PRP Records

Probable Primes Top 10000

(255312 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 ?
72512^240617-364572433Lelio R Paula05/2013
725211^69531-2400072410Enzo Doria12/2012
725318714^7367+7367^1871472373Hans Havermann11/2019
7254(22699*2^240396+1)/5572370Lelio R Paula06/2014
72556^92995+1372365Lelio R Paula01/2015
7256(11*10^72362-149)/372363Robert Price01/2017
725718567^7892+7892^1856772360Hans Havermann11/2019
7258(2^240381+3)/5165572358Lelio R Paula05/2012
72596^92974-5572348Lelio R Paula01/2015
72602^240295+1172337Lelio R Paula02/2012
7261(14*10^72326-53)/372327Robert Price12/2016
726215^61493-4672322Lelio R Paula01/2015
7263lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
72645*10^72302+972303Dmitry Domanov11/2010
7265(9787*2^240179-1)/26572303Lelio R Paula04/2015
726611^69419-312072293Enzo Doria12/2012
726718069^10016+10016^1806972289Hans Havermann11/2019
72684*10^72274-8372275Robert Price10/2017
726910^72267+3372268Robert Price01/2011
727010^72267-55394772267Patrick De Geest05/2013
727111^69389-138072262Enzo Doria12/2012
7272(16^60013-5^60013)/1172262Robert Price07/2013
72737^85507-3072262Lelio R Paula08/2014
7274(19*2^240026-1)/1572256Lelio R Paula02/2014
7275(3^151426-2)/66133772243Lelio R Paula06/2012
7276gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
72772^239863-11226772206Enzo Doria06/2014
72782^239853-11485372203Enzo Doria05/2015
7279(4*10^72174+149)/972174Robert Price03/2017
7281(2^239671+9)/29613172143Lelio R Paula05/2012
72802^239651-11066572143Enzo Doria05/2014
7282(29*2^239650-1)/330572140Lelio R Paula01/2014
7283241^30280+30280^24172128Norbert Schneider11/2014
7284(68*10^72120-23)/972121Robert Price10/2015
7285(9^75571+8^75571)/1772112Robert Price12/2012
7286(15*2^239530-1)/17372105Lelio R Paula01/2014
72872^239513-11251972101Enzo Doria06/2014
7288(10^72097+149)/372097Serge Batalov12/2014
72892^239442-655572080Lelio R Paula05/2012
72902*5^103106+372069Lelio R Paula10/2014
72912^239402-19772068Lelio R Paula02/2012
72922^239356-11187572054Enzo Doria05/2014
7293(38*10^72050-119)/972051Robert Price11/2016
72942^239339+1501572049Lelio R Paula01/2013
7295159^32728+272048Lelio R Paula05/2013
729615^61259-3872047Lelio R Paula01/2015
729792^36683-91^3668372038Robert Price08/2015
72982^239280+5461572031Lelio R Paula05/2012
7299(47*2^239267+1)/7772027Lelio R Paula04/2015
7300(85*10^72025-1)/372027Robert Price07/2017
73012^239236-9730572018Lelio R Paula05/2012
7302144^33361-14372006Norbert Schneider11/2018
73032^239169+5971998Lelio R Paula02/2012
7304lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
7305(15*2^239171-1)/10630171994Lelio R Paula01/2014
7307(29^49211-1)/2871965Robert Price04/2012
7306(299*10^71963+1)/371965Robert Price11/2017
7308L(344293)71953Renaud Lifchitz09/2003
7309V(344293)71953Serge Batalov03/2015
73106*10^71951+771952Dmitry Domanov11/2010
73113^150798+4071949Lelio R Paula01/2015
73122^238961+9571935Lelio R Paula02/2012
731312511^17556+17556^1251171933Norbert Schneider09/2019
73142^238936-40771927Yves Minet02/2012
73152^238923-2863571923Lelio R Paula05/2012
731610^71910+2511971911Patrick De Geest05/2016
731710^71910-80171910Robert Price04/2016
73182^238845-11265171900Enzo Doria06/2014
73192^238792-11124571884Enzo Doria05/2014
73206*7^85059+571884Lelio R Paula10/2014
732119312^5273+5273^1931271881Hans Havermann11/2019
732219176^5603+5603^1917671880Hans Havermann11/2019
73232^238752-11058971872Enzo Doria05/2014
732412^66581+771853Lelio R Paula07/2014
7325(7*2^238691+1)/4122971850Lelio R Paula06/2012
73264*3^150568-571840Lelio R Paula04/2014
73276^92301+6771825Lelio R Paula01/2015
73282^238568+9876533171817Jason Earls01/2009
73292^238541-11272371808Enzo Doria06/2014
73302^238529-1594971805Enzo Doria04/2013
73319*5^102721-871800Lelio R Paula10/2014
73322^238494-16571794Lelio R Paula02/2012
733318035^9562+9562^1803571790Hans Havermann10/2019
733418390^7993+7993^1839071771Hans Havermann11/2019
73352^238389-11090571763Enzo Doria05/2014
7336(145*10^71760-1)/971762Serge Batalov12/2014
73377^84913+506271760Mike Oakes02/2010
733821218^2409+2409^2121871756Hans Havermann10/2019
7339(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
73402^238268-9730571726Lelio R Paula05/2012
7341gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
73422^238235-11324771716Enzo Doria07/2014
73432*12^66450-5^6645071712Mike Oakes11/2010
7344(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
73452^238199-11181771706Enzo Doria05/2014
7346lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
73472^238144+9876533171689Jason Earls01/2009
734818^57102-426571679Enzo Doria03/2013
7349(73*10^71670-1)/971671Robert Price01/2015
73502^238081+1155*23808171670Henri Lifchitz02/2005
73512^238067-11192571666Enzo Doria05/2014
735219143^5528+5528^1914371644Hans Havermann10/2019
735365401!4+12871638Robert Price09/2019
735436^46030+3571637Norbert Schneider04/2014
7355(74*10^71621+313)/971622Robert Price11/2017
73562^237905-9171617Lelio R Paula02/2012
7357(31*2^237902-1)/12371616Lelio R Paula01/2014
7358(15185*2^237866-1)/4396771605Lelio R Paula04/2015
735916696^16957+16957^1669671603Norbert Schneider09/2019
7360(24737*2^237841+1)/2571601Lelio R Paula06/2014
73612^237846+129971599Lelio R Paula05/2012
73626^92004+19980171594Mike Oakes02/2011
7363159^32516+271581Lelio R Paula05/2013
73642^237781+85571580Lelio R Paula05/2012
73652^237720-407971561Yves Minet06/2011
73662^237698-11094571555Enzo Doria05/2014
73672^237695-11323971554Enzo Doria07/2014
73688*5^102362-971549Lelio R Paula10/2014
7369(4*10^71546-31)/971546Erik Branger05/2011
73702^237650+3771540Lelio R Paula02/2012
737118^56977-439171522Enzo Doria03/2013
7373(22699*2^237565+1)/413663771512Lelio R Paula06/2014
7372((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
7374(26*10^71503+7)/371504Erik Branger11/2013
7375(4*10^71498+173)/371499Robert Price01/2017
73763^149848+11071496Lelio R Paula11/2014
73772^237498+51371495Lelio R Paula05/2012
73782^237485+10771491Lelio R Paula02/2012
7379(2^237465+9)/241971481Lelio R Paula05/2012
73802^237439-11223771477Enzo Doria06/2014
73812^237407-978771467Lelio R Paula11/2009
73822^237383+7295371460Enzo Doria04/2016
738319768^4119+4119^1976871458Hans Havermann11/2019
738482^37337-81^3733771457Robert Price01/2015
7385(1017*2^237313-1)/1971441Lelio R Paula04/2015
73862^237311+19171438Lelio R Paula02/2012
738711699^17560+17560^1169971437Norbert Schneider09/2019
73882^237280-5971429Lelio R Paula02/2012
738911^68564-9871403Lelio R Paula01/2015
73902^237173+7480171397Enzo Doria04/2016
739115^60697+5671386Lelio R Paula01/2015
73922^237118+17771380Lelio R Paula02/2012
73932^237110+6971378Lelio R Paula02/2012
739415^60690-5871377Lelio R Paula01/2015
7395(5*2^237125-1)/59985119171374Lelio R Paula01/2014
739620311^3262+3262^2031171363Hans Havermann11/2019
7397(3^149567+2)/53971359Lelio R Paula06/2012
7398(5*10^71357-143)/371358Robert Price04/2016
73992^237039-11462171356Enzo Doria05/2015
740012^66116-3771352Lelio R Paula02/2015
7401(3^149497+2^149497)/571328Jean-Louis Charton10/2010
74022^236941-6694571327Lelio R Paula05/2012
74032^236911-114771318Yves Minet10/2009
740465^39337+4271315Lelio R Paula01/2016
74056*10^71299+771300Dmitry Domanov11/2010
7406(25*2^236843+1)/375371295Lelio R Paula06/2012
740710^71291+1518771292Patrick De Geest03/2016
740910^71291-558730911971291Robert Price03/2015
740810^71291-27358171291Patrick De Geest03/2016
7410-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
741115105^17054+17054^1510571271Norbert Schneider08/2018
7412(2^236738+9)/1371265Lelio R Paula05/2012
74135^101949+4271260Lelio R Paula07/2014
74145*10^71237+971238Dmitry Domanov11/2010
74152^236634-1602571234Enzo Doria04/2013
741671^38478+7071233Norbert Schneider12/2014
74179*7^84280+871226Lelio R Paula10/2014
7418(10^71223+59)/371223Serge Batalov12/2014
741923260^1153+1153^2326071219Hans Havermann10/2019
7420(15185*2^236569-1)/45371216Lelio R Paula04/2015
742151829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
74222^236528-17371203Lelio R Paula02/2012
74233*2^236511-571198Lelio R Paula04/2014
74242^236477-9971187Lelio R Paula02/2012
742511^68356-213071186Enzo Doria12/2012
742615128^17031+17031^1512871186Norbert Schneider08/2018
742711^68355-312071185Enzo Doria12/2012
742836^45737-35^4573771181Robert Price10/2012
7429(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
74302^236432+2571174Lelio R Paula02/2012
74315^101818-1280671168Enzo Doria02/2013
7432(7*10^71166-457)/971166Robert Price09/2017
743365^39253+6271163Lelio R Paula01/2016
743439^44718+3871150Norbert Schneider05/2014
743518996^5557+5557^1899671137Hans Havermann10/2019
743664983!4-25671135Robert Price11/2019
74372^236296-40771133Yves Minet02/2012
74382^236286-11771130Lelio R Paula02/2012
74392^236257-11119371121Enzo Doria05/2014
74407^84149-3671115Lelio R Paula08/2014
7441164176#-p(164176)71108Henri Lifchitz12/2018
74422^236209-11212371106Enzo Doria06/2014
744318^56644-498571104Enzo Doria03/2013
7444(46*10^71077+521)/971078Robert Price08/2017
744521^53753+271074Ray Chandler08/2011
7446(86*10^71068-311)/971069Robert Price10/2017
74472^236081-11092371068Enzo Doria05/2014
7448(293*27^49642-1736)/1371058Curtis Bright05/2015
744965^39192+2271052Lelio R Paula01/2016
7450(439#+1)^397-439#^39771038Mike Oakes11/2010
74517^84050-271031Lelio R Paula09/2013
745215813^16916+16916^1581371031Norbert Schneider09/2019
745364877!4+12871007Robert Price09/2019
745418562^6681+6681^1856270997Hans Havermann10/2019
745520^54558-2370982Lelio R Paula01/2015
74562^235793-11255570981Enzo Doria06/2014
745749936!3-3^4993670981Robert Price08/2015
74582^235787-7879570979Lelio R Paula05/2012
7459Perrin(581132)70970Eric W. Weisstein02/2011
746014^61913-9770961Lelio R Paula01/2015
74622^235720+1632170959Yves Minet03/2010
74612^235718+1609570959Lelio R Paula05/2012
7463163841#+34993370957Nicolas PALAU11/2016
74642^235710+770956Lelio R Paula02/2012
7465(175^31627+1)/17670939Eric Chen10/2017
74662^235635-11208770934Enzo Doria06/2014
7467153^32467+15270931Norbert Schneider11/2018
74692^235575-196570916Lelio R Paula05/2012
74686^91133+10170916Lelio R Paula01/2015
7470(21181*2^235505+1)/370898Lelio R Paula06/2014
7471(14*10^70896+211)/970897Robert Price11/2017
74725^101425+8470894Lelio R Paula07/2014
7473177^31536+270893Lelio R Paula05/2013
747443*71^38292+470891Serge Batalov03/2016
7475(29*2^235506-1)/11202978570888Lelio R Paula01/2014
747611^68045-153070862Enzo Doria12/2012
74775*10^70858+2170859Robert Price01/2017
74792^235326+370841Donovan Johnson02/2006
747834523!2+470841Robert Price02/2015
7480(31*2^235307+1)/370836Lelio R Paula06/2012
74812^235308+13570835Lelio R Paula02/2012
7482r(35414,90)*1000+91170831Patrick De Geest07/2004
74832^235274+15970825Lelio R Paula02/2012
74843^148409+7070810Lelio R Paula11/2014
7485(19*10^70794+17)/970795Robert Price03/2015
74862^235108-23270970775Paul Bourdelais03/2013
748722995^1196+1196^2299570773Hans Havermann11/2019
7488(2^235099-2^117550+1)/57077211/2006
748919^55325-670748Lelio R Paula08/2014
7490257^29356+29356^25770746Norbert Schneider10/2014
749122*10^70729+370731Robert Price10/2017
74922^234956+1171570729Lelio R Paula05/2012
7493(7*10^70727-43)/970727Robert Price10/2014
74942^234890-3034170709Enzo Doria11/2012
749517^57461+1470703Lelio R Paula01/2015
749618281^7366+7366^1828170697Hans Havermann09/2019
7497(9179*2^234834-1)/570696Lelio R Paula04/2015
74982*10^70688+5170689Robert Price10/2017
7499123^33822-12270685Norbert Schneider01/2015
75007*10^70680-9970681Robert Price11/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 14 2019 11:13 (Time in France)

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