PRP Records

Probable Primes Top 10000

(253476 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 ?
7001(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
70026^93815+14373003Lelio R Paula01/2015
70036^93812+573000Wojciech Florek03/2006
700419^57078-6272989Lelio R Paula01/2015
7005(29*10^72985+91)/372986Robert Price03/2016
700611^70082-252072983Enzo Doria12/2012
70076^93773+13372970Lelio R Paula01/2015
70082^242328-5972948Lelio R Paula03/2012
70095^104358-1301672944Enzo Doria02/2013
7010(75*10^72941-57)/9972941Ray Chandler03/2011
701112^67585-9572937Lelio R Paula02/2015
70122^242230-11328572919Enzo Doria07/2014
7013(5*10^72916-11)/372917Erik Branger12/2013
70142^242220-11039972916Enzo Doria05/2014
70152^242205-11341372911Enzo Doria07/2014
7016(3^152809+3^76405+1)/772908Serge Batalov03/2014
70172^242175+7424372902Yves Minet03/2011
70182^242150+1765972895Lelio R Paula11/2009
701911^69982-234072879Enzo Doria12/2012
7020(23*2^242093+1)/1011772875Lelio R Paula08/2012
7021(67607*2^242043+1)/3326372863Lelio R Paula06/2014
70222^242032+8772859Lelio R Paula03/2012
70232^241968-11059572840Enzo Doria05/2014
7024(10^72821+71)/972821Robert Price11/2014
70252^241852-6487572805Lelio R Paula05/2013
7026F(348307)/2056289086590809372776Donovan Johnson07/2007
7027(67*10^72772+23)/972773Ray Chandler11/2010
7028(8*10^72759+67)/372760Robert Price01/2017
70292^241670+14572750Lelio R Paula03/2012
70305^104074+5272745Lelio R Paula08/2014
7031(3^152466-5)/72472742Lelio R Paula06/2012
703220^55908-4172738Lelio R Paula01/2015
7033(73*10^72735+53)/972736Robert Price10/2015
703410^72730+22401172731Patrick De Geest05/2013
703510^72730-9972730Robert Price05/2011
70363*10^72723+6772724Robert Price11/2017
7037(11^69833+3^69833)/1472723Robert Price03/2013
7038(10^72723-79)/372723Robert Price10/2017
7039(88*10^72711-43)/972712Robert Price11/2015
70403^152379+28072704Lelio R Paula01/2015
7041(25*10^72703-241)/972704Robert Price01/2017
7042(47*10^72696+133)/972697Robert Price04/2017
704317^59077-9072692Lelio R Paula01/2015
704465^40096+5872691Lelio R Paula01/2016
7045(29*2^241446-1)/24572682Lelio R Paula01/2014
704711^69783-3840000072672Enzo Doria01/2013
70462^241409-11290372672Enzo Doria06/2014
7048(3^152287+1)/472659Paul Bourdelais04/2008
70493^152249-5672642Lelio R Paula01/2015
705010^72631+3772632Robert Price01/2011
705110^72631-881372631Patrick De Geest05/2013
7052(19*2^241254+1)/10172624Lelio R Paula08/2012
7053(9^76103+8^76103)/1772620Robert Price12/2012
70542^241220-11233772615Enzo Doria06/2014
7055(82*10^72612+449)/972613Robert Price02/2017
70562^241169-1579372600Enzo Doria04/2013
70579*10^72595+1172596Robert Kinser01/2017
7058(25*2^241048+1)/8972563Lelio R Paula08/2012
7059(22*10^72560+17)/372561Robert Price09/2015
70602^241032-2372558Lelio R Paula02/2012
706134485*10^72550+2^241004-372555Gilbert Mozzo12/2012
70622^241004-372550M. Frind & P. Underwood07/2002
706397*10^72522-372524Robert Price01/2017
7064(68*10^72516+7)/372518Robert Price03/2016
7065(78557*2^240844+1)/6372505Lelio R Paula06/2014
706667^39701-6672497Norbert Schneider11/2014
7067(185*10^72484+7)/372486Robert Price02/2017
7069(293*27^50631-1736)/1372473Curtis Bright05/2015
7068103^36005-10272473Norbert Schneider10/2016
707015^61616+8872467Lelio R Paula01/2015
707145^43831+272462Lelio R Paula05/2013
70722^240692-49238972456Paul Bourdelais03/2013
7073(646*10^72446-7)/972448Robert Price07/2016
70749*6^93083+772434Lelio R Paula10/2014
70752^240617-364572433Lelio R Paula05/2013
707611^69531-2400072410Enzo Doria12/2012
7077(22699*2^240396+1)/5572370Lelio R Paula06/2014
70786^92995+1372365Lelio R Paula01/2015
7079(11*10^72362-149)/372363Robert Price01/2017
7080(2^240381+3)/5165572358Lelio R Paula05/2012
70816^92974-5572348Lelio R Paula01/2015
70822^240295+1172337Lelio R Paula02/2012
7083(14*10^72326-53)/372327Robert Price12/2016
708415^61493-4672322Lelio R Paula01/2015
7085lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
70865*10^72302+972303Dmitry Domanov11/2010
7087(9787*2^240179-1)/26572303Lelio R Paula04/2015
708811^69419-312072293Enzo Doria12/2012
70894*10^72274-8372275Robert Price10/2017
709010^72267+3372268Robert Price01/2011
709110^72267-55394772267Patrick De Geest05/2013
709211^69389-138072262Enzo Doria12/2012
7093(16^60013-5^60013)/1172262Robert Price07/2013
70947^85507-3072262Lelio R Paula08/2014
7095(19*2^240026-1)/1572256Lelio R Paula02/2014
7096(3^151426-2)/66133772243Lelio R Paula06/2012
7097gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
70982^239863-11226772206Enzo Doria06/2014
70992^239853-11485372203Enzo Doria05/2015
7100(4*10^72174+149)/972174Robert Price03/2017
7102(2^239671+9)/29613172143Lelio R Paula05/2012
71012^239651-11066572143Enzo Doria05/2014
7103(29*2^239650-1)/330572140Lelio R Paula01/2014
7104241^30280+30280^24172128Norbert Schneider11/2014
7105(68*10^72120-23)/972121Robert Price10/2015
7106(9^75571+8^75571)/1772112Robert Price12/2012
7107(15*2^239530-1)/17372105Lelio R Paula01/2014
71082^239513-11251972101Enzo Doria06/2014
7109(10^72097+149)/372097Serge Batalov12/2014
71102^239442-655572080Lelio R Paula05/2012
71112*5^103106+372069Lelio R Paula10/2014
71122^239402-19772068Lelio R Paula02/2012
71132^239356-11187572054Enzo Doria05/2014
7114(38*10^72050-119)/972051Robert Price11/2016
71152^239339+1501572049Lelio R Paula01/2013
7116159^32728+272048Lelio R Paula05/2013
711715^61259-3872047Lelio R Paula01/2015
711892^36683-91^3668372038Robert Price08/2015
71192^239280+5461572031Lelio R Paula05/2012
7120(47*2^239267+1)/7772027Lelio R Paula04/2015
7121(85*10^72025-1)/372027Robert Price07/2017
71222^239236-9730572018Lelio R Paula05/2012
7123144^33361-14372006Norbert Schneider11/2018
71242^239169+5971998Lelio R Paula02/2012
7125lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
7126(15*2^239171-1)/10630171994Lelio R Paula01/2014
7127(29^49211-1)/2871965Robert Price04/2012
7128(299*10^71963+1)/371965Robert Price11/2017
7130L(344293)71953Renaud Lifchitz09/2003
7129V(344293)71953Serge Batalov03/2015
71316*10^71951+771952Dmitry Domanov11/2010
71323^150798+4071949Lelio R Paula01/2015
71332^238961+9571935Lelio R Paula02/2012
71342^238936-40771927Yves Minet02/2012
71352^238923-2863571923Lelio R Paula05/2012
713610^71910+2511971911Patrick De Geest05/2016
713710^71910-80171910Robert Price04/2016
71382^238845-11265171900Enzo Doria06/2014
71392^238792-11124571884Enzo Doria05/2014
71406*7^85059+571884Lelio R Paula10/2014
71412^238752-11058971872Enzo Doria05/2014
714212^66581+771853Lelio R Paula07/2014
7143(7*2^238691+1)/4122971850Lelio R Paula06/2012
71444*3^150568-571840Lelio R Paula04/2014
71456^92301+6771825Lelio R Paula01/2015
71462^238568+9876533171817Jason Earls01/2009
71472^238541-11272371808Enzo Doria06/2014
71482^238529-1594971805Enzo Doria04/2013
71499*5^102721-871800Lelio R Paula10/2014
71502^238494-16571794Lelio R Paula02/2012
71512^238389-11090571763Enzo Doria05/2014
7152(145*10^71760-1)/971762Serge Batalov12/2014
71537^84913+506271760Mike Oakes02/2010
7154(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
71552^238268-9730571726Lelio R Paula05/2012
7156gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
71572^238235-11324771716Enzo Doria07/2014
71582*12^66450-5^6645071712Mike Oakes11/2010
7159(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
71602^238199-11181771706Enzo Doria05/2014
7161lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
71622^238144+9876533171689Jason Earls01/2009
716318^57102-426571679Enzo Doria03/2013
7164(73*10^71670-1)/971671Robert Price01/2015
71652^238081+1155*23808171670Henri Lifchitz02/2005
71662^238067-11192571666Enzo Doria05/2014
716736^46030+3571637Norbert Schneider04/2014
7168(74*10^71621+313)/971622Robert Price11/2017
71692^237905-9171617Lelio R Paula02/2012
7170(31*2^237902-1)/12371616Lelio R Paula01/2014
7171(15185*2^237866-1)/4396771605Lelio R Paula04/2015
7172(24737*2^237841+1)/2571601Lelio R Paula06/2014
71732^237846+129971599Lelio R Paula05/2012
71746^92004+19980171594Mike Oakes02/2011
7175159^32516+271581Lelio R Paula05/2013
71762^237781+85571580Lelio R Paula05/2012
71772^237720-407971561Yves Minet06/2011
71782^237698-11094571555Enzo Doria05/2014
71792^237695-11323971554Enzo Doria07/2014
71808*5^102362-971549Lelio R Paula10/2014
7181(4*10^71546-31)/971546Erik Branger05/2011
71822^237650+3771540Lelio R Paula02/2012
718318^56977-439171522Enzo Doria03/2013
7184(22699*2^237565+1)/413663771512Lelio R Paula06/2014
7185((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
7186(26*10^71503+7)/371504Erik Branger11/2013
7187(4*10^71498+173)/371499Robert Price01/2017
71883^149848+11071496Lelio R Paula11/2014
71892^237498+51371495Lelio R Paula05/2012
71902^237485+10771491Lelio R Paula02/2012
7191(2^237465+9)/241971481Lelio R Paula05/2012
71922^237439-11223771477Enzo Doria06/2014
71932^237407-978771467Lelio R Paula11/2009
71942^237383+7295371460Enzo Doria04/2016
719582^37337-81^3733771457Robert Price01/2015
7196(1017*2^237313-1)/1971441Lelio R Paula04/2015
71972^237311+19171438Lelio R Paula02/2012
71982^237280-5971429Lelio R Paula02/2012
719911^68564-9871403Lelio R Paula01/2015
72002^237173+7480171397Enzo Doria04/2016
720115^60697+5671386Lelio R Paula01/2015
72022^237118+17771380Lelio R Paula02/2012
72032^237110+6971378Lelio R Paula02/2012
720415^60690-5871377Lelio R Paula01/2015
7205(5*2^237125-1)/59985119171374Lelio R Paula01/2014
7206(3^149567+2)/53971359Lelio R Paula06/2012
7207(5*10^71357-143)/371358Robert Price04/2016
72082^237039-11462171356Enzo Doria05/2015
720912^66116-3771352Lelio R Paula02/2015
7210(3^149497+2^149497)/571328Jean-Louis Charton10/2010
72112^236941-6694571327Lelio R Paula05/2012
72122^236911-114771318Yves Minet10/2009
721365^39337+4271315Lelio R Paula01/2016
72146*10^71299+771300Dmitry Domanov11/2010
7215(25*2^236843+1)/375371295Lelio R Paula06/2012
721610^71291+1518771292Patrick De Geest03/2016
721810^71291-558730911971291Robert Price03/2015
721710^71291-27358171291Patrick De Geest03/2016
7219-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
722015105^17054+17054^1510571271Norbert Schneider08/2018
7221(2^236738+9)/1371265Lelio R Paula05/2012
72225^101949+4271260Lelio R Paula07/2014
72235*10^71237+971238Dmitry Domanov11/2010
72242^236634-1602571234Enzo Doria04/2013
722571^38478+7071233Norbert Schneider12/2014
72269*7^84280+871226Lelio R Paula10/2014
7227(10^71223+59)/371223Serge Batalov12/2014
7228(15185*2^236569-1)/45371216Lelio R Paula04/2015
722951829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
72302^236528-17371203Lelio R Paula02/2012
72313*2^236511-571198Lelio R Paula04/2014
72322^236477-9971187Lelio R Paula02/2012
723311^68356-213071186Enzo Doria12/2012
723415128^17031+17031^1512871186Norbert Schneider08/2018
723511^68355-312071185Enzo Doria12/2012
723636^45737-35^4573771181Robert Price10/2012
7237(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
72382^236432+2571174Lelio R Paula02/2012
72395^101818-1280671168Enzo Doria02/2013
7240(7*10^71166-457)/971166Robert Price09/2017
724165^39253+6271163Lelio R Paula01/2016
724239^44718+3871150Norbert Schneider05/2014
72432^236296-40771133Yves Minet02/2012
72442^236286-11771130Lelio R Paula02/2012
72452^236257-11119371121Enzo Doria05/2014
72467^84149-3671115Lelio R Paula08/2014
7247164176#-p(164176)71108Henri Lifchitz12/2018
72482^236209-11212371106Enzo Doria06/2014
724918^56644-498571104Enzo Doria03/2013
7250(46*10^71077+521)/971078Robert Price08/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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