PRP Records

Probable Primes Top 10000

(212140 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 ?
62512^239356-11187572054Enzo Doria05/2014
6252(38*10^72050-119)/972051Robert Price11/2016
62532^239339+1501572049Lelio R Paula01/2013
6254159^32728+272048Lelio R Paula05/2013
625515^61259-3872047Lelio R Paula01/2015
625692^36683-91^3668372038Robert Price08/2015
62572^239280+5461572031Lelio R Paula05/2012
6258(47*2^239267+1)/7772027Lelio R Paula04/2015
6259(85*10^72025-1)/372027Robert Price07/2017
62602^239236-9730572018Lelio R Paula05/2012
62612^239169+5971998Lelio R Paula02/2012
6262lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6263(15*2^239171-1)/10630171994Lelio R Paula01/2014
6264(29^49211-1)/2871965Robert Price04/2012
6265(299*10^71963+1)/371965Robert Price11/2017
6267L(344293)71953Renaud Lifchitz09/2003
6266V(344293)71953Serge Batalov03/2015
62686*10^71951+771952Dmitry Domanov11/2010
62693^150798+4071949Lelio R Paula01/2015
62702^238961+9571935Lelio R Paula02/2012
62712^238936-40771927Yves Minet02/2012
62722^238923-2863571923Lelio R Paula05/2012
627310^71910+2511971911Patrick De Geest05/2016
627410^71910-80171910Robert Price04/2016
62752^238845-11265171900Enzo Doria06/2014
62762^238792-11124571884Enzo Doria05/2014
62776*7^85059+571884Lelio R Paula10/2014
62782^238752-11058971872Enzo Doria05/2014
627912^66581+771853Lelio R Paula07/2014
6280(7*2^238691+1)/4122971850Lelio R Paula06/2012
62814*3^150568-571840Lelio R Paula04/2014
62826^92301+6771825Lelio R Paula01/2015
62832^238568+9876533171817Jason Earls01/2009
62842^238541-11272371808Enzo Doria06/2014
62852^238529-1594971805Enzo Doria04/2013
62869*5^102721-871800Lelio R Paula10/2014
62872^238494-16571794Lelio R Paula02/2012
62882^238389-11090571763Enzo Doria05/2014
6289(145*10^71760-1)/971762Serge Batalov12/2014
62907^84913+506271760Mike Oakes02/2010
6291(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
62922^238268-9730571726Lelio R Paula05/2012
6293gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
62942^238235-11324771716Enzo Doria07/2014
62952*12^66450-5^6645071712Mike Oakes11/2010
6296(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
62972^238199-11181771706Enzo Doria05/2014
6298lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
62992^238144+9876533171689Jason Earls01/2009
630018^57102-426571679Enzo Doria03/2013
6301(73*10^71670-1)/971671Robert Price01/2015
63022^238081+1155*23808171670Henri Lifchitz02/2005
63032^238067-11192571666Enzo Doria05/2014
630436^46030+3571637Norbert Schneider04/2014
6305(74*10^71621+313)/971622Robert Price11/2017
63062^237905-9171617Lelio R Paula02/2012
6307(31*2^237902-1)/12371616Lelio R Paula01/2014
6308(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6309(24737*2^237841+1)/2571601Lelio R Paula06/2014
63102^237846+129971599Lelio R Paula05/2012
63116^92004+19980171594Mike Oakes02/2011
6312159^32516+271581Lelio R Paula05/2013
63132^237781+85571580Lelio R Paula05/2012
63142^237720-407971561Yves Minet06/2011
63152^237698-11094571555Enzo Doria05/2014
63162^237695-11323971554Enzo Doria07/2014
63178*5^102362-971549Lelio R Paula10/2014
6318(4*10^71546-31)/971546Erik Branger05/2011
63192^237650+3771540Lelio R Paula02/2012
632018^56977-439171522Enzo Doria03/2013
6321(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6322((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
6323(26*10^71503+7)/371504Erik Branger11/2013
6324(4*10^71498+173)/371499Robert Price01/2017
63253^149848+11071496Lelio R Paula11/2014
63262^237498+51371495Lelio R Paula05/2012
63272^237485+10771491Lelio R Paula02/2012
6328(2^237465+9)/241971481Lelio R Paula05/2012
63292^237439-11223771477Enzo Doria06/2014
63302^237407-978771467Lelio R Paula11/2009
63312^237383+7295371460Enzo Doria04/2016
633282^37337-81^3733771457Robert Price01/2015
6333(1017*2^237313-1)/1971441Lelio R Paula04/2015
63342^237311+19171438Lelio R Paula02/2012
63352^237280-5971429Lelio R Paula02/2012
633611^68564-9871403Lelio R Paula01/2015
63372^237173+7480171397Enzo Doria04/2016
633815^60697+5671386Lelio R Paula01/2015
63392^237118+17771380Lelio R Paula02/2012
63402^237110+6971378Lelio R Paula02/2012
634115^60690-5871377Lelio R Paula01/2015
6342(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6343(3^149567+2)/53971359Lelio R Paula06/2012
6344(5*10^71357-143)/371358Robert Price04/2016
63452^237039-11462171356Enzo Doria05/2015
634612^66116-3771352Lelio R Paula02/2015
6347(3^149497+2^149497)/571328Jean-Louis Charton10/2010
63482^236941-6694571327Lelio R Paula05/2012
63492^236911-114771318Yves Minet10/2009
635065^39337+4271315Lelio R Paula01/2016
63516*10^71299+771300Dmitry Domanov11/2010
6352(25*2^236843+1)/375371295Lelio R Paula06/2012
635310^71291+1518771292Patrick De Geest03/2016
635510^71291-558730911971291Robert Price03/2015
635410^71291-27358171291Patrick De Geest03/2016
6356-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
6357(2^236738+9)/1371265Lelio R Paula05/2012
63585^101949+4271260Lelio R Paula07/2014
63595*10^71237+971238Dmitry Domanov11/2010
63602^236634-1602571234Enzo Doria04/2013
636171^38478+7071233Norbert Schneider12/2014
63629*7^84280+871226Lelio R Paula10/2014
6363(10^71223+59)/371223Serge Batalov12/2014
6364(15185*2^236569-1)/45371216Lelio R Paula04/2015
636551829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
63662^236528-17371203Lelio R Paula02/2012
63673*2^236511-571198Lelio R Paula04/2014
63682^236477-9971187Lelio R Paula02/2012
636911^68356-213071186Enzo Doria12/2012
637011^68355-312071185Enzo Doria12/2012
637136^45737-35^4573771181Robert Price10/2012
6372(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
63732^236432+2571174Lelio R Paula02/2012
63745^101818-1280671168Enzo Doria02/2013
6375(7*10^71166-457)/971166Robert Price09/2017
637665^39253+6271163Lelio R Paula01/2016
637739^44718+3871150Norbert Schneider05/2014
63782^236296-40771133Yves Minet02/2012
63792^236286-11771130Lelio R Paula02/2012
63802^236257-11119371121Enzo Doria05/2014
63817^84149-3671115Lelio R Paula08/2014
63822^236209-11212371106Enzo Doria06/2014
638318^56644-498571104Enzo Doria03/2013
6384(46*10^71077+521)/971078Robert Price08/2017
638521^53753+271074Ray Chandler08/2011
6386(86*10^71068-311)/971069Robert Price10/2017
63872^236081-11092371068Enzo Doria05/2014
6388(293*27^49642-1736)/1371058Curtis Bright05/2015
638965^39192+2271052Lelio R Paula01/2016
6390(439#+1)^397-439#^39771038Mike Oakes11/2010
63917^84050-271031Lelio R Paula09/2013
639220^54558-2370982Lelio R Paula01/2015
63932^235793-11255570981Enzo Doria06/2014
639449936!3-3^4993670981Robert Price08/2015
63952^235787-7879570979Lelio R Paula05/2012
6396Perrin(581132)70970Eric W. Weisstein02/2011
639714^61913-9770961Lelio R Paula01/2015
63982^235720+1632170959Yves Minet03/2010
63992^235718+1609570959Lelio R Paula05/2012
6400163841#+34993370957Nicolas PALAU11/2016
64012^235710+770956Lelio R Paula02/2012
6402(175^31627+1)/17670939Eric Chen10/2017
64032^235635-11208770934Enzo Doria06/2014
64052^235575-196570916Lelio R Paula05/2012
64046^91133+10170916Lelio R Paula01/2015
6406(21181*2^235505+1)/370898Lelio R Paula06/2014
6407(14*10^70896+211)/970897Robert Price11/2017
64085^101425+8470894Lelio R Paula07/2014
6409177^31536+270893Lelio R Paula05/2013
641043*71^38292+470891Serge Batalov03/2016
6411(29*2^235506-1)/11202978570888Lelio R Paula01/2014
641211^68045-153070862Enzo Doria12/2012
64135*10^70858+2170859Robert Price01/2017
64142^235326+370841Donovan Johnson02/2006
641534523!2+470841Robert Price02/2015
6416(31*2^235307+1)/370836Lelio R Paula06/2012
64172^235308+13570835Lelio R Paula02/2012
6418r(35414,90)*1000+91170831Patrick De Geest07/2004
64192^235274+15970825Lelio R Paula02/2012
64203^148409+7070810Lelio R Paula11/2014
6421(19*10^70794+17)/970795Robert Price03/2015
64222^235108-23270970775Paul Bourdelais03/2013
6423(2^235099-2^117550+1)/57077211/2006
642419^55325-670748Lelio R Paula08/2014
6425257^29356+29356^25770746Norbert Schneider10/2014
642622*10^70729+370731Robert Price10/2017
64272^234956+1171570729Lelio R Paula05/2012
6428(7*10^70727-43)/970727Robert Price10/2014
64292^234890-3034170709Enzo Doria11/2012
643017^57461+1470703Lelio R Paula01/2015
6431(9179*2^234834-1)/570696Lelio R Paula04/2015
64322*10^70688+5170689Robert Price10/2017
6433123^33822-12270685Norbert Schneider01/2015
64347*10^70680-9970681Robert Price11/2017
6435(21*2^234772-1)/209570672Lelio R Paula01/2014
6436(29*2^234686-1)/2114570645Lelio R Paula01/2014
6437(15*2^234688-1)/527814170643Lelio R Paula01/2014
64392^234655-6770639Lelio R Paula02/2012
6438(79*10^70638-61)/970639Robert Price10/2015
64402^234652-17370638Lelio R Paula02/2012
64412^234618-364570628Lelio R Paula05/2012
6442(2^234610-5)/1970624Lelio R Paula05/2012
64434*5^101038+970624Lelio R Paula10/2014
64442^234603+7196370623Enzo Doria04/2016
64452^234600-11312970622Enzo Doria07/2014
64462^234586+970618Lelio R Paula02/2012
64473^148008+2670618Robert Price11/2013
6448(7*10^70616-151)/970616Robert Price09/2017
644965^38947+3270608Lelio R Paula01/2016
6450(2^234488-3)/1170587Lelio R Paula05/2012
6451(3*2^234451+1)/3570576Lelio R Paula08/2012
6452Phi(159495,10)70560Maksym Voznyy09/2015
64532^234383-403570557Lelio R Paula05/2012
64542^234315-11124170536Enzo Doria05/2014
645514^61526+9770517Lelio R Paula01/2015
6456(3*2^234170+1)/1370492Lelio R Paula08/2012
645751^41281-50^4128170491Robert Price02/2013
64582^234141-11212370484Enzo Doria06/2014
64592^234139+1228570483Lelio R Paula04/2012
64602^234133-316370482Yves Minet04/2009
64612^234115+8370476Lelio R Paula02/2012
64622^234114-159570476Lelio R Paula05/2012
646324^51061-23^5106170475Robert Price07/2012
646419471^16428-270467Faysal YAtim09/2005
64657^83381+1270466Robert Price01/2014
64662^234067-11142770462Enzo Doria05/2014
6467(266*10^70457+1)/370459Robert Price02/2016
6468(31*2^234041-1)/9770453Lelio R Paula01/2014
64692^234026+1290970449Lelio R Paula04/2012
64702^233965-1970431Lelio R Paula02/2012
6471(5*2^233932-1)/17970419Lelio R Paula01/2014
64722^233908-1710970414Enzo Doria05/2013
6473695^24772+24772^69570402Norbert Schneider09/2016
64743*5^100719-270401Lelio R Paula10/2014
64752^233829-11135570390Enzo Doria05/2014
6476(19775^16384+1)/270388Henri Lifchitz03/2007
64777*3^147519+870386Lelio R Paula04/2014
6478141^32749-270385Lelio R Paula10/2017
64795*7^83265+270368Lelio R Paula10/2014
6480(23*10^70363+97)/370364Robert Price02/2017
6481(23*2^233749-1)/3532570363Lelio R Paula01/2014
64825^100652-1391670353Enzo Doria02/2013
648345^42555-270353Lelio R Paula08/2013
64842^233661-6170339Lelio R Paula02/2012
64852^233523-11224970298Enzo Doria06/2014
64865*3^147324-870293Lelio R Paula04/2014
64872^233488-1306570287Enzo Doria11/2012
6488(3^147322+8)/4285170286Lelio R Paula06/2012
6489(22*10^70259+161)/370260Robert Price02/2017
64902^233388+46570257Lelio R Paula11/2012
649114^61299+5970257Lelio R Paula01/2015
64922^233383+9406570256Lelio R Paula04/2012
649349471!3-656170253Robert Price11/2015
64947^83121+6^(83121-1)70246Robert Price03/2016
6495(197*10^70241-11)/370243Robert Price10/2017
649623*10^70240-770242Robert Price03/2016
6497(71*10^70227-53)/970228Robert Price10/2015
6498(2^233247-9)/1770214Lelio R Paula05/2012
6499(11^67421-2^67421)/970211Robert Price01/2013
6500(23*10^70209-41)/970210Robert Price03/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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