PRP Records

Probable Primes Top 10000

(252932 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
700115105^17054+17054^1510571271Norbert Schneider08/2018
7002(2^236738+9)/1371265Lelio R Paula05/2012
70035^101949+4271260Lelio R Paula07/2014
70045*10^71237+971238Dmitry Domanov11/2010
70052^236634-1602571234Enzo Doria04/2013
700671^38478+7071233Norbert Schneider12/2014
70079*7^84280+871226Lelio R Paula10/2014
7008(10^71223+59)/371223Serge Batalov12/2014
7009(15185*2^236569-1)/45371216Lelio R Paula04/2015
701051829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
70112^236528-17371203Lelio R Paula02/2012
70123*2^236511-571198Lelio R Paula04/2014
70132^236477-9971187Lelio R Paula02/2012
701411^68356-213071186Enzo Doria12/2012
701515128^17031+17031^1512871186Norbert Schneider08/2018
701611^68355-312071185Enzo Doria12/2012
701736^45737-35^4573771181Robert Price10/2012
7018(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
70192^236432+2571174Lelio R Paula02/2012
70205^101818-1280671168Enzo Doria02/2013
7021(7*10^71166-457)/971166Robert Price09/2017
702265^39253+6271163Lelio R Paula01/2016
702339^44718+3871150Norbert Schneider05/2014
70242^236296-40771133Yves Minet02/2012
70252^236286-11771130Lelio R Paula02/2012
70262^236257-11119371121Enzo Doria05/2014
70277^84149-3671115Lelio R Paula08/2014
7028164176#-p(164176)71108Henri Lifchitz12/2018
70292^236209-11212371106Enzo Doria06/2014
703018^56644-498571104Enzo Doria03/2013
7031(46*10^71077+521)/971078Robert Price08/2017
703221^53753+271074Ray Chandler08/2011
7033(86*10^71068-311)/971069Robert Price10/2017
70342^236081-11092371068Enzo Doria05/2014
7035(293*27^49642-1736)/1371058Curtis Bright05/2015
703665^39192+2271052Lelio R Paula01/2016
7037(439#+1)^397-439#^39771038Mike Oakes11/2010
70387^84050-271031Lelio R Paula09/2013
703920^54558-2370982Lelio R Paula01/2015
70402^235793-11255570981Enzo Doria06/2014
704149936!3-3^4993670981Robert Price08/2015
70422^235787-7879570979Lelio R Paula05/2012
7043Perrin(581132)70970Eric W. Weisstein02/2011
704414^61913-9770961Lelio R Paula01/2015
70452^235720+1632170959Yves Minet03/2010
70462^235718+1609570959Lelio R Paula05/2012
7047163841#+34993370957Nicolas PALAU11/2016
70482^235710+770956Lelio R Paula02/2012
7049(175^31627+1)/17670939Eric Chen10/2017
70502^235635-11208770934Enzo Doria06/2014
7051153^32467+15270931Norbert Schneider11/2018
70532^235575-196570916Lelio R Paula05/2012
70526^91133+10170916Lelio R Paula01/2015
7054(21181*2^235505+1)/370898Lelio R Paula06/2014
7055(14*10^70896+211)/970897Robert Price11/2017
70565^101425+8470894Lelio R Paula07/2014
7057177^31536+270893Lelio R Paula05/2013
705843*71^38292+470891Serge Batalov03/2016
7059(29*2^235506-1)/11202978570888Lelio R Paula01/2014
706011^68045-153070862Enzo Doria12/2012
70615*10^70858+2170859Robert Price01/2017
70632^235326+370841Donovan Johnson02/2006
706234523!2+470841Robert Price02/2015
7064(31*2^235307+1)/370836Lelio R Paula06/2012
70652^235308+13570835Lelio R Paula02/2012
7066r(35414,90)*1000+91170831Patrick De Geest07/2004
70672^235274+15970825Lelio R Paula02/2012
70683^148409+7070810Lelio R Paula11/2014
7069(19*10^70794+17)/970795Robert Price03/2015
70702^235108-23270970775Paul Bourdelais03/2013
7071(2^235099-2^117550+1)/57077211/2006
707219^55325-670748Lelio R Paula08/2014
7073257^29356+29356^25770746Norbert Schneider10/2014
707422*10^70729+370731Robert Price10/2017
70752^234956+1171570729Lelio R Paula05/2012
7076(7*10^70727-43)/970727Robert Price10/2014
70772^234890-3034170709Enzo Doria11/2012
707817^57461+1470703Lelio R Paula01/2015
7079(9179*2^234834-1)/570696Lelio R Paula04/2015
70802*10^70688+5170689Robert Price10/2017
7081123^33822-12270685Norbert Schneider01/2015
70827*10^70680-9970681Robert Price11/2017
7083(21*2^234772-1)/209570672Lelio R Paula01/2014
7084(29*2^234686-1)/2114570645Lelio R Paula01/2014
7085(15*2^234688-1)/527814170643Lelio R Paula01/2014
70872^234655-6770639Lelio R Paula02/2012
7086(79*10^70638-61)/970639Robert Price10/2015
70882^234652-17370638Lelio R Paula02/2012
70892^234618-364570628Lelio R Paula05/2012
7090(2^234610-5)/1970624Lelio R Paula05/2012
70914*5^101038+970624Lelio R Paula10/2014
70922^234603+7196370623Enzo Doria04/2016
70932^234600-11312970622Enzo Doria07/2014
70952^234586+970618Lelio R Paula02/2012
70943^148008+2670618Robert Price11/2013
7096(7*10^70616-151)/970616Robert Price09/2017
709765^38947+3270608Lelio R Paula01/2016
7098(2^234488-3)/1170587Lelio R Paula05/2012
7099(3*2^234451+1)/3570576Lelio R Paula08/2012
7100Phi(159495,10)70560Maksym Voznyy09/2015
71012^234383-403570557Lelio R Paula05/2012
71022^234315-11124170536Enzo Doria05/2014
710314^61526+9770517Lelio R Paula01/2015
7104(3*2^234170+1)/1370492Lelio R Paula08/2012
710551^41281-50^4128170491Robert Price02/2013
71062^234141-11212370484Enzo Doria06/2014
71072^234139+1228570483Lelio R Paula04/2012
71082^234133-316370482Yves Minet04/2009
71092^234115+8370476Lelio R Paula02/2012
71102^234114-159570476Lelio R Paula05/2012
711124^51061-23^5106170475Robert Price07/2012
711219471^16428-270467Faysal YAtim09/2005
71137^83381+1270466Robert Price01/2014
71142^234067-11142770462Enzo Doria05/2014
7115(266*10^70457+1)/370459Robert Price02/2016
7116(31*2^234041-1)/9770453Lelio R Paula01/2014
71172^234026+1290970449Lelio R Paula04/2012
71182^233965-1970431Lelio R Paula02/2012
7119(5*2^233932-1)/17970419Lelio R Paula01/2014
71202^233908-1710970414Enzo Doria05/2013
7121695^24772+24772^69570402Norbert Schneider09/2016
71223*5^100719-270401Lelio R Paula10/2014
71232^233829-11135570390Enzo Doria05/2014
7124(19775^16384+1)/270388Henri Lifchitz03/2007
71257*3^147519+870386Lelio R Paula04/2014
7126141^32749-270385Lelio R Paula10/2017
71275*7^83265+270368Lelio R Paula10/2014
7128(23*10^70363+97)/370364Robert Price02/2017
7129(23*2^233749-1)/3532570363Lelio R Paula01/2014
71315^100652-1391670353Enzo Doria02/2013
713045^42555-270353Lelio R Paula08/2013
71322^233661-6170339Lelio R Paula02/2012
71332^233523-11224970298Enzo Doria06/2014
71345*3^147324-870293Lelio R Paula04/2014
71352^233488-1306570287Enzo Doria11/2012
7136(3^147322+8)/4285170286Lelio R Paula06/2012
7137(22*10^70259+161)/370260Robert Price02/2017
71392^233388+46570257Lelio R Paula11/2012
713814^61299+5970257Lelio R Paula01/2015
71402^233383+9406570256Lelio R Paula04/2012
714149471!3-656170253Robert Price11/2015
71427^83121+6^(83121-1)70246Robert Price03/2016
7143(197*10^70241-11)/370243Robert Price10/2017
714423*10^70240-770242Robert Price03/2016
7145(71*10^70227-53)/970228Robert Price10/2015
714610815^17408+17408^1081570225Norbert Schneider05/2019
7147(2^233247-9)/1770214Lelio R Paula05/2012
7148(11^67421-2^67421)/970211Robert Price01/2013
7149(23*10^70209-41)/970210Robert Price03/2015
7150(29*10^70194-11)/970195Robert Price04/2015
71513^147109+19670189Lelio R Paula05/2014
7152(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
71539^73538+8^(73538+1)70174Robert Price06/2016
71542*5^100391+770171Lelio R Paula10/2014
715599^35156-270159Lelio R Paula08/2013
7156(68*10^70148+7)/370150Robert Price03/2016
715711^67360-603070149Enzo Doria01/2013
7158(35*10^70130-377)/970131Robert Price12/2017
715949391!3+3^4939170128Robert Price09/2015
7160(229*10^70122-1)/370124Robert Price12/2016
71617^82975-9270123Lelio R Paula07/2014
716265^38670+5870106Lelio R Paula01/2016
7163105^34684+34684^10570103Serge Batalov05/2014
7164134^32955-13370099Norbert Schneider03/2015
71662^232836-22790370091Enzo Doria12/2012
71652^232837-185917370091Enzo Doria03/2016
71673*2^232820+570087Lelio R Paula04/2014
71692^232799+9019570080Lelio R Paula02/2013
71682^232799-11223770080Enzo Doria06/2014
71702^232759+26214570068Lelio R Paula04/2012
71713*2^232750+770066Lelio R Paula04/2014
717212^64918-1170059Lelio R Paula01/2015
71737^82899-1270058Lelio R Paula09/2013
7174(22*10^70051-13)/970052Robert Price03/2015
7175(2^232685-7)/251462570039Lelio R Paula04/2012
717618^55786-536370027Enzo Doria03/2013
7177(2^(77537*3+1)+243)/770023Kevin Acres11/2013
71782^232602+16970021Lelio R Paula02/2012
7179(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
71802^232580+7213370014Enzo Doria04/2016
71814*6^89958-770002Lelio R Paula09/2014
718210^70000+8048770001Milton L. Brown05/2006
718310^69999+13485770000Patrick De Geest02/2007
718810^70000-927370000Patrick De Geest08/2009
7187(79*10^69999-7)/970000Robert Price01/2015
7184((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
7185(2^756839/10^36014)%10^7000070000Michael Vang12/2016
7186(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
718910^69999-8825169999Patrick De Geest08/2009
71902^232507+108969992Lelio R Paula04/2012
7191(17*2^232445+1)/569974Lelio R Paula08/2012
7192(529^25693+1)/53069972Richard Fischer12/2017
71937^82778+4869956Lelio R Paula09/2013
71947*2^232381+369955Lelio R Paula04/2014
71952^232362-11054169948Enzo Doria05/2014
71962^232326-11239169938Enzo Doria06/2014
71973^146575+23669935Lelio R Paula09/2013
719830^47341-2969929Norbert Schneider02/2014
71995^100040-6869925Lelio R Paula09/2013
7200(35*10^69866-593)/969867Robert Price08/2017
72012^232045-1729569853Lelio R Paula04/2012
7202(2^231987+78557)/9569834Lelio R Paula05/2012
72032^231955+7424369826Yves Minet03/2011
72042^231946-1587369823Enzo Doria04/2013
720518^55618+9569816Lelio R Paula09/2013
72066^89712+5^(89712-1)69810Robert Price02/2016
72072^231870+13569800Lelio R Paula02/2012
7208(23*2^231827-1)/417969785Lelio R Paula01/2014
72092^231778+5461569773Lelio R Paula04/2012
7210(19*2^231780+1)/23569772Lelio R Paula08/2012
721114^60866+2769761Lelio R Paula09/2013
721213^62619-4469755Lelio R Paula09/2013
7213(2^231715-509203)/3569752Lelio R Paula05/2012
72142^231711-11046769752Enzo Doria05/2014
7215(19^54547+18^54547)/3769751Robert Price08/2013
7216(23*2^231697-1)/4569748Lelio R Paula01/2014
72172^231696-186149969748Enzo Doria03/2016
72182^231684-14769744Lelio R Paula02/2012
7219(23*2^231686-1)/118369743Lelio R Paula01/2014
72202^231591-47739769716Paul Bourdelais03/2013
722111^66916-42069686Enzo Doria08/2012
72225^99680-1370669674Enzo Doria02/2013
7223(8*10^69674-53)/969674Robert Price11/2014
7224(44*10^69663-413)/969664Robert Price10/2017
7225(77*10^69656-23)/969657Robert Price10/2015
72266^89509+13169652Lelio R Paula09/2013
7227(78557*2^231349+1)/3569647Lelio R Paula06/2014
7228(11*10^69645+19)/369646Robert Price03/2016
722911^66875-2869644Lelio R Paula09/2013
72302^231347+7148369643Enzo Doria04/2016
7231(14^60763+3^60763)/1769641Robert Price04/2013
7232(4*10^69626+173)/369627Robert Price01/2017
72332^231289+25569625Lelio R Paula04/2012
72342^231234-11291369609Enzo Doria06/2014
7235(265*10^69602-7)/369604Robert Price07/2016
72362^231182-11284169593Enzo Doria06/2014
7237(15*2^231129+1)/2369577Lelio R Paula08/2012
72383^145806-2869568Lelio R Paula09/2013
7239(265*10^69554-7)/369556Robert Price07/2016
72402^231052-11315969554Enzo Doria07/2014
7241(10^9+1)*(10^129+1)*(10^831+1)*(10^107199+1)/1001/(10^387+1)/(10^2493+1)/(10^35733+1)69552Makoto Kamada03/2019
724211^66784-869549Lelio R Paula09/2013
7243Phi(104409,10)/229699969546Maksym Voznyy07/2015
72442^231016-11052369543Enzo Doria05/2014
72452^231014+57729457569543Lelio R Paula02/2016
724614^60658+6769522Lelio R Paula09/2013
72475^99418+3669491Lelio R Paula06/2013
72487^82203-3069470Lelio R Paula09/2013
7249(63^38609-1)/6269469Paul Bourdelais08/2017
72505^99359-2^9936069449Mike Oakes12/2010


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!