PRP Records

Probable Primes Top 10000

(180278 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 ?
5751(16^60013-5^60013)/1172262Robert Price07/2013
57527^85507-3072262Lelio R Paula08/2014
5753(19*2^240026-1)/1572256Lelio R Paula02/2014
5754(3^151426-2)/66133772243Lelio R Paula06/2012
5755gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
57562^239863-11226772206Enzo Doria06/2014
57572^239853-11485372203Enzo Doria05/2015
5758(4*10^72174+149)/972174Robert Price03/2017
5760(2^239671+9)/29613172143Lelio R Paula05/2012
57592^239651-11066572143Enzo Doria05/2014
5761(29*2^239650-1)/330572140Lelio R Paula01/2014
5762241^30280+30280^24172128Norbert Schneider11/2014
5763(68*10^72120-23)/972121Robert Price10/2015
5764(9^75571+8^75571)/1772112Robert Price12/2012
5765(15*2^239530-1)/17372105Lelio R Paula01/2014
57662^239513-11251972101Enzo Doria06/2014
5767(10^72097+149)/372097Serge Batalov12/2014
57682^239442-655572080Lelio R Paula05/2012
57692*5^103106+372069Lelio R Paula10/2014
57702^239402-19772068Lelio R Paula02/2012
57712^239356-11187572054Enzo Doria05/2014
5772(38*10^72050-119)/972051Robert Price11/2016
57732^239339+1501572049Lelio R Paula01/2013
5774159^32728+272048Lelio R Paula05/2013
577515^61259-3872047Lelio R Paula01/2015
577692^36683-91^3668372038Robert Price08/2015
57772^239280+5461572031Lelio R Paula05/2012
5778(47*2^239267+1)/7772027Lelio R Paula04/2015
5779(85*10^72025-1)/372027Robert Price07/2017
57802^239236-9730572018Lelio R Paula05/2012
57812^239169+5971998Lelio R Paula02/2012
5782lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
5783(15*2^239171-1)/10630171994Lelio R Paula01/2014
5784(29^49211-1)/2871965Robert Price04/2012
5786L(344293)71953Renaud Lifchitz09/2003
5785V(344293)71953Serge Batalov03/2015
57876*10^71951+771952Dmitry Domanov11/2010
57883^150798+4071949Lelio R Paula01/2015
57892^238961+9571935Lelio R Paula02/2012
57902^238936-40771927Yves Minet02/2012
57912^238923-2863571923Lelio R Paula05/2012
579210^71910+2511971911Patrick De Geest05/2016
579310^71910-80171910Robert Price04/2016
57942^238845-11265171900Enzo Doria06/2014
57952^238792-11124571884Enzo Doria05/2014
57966*7^85059+571884Lelio R Paula10/2014
57972^238752-11058971872Enzo Doria05/2014
579812^66581+771853Lelio R Paula07/2014
5799(7*2^238691+1)/4122971850Lelio R Paula06/2012
58004*3^150568-571840Lelio R Paula04/2014
58016^92301+6771825Lelio R Paula01/2015
58022^238568+9876533171817Jason Earls01/2009
58032^238541-11272371808Enzo Doria06/2014
58042^238529-1594971805Enzo Doria04/2013
58059*5^102721-871800Lelio R Paula10/2014
58062^238494-16571794Lelio R Paula02/2012
58072^238389-11090571763Enzo Doria05/2014
5808(145*10^71760-1)/971762Serge Batalov12/2014
58097^84913+506271760Mike Oakes02/2010
5810(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
58112^238268-9730571726Lelio R Paula05/2012
5812gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
58132^238235-11324771716Enzo Doria07/2014
58142*12^66450-5^6645071712Mike Oakes11/2010
5815(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
58162^238199-11181771706Enzo Doria05/2014
5817lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
58182^238144+9876533171689Jason Earls01/2009
581918^57102-426571679Enzo Doria03/2013
5820(73*10^71670-1)/971671Robert Price01/2015
58212^238081+1155*23808171670Henri Lifchitz02/2005
58222^238067-11192571666Enzo Doria05/2014
582336^46030+3571637Norbert Schneider04/2014
58242^237905-9171617Lelio R Paula02/2012
5825(31*2^237902-1)/12371616Lelio R Paula01/2014
5826(15185*2^237866-1)/4396771605Lelio R Paula04/2015
5827(24737*2^237841+1)/2571601Lelio R Paula06/2014
58282^237846+129971599Lelio R Paula05/2012
58296^92004+19980171594Mike Oakes02/2011
5830159^32516+271581Lelio R Paula05/2013
58312^237781+85571580Lelio R Paula05/2012
58322^237720-407971561Yves Minet06/2011
58332^237698-11094571555Enzo Doria05/2014
58342^237695-11323971554Enzo Doria07/2014
58358*5^102362-971549Lelio R Paula10/2014
5836(4*10^71546-31)/971546Erik Branger05/2011
58372^237650+3771540Lelio R Paula02/2012
583818^56977-439171522Enzo Doria03/2013
5839(22699*2^237565+1)/413663771512Lelio R Paula06/2014
5840((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
5841(26*10^71503+7)/371504Erik Branger11/2013
5842(4*10^71498+173)/371499Robert Price01/2017
58433^149848+11071496Lelio R Paula11/2014
58442^237498+51371495Lelio R Paula05/2012
58452^237485+10771491Lelio R Paula02/2012
5846(2^237465+9)/241971481Lelio R Paula05/2012
58472^237439-11223771477Enzo Doria06/2014
58482^237407-978771467Lelio R Paula11/2009
58492^237383+7295371460Enzo Doria04/2016
585082^37337-81^3733771457Robert Price01/2015
5851(1017*2^237313-1)/1971441Lelio R Paula04/2015
58522^237311+19171438Lelio R Paula02/2012
58532^237280-5971429Lelio R Paula02/2012
585411^68564-9871403Lelio R Paula01/2015
58552^237173+7480171397Enzo Doria04/2016
585615^60697+5671386Lelio R Paula01/2015
58572^237118+17771380Lelio R Paula02/2012
58582^237110+6971378Lelio R Paula02/2012
585915^60690-5871377Lelio R Paula01/2015
5860(5*2^237125-1)/59985119171374Lelio R Paula01/2014
5861(3^149567+2)/53971359Lelio R Paula06/2012
5862(5*10^71357-143)/371358Robert Price04/2016
58632^237039-11462171356Enzo Doria05/2015
586412^66116-3771352Lelio R Paula02/2015
5865(3^149497+2^149497)/571328Jean-Louis Charton10/2010
58662^236941-6694571327Lelio R Paula05/2012
58672^236911-114771318Yves Minet10/2009
586865^39337+4271315Lelio R Paula01/2016
58696*10^71299+771300Dmitry Domanov11/2010
5870(25*2^236843+1)/375371295Lelio R Paula06/2012
587110^71291+1518771292Patrick De Geest03/2016
587310^71291-558730911971291Robert Price03/2015
587210^71291-27358171291Patrick De Geest03/2016
5874-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
5875(2^236738+9)/1371265Lelio R Paula05/2012
58765^101949+4271260Lelio R Paula07/2014
58775*10^71237+971238Dmitry Domanov11/2010
58782^236634-1602571234Enzo Doria04/2013
587971^38478+7071233Norbert Schneider12/2014
58809*7^84280+871226Lelio R Paula10/2014
5881(10^71223+59)/371223Serge Batalov12/2014
5882(15185*2^236569-1)/45371216Lelio R Paula04/2015
588351829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
58842^236528-17371203Lelio R Paula02/2012
58853*2^236511-571198Lelio R Paula04/2014
58862^236477-9971187Lelio R Paula02/2012
588711^68356-213071186Enzo Doria12/2012
588811^68355-312071185Enzo Doria12/2012
588936^45737-35^4573771181Robert Price10/2012
58902^236432+2571174Lelio R Paula02/2012
58915^101818-1280671168Enzo Doria02/2013
589265^39253+6271163Lelio R Paula01/2016
589339^44718+3871150Norbert Schneider05/2014
58942^236296-40771133Yves Minet02/2012
58952^236286-11771130Lelio R Paula02/2012
58962^236257-11119371121Enzo Doria05/2014
58977^84149-3671115Lelio R Paula08/2014
58982^236209-11212371106Enzo Doria06/2014
589918^56644-498571104Enzo Doria03/2013
590021^53753+271074Ray Chandler08/2011
59012^236081-11092371068Enzo Doria05/2014
5902(293*27^49642-1736)/1371058Curtis Bright05/2015
590365^39192+2271052Lelio R Paula01/2016
5904(439#+1)^397-439#^39771038Mike Oakes11/2010
59057^84050-271031Lelio R Paula09/2013
590620^54558-2370982Lelio R Paula01/2015
59072^235793-11255570981Enzo Doria06/2014
590849936!3-3^4993670981Robert Price08/2015
59092^235787-7879570979Lelio R Paula05/2012
5910Perrin(581132)70970Eric W. Weisstein02/2011
591114^61913-9770961Lelio R Paula01/2015
59132^235720+1632170959Yves Minet03/2010
59122^235718+1609570959Lelio R Paula05/2012
5914163841#+34993370957Nicolas PALAU11/2016
59152^235710+770956Lelio R Paula02/2012
59162^235635-11208770934Enzo Doria06/2014
59182^235575-196570916Lelio R Paula05/2012
59176^91133+10170916Lelio R Paula01/2015
5919(21181*2^235505+1)/370898Lelio R Paula06/2014
59205^101425+8470894Lelio R Paula07/2014
5921177^31536+270893Lelio R Paula05/2013
592243*71^38292+470891Serge Batalov03/2016
5923(29*2^235506-1)/11202978570888Lelio R Paula01/2014
592411^68045-153070862Enzo Doria12/2012
59255*10^70858+2170859Robert Price01/2017
59272^235326+370841Donovan Johnson02/2006
592634523!2+470841Robert Price02/2015
5928(31*2^235307+1)/370836Lelio R Paula06/2012
59292^235308+13570835Lelio R Paula02/2012
5930r(35414,90)*1000+91170831Patrick De Geest07/2004
59312^235274+15970825Lelio R Paula02/2012
59323^148409+7070810Lelio R Paula11/2014
5933(19*10^70794+17)/970795Robert Price03/2015
59342^235108-23270970775Paul Bourdelais03/2013
5935(2^235099-2^117550+1)/57077211/2006
593619^55325-670748Lelio R Paula08/2014
5937257^29356+29356^25770746Norbert Schneider10/2014
59382^234956+1171570729Lelio R Paula05/2012
5939(7*10^70727-43)/970727Robert Price10/2014
59402^234890-3034170709Enzo Doria11/2012
594117^57461+1470703Lelio R Paula01/2015
5942(9179*2^234834-1)/570696Lelio R Paula04/2015
5943123^33822-12270685Norbert Schneider01/2015
5944(21*2^234772-1)/209570672Lelio R Paula01/2014
5945(29*2^234686-1)/2114570645Lelio R Paula01/2014
5946(15*2^234688-1)/527814170643Lelio R Paula01/2014
59482^234655-6770639Lelio R Paula02/2012
5947(79*10^70638-61)/970639Robert Price10/2015
59492^234652-17370638Lelio R Paula02/2012
59502^234618-364570628Lelio R Paula05/2012
5951(2^234610-5)/1970624Lelio R Paula05/2012
59524*5^101038+970624Lelio R Paula10/2014
59532^234603+7196370623Enzo Doria04/2016
59542^234600-11312970622Enzo Doria07/2014
59562^234586+970618Lelio R Paula02/2012
59553^148008+2670618Robert Price11/2013
595765^38947+3270608Lelio R Paula01/2016
5958(2^234488-3)/1170587Lelio R Paula05/2012
5959(3*2^234451+1)/3570576Lelio R Paula08/2012
5960Phi(159495,10)70560Maksym Voznyy09/2015
59612^234383-403570557Lelio R Paula05/2012
59622^234315-11124170536Enzo Doria05/2014
596314^61526+9770517Lelio R Paula01/2015
5964(3*2^234170+1)/1370492Lelio R Paula08/2012
596551^41281-50^4128170491Robert Price02/2013
59662^234141-11212370484Enzo Doria06/2014
59672^234139+1228570483Lelio R Paula04/2012
59682^234133-316370482Yves Minet04/2009
59692^234115+8370476Lelio R Paula02/2012
59702^234114-159570476Lelio R Paula05/2012
597124^51061-23^5106170475Robert Price07/2012
597219471^16428-270467Faysal YAtim09/2005
59737^83381+1270466Robert Price01/2014
59742^234067-11142770462Enzo Doria05/2014
5975(266*10^70457+1)/370459Robert Price02/2016
5976(31*2^234041-1)/9770453Lelio R Paula01/2014
59772^234026+1290970449Lelio R Paula04/2012
59782^233965-1970431Lelio R Paula02/2012
5979(5*2^233932-1)/17970419Lelio R Paula01/2014
59802^233908-1710970414Enzo Doria05/2013
5981695^24772+24772^69570402Norbert Schneider09/2016
59823*5^100719-270401Lelio R Paula10/2014
59832^233829-11135570390Enzo Doria05/2014
5984(19775^16384+1)/270388Henri Lifchitz03/2007
59857*3^147519+870386Lelio R Paula04/2014
59865*7^83265+270368Lelio R Paula10/2014
5987(23*10^70363+97)/370364Robert Price02/2017
5988(23*2^233749-1)/3532570363Lelio R Paula01/2014
59895^100652-1391670353Enzo Doria02/2013
599045^42555-270353Lelio R Paula08/2013
59912^233661-6170339Lelio R Paula02/2012
59922^233523-11224970298Enzo Doria06/2014
59935*3^147324-870293Lelio R Paula04/2014
59942^233488-1306570287Enzo Doria11/2012
5995(3^147322+8)/4285170286Lelio R Paula06/2012
5996(22*10^70259+161)/370260Robert Price02/2017
59972^233388+46570257Lelio R Paula11/2012
599814^61299+5970257Lelio R Paula01/2015
59992^233383+9406570256Lelio R Paula04/2012
600049471!3-656170253Robert Price11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

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