
63332^239442-655572080Lelio R Paula05/2012
63342*5^103106+372069Lelio R Paula10/2014
63352^239402-19772068Lelio R Paula02/2012
63362^239356-11187572054Enzo Doria05/2014
6337(38*10^72050-119)/972051Robert Price11/2016
63382^239339+1501572049Lelio R Paula01/2013
6339159^32728+272048Lelio R Paula05/2013
634015^61259-3872047Lelio R Paula01/2015
634192^36683-91^3668372038Robert Price08/2015
63422^239280+5461572031Lelio R Paula05/2012
6343(47*2^239267+1)/7772027Lelio R Paula04/2015
6344(85*10^72025-1)/372027Robert Price07/2017
63452^239236-9730572018Lelio R Paula05/2012
63462^239169+5971998Lelio R Paula02/2012
6347lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6348(15*2^239171-1)/10630171994Lelio R Paula01/2014
6349(29^49211-1)/2871965Robert Price04/2012
6350(299*10^71963+1)/371965Robert Price11/2017
6351L(344293)71953Renaud Lifchitz09/2003
6352V(344293)71953Serge Batalov03/2015
63536*10^71951+771952Dmitry Domanov11/2010
63543^150798+4071949Lelio R Paula01/2015
63552^238961+9571935Lelio R Paula02/2012
63562^238936-40771927Yves Minet02/2012
63572^238923-2863571923Lelio R Paula05/2012
635810^71910+2511971911Patrick De Geest05/2016
635910^71910-80171910Robert Price04/2016
63602^238845-11265171900Enzo Doria06/2014
63612^238792-11124571884Enzo Doria05/2014
63626*7^85059+571884Lelio R Paula10/2014
63632^238752-11058971872Enzo Doria05/2014
636412^66581+771853Lelio R Paula07/2014
6365(7*2^238691+1)/4122971850Lelio R Paula06/2012
63664*3^150568-571840Lelio R Paula04/2014
63676^92301+6771825Lelio R Paula01/2015
63682^238568+9876533171817Jason Earls01/2009
63692^238541-11272371808Enzo Doria06/2014
63702^238529-1594971805Enzo Doria04/2013
63719*5^102721-871800Lelio R Paula10/2014
63722^238494-16571794Lelio R Paula02/2012
63732^238389-11090571763Enzo Doria05/2014
6374(145*10^71760-1)/971762Serge Batalov12/2014
63757^84913+506271760Mike Oakes02/2010
6376(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
63772^238268-9730571726Lelio R Paula05/2012
6378gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
63792^238235-11324771716Enzo Doria07/2014
63802*12^66450-5^6645071712Mike Oakes11/2010
6381(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
63822^238199-11181771706Enzo Doria05/2014
6383lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
63842^238144+9876533171689Jason Earls01/2009
638518^57102-426571679Enzo Doria03/2013
6386(73*10^71670-1)/971671Robert Price01/2015
63872^238081+1155*23808171670Henri Lifchitz02/2005
63882^238067-11192571666Enzo Doria05/2014
638936^46030+3571637Norbert Schneider04/2014
6390(74*10^71621+313)/971622Robert Price11/2017
63912^237905-9171617Lelio R Paula02/2012
6392(31*2^237902-1)/12371616Lelio R Paula01/2014
6393(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6394(24737*2^237841+1)/2571601Lelio R Paula06/2014
63952^237846+129971599Lelio R Paula05/2012
63966^92004+19980171594Mike Oakes02/2011
6397159^32516+271581Lelio R Paula05/2013
63982^237781+85571580Lelio R Paula05/2012
63992^237720-407971561Yves Minet06/2011
64002^237698-11094571555Enzo Doria05/2014
64012^237695-11323971554Enzo Doria07/2014
64028*5^102362-971549Lelio R Paula10/2014
6403(4*10^71546-31)/971546Erik Branger05/2011
64042^237650+3771540Lelio R Paula02/2012
640518^56977-439171522Enzo Doria03/2013
6406(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6407((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
6408(26*10^71503+7)/371504Erik Branger11/2013
6409(4*10^71498+173)/371499Robert Price01/2017
64103^149848+11071496Lelio R Paula11/2014
64112^237498+51371495Lelio R Paula05/2012
64122^237485+10771491Lelio R Paula02/2012
6413(2^237465+9)/241971481Lelio R Paula05/2012
64142^237439-11223771477Enzo Doria06/2014
64152^237407-978771467Lelio R Paula11/2009
64162^237383+7295371460Enzo Doria04/2016
641782^37337-81^3733771457Robert Price01/2015
6418(1017*2^237313-1)/1971441Lelio R Paula04/2015
64192^237311+19171438Lelio R Paula02/2012
64202^237280-5971429Lelio R Paula02/2012
642111^68564-9871403Lelio R Paula01/2015
64222^237173+7480171397Enzo Doria04/2016
642315^60697+5671386Lelio R Paula01/2015
64242^237118+17771380Lelio R Paula02/2012
64252^237110+6971378Lelio R Paula02/2012
642615^60690-5871377Lelio R Paula01/2015
6427(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6428(3^149567+2)/53971359Lelio R Paula06/2012
6429(5*10^71357-143)/371358Robert Price04/2016
64302^237039-11462171356Enzo Doria05/2015
643112^66116-3771352Lelio R Paula02/2015
6432(3^149497+2^149497)/571328Jean-Louis Charton10/2010
64332^236941-6694571327Lelio R Paula05/2012
64342^236911-114771318Yves Minet10/2009
643565^39337+4271315Lelio R Paula01/2016
64366*10^71299+771300Dmitry Domanov11/2010
6437(25*2^236843+1)/375371295Lelio R Paula06/2012
643810^71291+1518771292Patrick De Geest03/2016
644010^71291-558730911971291Robert Price03/2015
643910^71291-27358171291Patrick De Geest03/2016
6441-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
6442(2^236738+9)/1371265Lelio R Paula05/2012
64435^101949+4271260Lelio R Paula07/2014
64445*10^71237+971238Dmitry Domanov11/2010
64452^236634-1602571234Enzo Doria04/2013
644671^38478+7071233Norbert Schneider12/2014
64479*7^84280+871226Lelio R Paula10/2014
6448(10^71223+59)/371223Serge Batalov12/2014
6449(15185*2^236569-1)/45371216Lelio R Paula04/2015
645051829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
64512^236528-17371203Lelio R Paula02/2012
64523*2^236511-571198Lelio R Paula04/2014
64532^236477-9971187Lelio R Paula02/2012
645411^68356-213071186Enzo Doria12/2012
645511^68355-312071185Enzo Doria12/2012
645636^45737-35^4573771181Robert Price10/2012
6457(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
64582^236432+2571174Lelio R Paula02/2012
64595^101818-1280671168Enzo Doria02/2013
6460(7*10^71166-457)/971166Robert Price09/2017
646165^39253+6271163Lelio R Paula01/2016
646239^44718+3871150Norbert Schneider05/2014
64632^236296-40771133Yves Minet02/2012
64642^236286-11771130Lelio R Paula02/2012
64652^236257-11119371121Enzo Doria05/2014
64667^84149-3671115Lelio R Paula08/2014
64672^236209-11212371106Enzo Doria06/2014
646818^56644-498571104Enzo Doria03/2013
6469(46*10^71077+521)/971078Robert Price08/2017
647021^53753+271074Ray Chandler08/2011
6471(86*10^71068-311)/971069Robert Price10/2017
64722^236081-11092371068Enzo Doria05/2014
6473(293*27^49642-1736)/1371058Curtis Bright05/2015
647465^39192+2271052Lelio R Paula01/2016
6475(439#+1)^397-439#^39771038Mike Oakes11/2010
64767^84050-271031Lelio R Paula09/2013
647720^54558-2370982Lelio R Paula01/2015
64782^235793-11255570981Enzo Doria06/2014
647949936!3-3^4993670981Robert Price08/2015
64802^235787-7879570979Lelio R Paula05/2012
6481Perrin(581132)70970Eric W. Weisstein02/2011
648214^61913-9770961Lelio R Paula01/2015
64842^235720+1632170959Yves Minet03/2010
64832^235718+1609570959Lelio R Paula05/2012
6485163841#+34993370957Nicolas PALAU11/2016
64862^235710+770956Lelio R Paula02/2012
6487(175^31627+1)/17670939Eric Chen10/2017
64882^235635-11208770934Enzo Doria06/2014
64902^235575-196570916Lelio R Paula05/2012
64896^91133+10170916Lelio R Paula01/2015
6491(21181*2^235505+1)/370898Lelio R Paula06/2014
6492(14*10^70896+211)/970897Robert Price11/2017
64935^101425+8470894Lelio R Paula07/2014
6494177^31536+270893Lelio R Paula05/2013
649543*71^38292+470891Serge Batalov03/2016
6496(29*2^235506-1)/11202978570888Lelio R Paula01/2014
649711^68045-153070862Enzo Doria12/2012
64985*10^70858+2170859Robert Price01/2017
64992^235326+370841Donovan Johnson02/2006
650034523!2+470841Robert Price02/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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