PRP Records

Probable Primes Top 10000

(224926 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 (> 30000) Who ? When ?
650136^46030+3571637Norbert Schneider04/2014
6502(74*10^71621+313)/971622Robert Price11/2017
65032^237905-9171617Lelio R Paula02/2012
6504(31*2^237902-1)/12371616Lelio R Paula01/2014
6505(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6506(24737*2^237841+1)/2571601Lelio R Paula06/2014
65072^237846+129971599Lelio R Paula05/2012
65086^92004+19980171594Mike Oakes02/2011
6509159^32516+271581Lelio R Paula05/2013
65102^237781+85571580Lelio R Paula05/2012
65112^237720-407971561Yves Minet06/2011
65122^237698-11094571555Enzo Doria05/2014
65132^237695-11323971554Enzo Doria07/2014
65148*5^102362-971549Lelio R Paula10/2014
6515(4*10^71546-31)/971546Erik Branger05/2011
65162^237650+3771540Lelio R Paula02/2012
651718^56977-439171522Enzo Doria03/2013
6519(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6518((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
6520(26*10^71503+7)/371504Erik Branger11/2013
6521(4*10^71498+173)/371499Robert Price01/2017
65223^149848+11071496Lelio R Paula11/2014
65232^237498+51371495Lelio R Paula05/2012
65242^237485+10771491Lelio R Paula02/2012
6525(2^237465+9)/241971481Lelio R Paula05/2012
65262^237439-11223771477Enzo Doria06/2014
65272^237407-978771467Lelio R Paula11/2009
65282^237383+7295371460Enzo Doria04/2016
652982^37337-81^3733771457Robert Price01/2015
6530(1017*2^237313-1)/1971441Lelio R Paula04/2015
65312^237311+19171438Lelio R Paula02/2012
65322^237280-5971429Lelio R Paula02/2012
653311^68564-9871403Lelio R Paula01/2015
65342^237173+7480171397Enzo Doria04/2016
653515^60697+5671386Lelio R Paula01/2015
65362^237118+17771380Lelio R Paula02/2012
65372^237110+6971378Lelio R Paula02/2012
653815^60690-5871377Lelio R Paula01/2015
6539(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6540(3^149567+2)/53971359Lelio R Paula06/2012
6541(5*10^71357-143)/371358Robert Price04/2016
65422^237039-11462171356Enzo Doria05/2015
654312^66116-3771352Lelio R Paula02/2015
6544(3^149497+2^149497)/571328Jean-Louis Charton10/2010
65452^236941-6694571327Lelio R Paula05/2012
65462^236911-114771318Yves Minet10/2009
654765^39337+4271315Lelio R Paula01/2016
65486*10^71299+771300Dmitry Domanov11/2010
6549(25*2^236843+1)/375371295Lelio R Paula06/2012
655010^71291+1518771292Patrick De Geest03/2016
655210^71291-558730911971291Robert Price03/2015
655110^71291-27358171291Patrick De Geest03/2016
6553-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
655415105^17054+17054^1510571271Norbert Schneider08/2018
6555(2^236738+9)/1371265Lelio R Paula05/2012
65565^101949+4271260Lelio R Paula07/2014
65575*10^71237+971238Dmitry Domanov11/2010
65582^236634-1602571234Enzo Doria04/2013
655971^38478+7071233Norbert Schneider12/2014
65609*7^84280+871226Lelio R Paula10/2014
6561(10^71223+59)/371223Serge Batalov12/2014
6562(15185*2^236569-1)/45371216Lelio R Paula04/2015
656351829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
65642^236528-17371203Lelio R Paula02/2012
65653*2^236511-571198Lelio R Paula04/2014
65662^236477-9971187Lelio R Paula02/2012
656711^68356-213071186Enzo Doria12/2012
656815128^17031+17031^1512871186Norbert Schneider08/2018
656911^68355-312071185Enzo Doria12/2012
657036^45737-35^4573771181Robert Price10/2012
6571(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
65722^236432+2571174Lelio R Paula02/2012
65735^101818-1280671168Enzo Doria02/2013
6574(7*10^71166-457)/971166Robert Price09/2017
657565^39253+6271163Lelio R Paula01/2016
657639^44718+3871150Norbert Schneider05/2014
65772^236296-40771133Yves Minet02/2012
65782^236286-11771130Lelio R Paula02/2012
65792^236257-11119371121Enzo Doria05/2014
65807^84149-3671115Lelio R Paula08/2014
65812^236209-11212371106Enzo Doria06/2014
658218^56644-498571104Enzo Doria03/2013
6583(46*10^71077+521)/971078Robert Price08/2017
658421^53753+271074Ray Chandler08/2011
6585(86*10^71068-311)/971069Robert Price10/2017
65862^236081-11092371068Enzo Doria05/2014
6587(293*27^49642-1736)/1371058Curtis Bright05/2015
658865^39192+2271052Lelio R Paula01/2016
6589(439#+1)^397-439#^39771038Mike Oakes11/2010
65907^84050-271031Lelio R Paula09/2013
659120^54558-2370982Lelio R Paula01/2015
65922^235793-11255570981Enzo Doria06/2014
659349936!3-3^4993670981Robert Price08/2015
65942^235787-7879570979Lelio R Paula05/2012
6595Perrin(581132)70970Eric W. Weisstein02/2011
659614^61913-9770961Lelio R Paula01/2015
65972^235720+1632170959Yves Minet03/2010
65982^235718+1609570959Lelio R Paula05/2012
6599163841#+34993370957Nicolas PALAU11/2016
66002^235710+770956Lelio R Paula02/2012
6601(175^31627+1)/17670939Eric Chen10/2017
66022^235635-11208770934Enzo Doria06/2014
66042^235575-196570916Lelio R Paula05/2012
66036^91133+10170916Lelio R Paula01/2015
6605(21181*2^235505+1)/370898Lelio R Paula06/2014
6606(14*10^70896+211)/970897Robert Price11/2017
66075^101425+8470894Lelio R Paula07/2014
6608177^31536+270893Lelio R Paula05/2013
660943*71^38292+470891Serge Batalov03/2016
6610(29*2^235506-1)/11202978570888Lelio R Paula01/2014
661111^68045-153070862Enzo Doria12/2012
66125*10^70858+2170859Robert Price01/2017
66132^235326+370841Donovan Johnson02/2006
661434523!2+470841Robert Price02/2015
6615(31*2^235307+1)/370836Lelio R Paula06/2012
66162^235308+13570835Lelio R Paula02/2012
6617r(35414,90)*1000+91170831Patrick De Geest07/2004
66182^235274+15970825Lelio R Paula02/2012
66193^148409+7070810Lelio R Paula11/2014
6620(19*10^70794+17)/970795Robert Price03/2015
66212^235108-23270970775Paul Bourdelais03/2013
6622(2^235099-2^117550+1)/57077211/2006
662319^55325-670748Lelio R Paula08/2014
6624257^29356+29356^25770746Norbert Schneider10/2014
662522*10^70729+370731Robert Price10/2017
66262^234956+1171570729Lelio R Paula05/2012
6627(7*10^70727-43)/970727Robert Price10/2014
66282^234890-3034170709Enzo Doria11/2012
662917^57461+1470703Lelio R Paula01/2015
6630(9179*2^234834-1)/570696Lelio R Paula04/2015
66312*10^70688+5170689Robert Price10/2017
6632123^33822-12270685Norbert Schneider01/2015
66337*10^70680-9970681Robert Price11/2017
6634(21*2^234772-1)/209570672Lelio R Paula01/2014
6635(29*2^234686-1)/2114570645Lelio R Paula01/2014
6636(15*2^234688-1)/527814170643Lelio R Paula01/2014
66382^234655-6770639Lelio R Paula02/2012
6637(79*10^70638-61)/970639Robert Price10/2015
66392^234652-17370638Lelio R Paula02/2012
66402^234618-364570628Lelio R Paula05/2012
6641(2^234610-5)/1970624Lelio R Paula05/2012
66424*5^101038+970624Lelio R Paula10/2014
66432^234603+7196370623Enzo Doria04/2016
66442^234600-11312970622Enzo Doria07/2014
66452^234586+970618Lelio R Paula02/2012
66463^148008+2670618Robert Price11/2013
6647(7*10^70616-151)/970616Robert Price09/2017
664865^38947+3270608Lelio R Paula01/2016
6649(2^234488-3)/1170587Lelio R Paula05/2012
6650(3*2^234451+1)/3570576Lelio R Paula08/2012
6651Phi(159495,10)70560Maksym Voznyy09/2015
66522^234383-403570557Lelio R Paula05/2012
66532^234315-11124170536Enzo Doria05/2014
665414^61526+9770517Lelio R Paula01/2015
6655(3*2^234170+1)/1370492Lelio R Paula08/2012
665651^41281-50^4128170491Robert Price02/2013
66572^234141-11212370484Enzo Doria06/2014
66582^234139+1228570483Lelio R Paula04/2012
66592^234133-316370482Yves Minet04/2009
66602^234115+8370476Lelio R Paula02/2012
66612^234114-159570476Lelio R Paula05/2012
666224^51061-23^5106170475Robert Price07/2012
666319471^16428-270467Faysal YAtim09/2005
66647^83381+1270466Robert Price01/2014
66652^234067-11142770462Enzo Doria05/2014
6666(266*10^70457+1)/370459Robert Price02/2016
6667(31*2^234041-1)/9770453Lelio R Paula01/2014
66682^234026+1290970449Lelio R Paula04/2012
66692^233965-1970431Lelio R Paula02/2012
6670(5*2^233932-1)/17970419Lelio R Paula01/2014
66712^233908-1710970414Enzo Doria05/2013
6672695^24772+24772^69570402Norbert Schneider09/2016
66733*5^100719-270401Lelio R Paula10/2014
66742^233829-11135570390Enzo Doria05/2014
6675(19775^16384+1)/270388Henri Lifchitz03/2007
66767*3^147519+870386Lelio R Paula04/2014
6677141^32749-270385Lelio R Paula10/2017
66785*7^83265+270368Lelio R Paula10/2014
6679(23*10^70363+97)/370364Robert Price02/2017
6680(23*2^233749-1)/3532570363Lelio R Paula01/2014
66815^100652-1391670353Enzo Doria02/2013
668245^42555-270353Lelio R Paula08/2013
66832^233661-6170339Lelio R Paula02/2012
66842^233523-11224970298Enzo Doria06/2014
66855*3^147324-870293Lelio R Paula04/2014
66862^233488-1306570287Enzo Doria11/2012
6687(3^147322+8)/4285170286Lelio R Paula06/2012
6688(22*10^70259+161)/370260Robert Price02/2017
66892^233388+46570257Lelio R Paula11/2012
669014^61299+5970257Lelio R Paula01/2015
66912^233383+9406570256Lelio R Paula04/2012
669249471!3-656170253Robert Price11/2015
66937^83121+6^(83121-1)70246Robert Price03/2016
6694(197*10^70241-11)/370243Robert Price10/2017
669523*10^70240-770242Robert Price03/2016
6696(71*10^70227-53)/970228Robert Price10/2015
6697(2^233247-9)/1770214Lelio R Paula05/2012
6698(11^67421-2^67421)/970211Robert Price01/2013
6699(23*10^70209-41)/970210Robert Price03/2015
6700(29*10^70194-11)/970195Robert Price04/2015
67013^147109+19670189Lelio R Paula05/2014
6702(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
67039^73538+8^(73538+1)70174Robert Price06/2016
67042*5^100391+770171Lelio R Paula10/2014
670599^35156-270159Lelio R Paula08/2013
6706(68*10^70148+7)/370150Robert Price03/2016
670711^67360-603070149Enzo Doria01/2013
6708(35*10^70130-377)/970131Robert Price12/2017
670949391!3+3^4939170128Robert Price09/2015
6710(229*10^70122-1)/370124Robert Price12/2016
67117^82975-9270123Lelio R Paula07/2014
671265^38670+5870106Lelio R Paula01/2016
6713105^34684+34684^10570103Serge Batalov05/2014
6714134^32955-13370099Norbert Schneider03/2015
67152^232836-22790370091Enzo Doria12/2012
67162^232837-185917370091Enzo Doria03/2016
67173*2^232820+570087Lelio R Paula04/2014
67192^232799+9019570080Lelio R Paula02/2013
67182^232799-11223770080Enzo Doria06/2014
67202^232759+26214570068Lelio R Paula04/2012
67213*2^232750+770066Lelio R Paula04/2014
672212^64918-1170059Lelio R Paula01/2015
67237^82899-1270058Lelio R Paula09/2013
6724(22*10^70051-13)/970052Robert Price03/2015
6725(2^232685-7)/251462570039Lelio R Paula04/2012
672618^55786-536370027Enzo Doria03/2013
6727(2^(77537*3+1)+243)/770023Kevin Acres11/2013
67282^232602+16970021Lelio R Paula02/2012
6729(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
67302^232580+7213370014Enzo Doria04/2016
67314*6^89958-770002Lelio R Paula09/2014
673210^70000+8048770001Milton L. Brown05/2006
673310^69999+13485770000Patrick De Geest02/2007
673810^70000-927370000Patrick De Geest08/2009
6737(79*10^69999-7)/970000Robert Price01/2015
6734((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
6735(2^756839/10^36014)%10^7000070000Michael Vang12/2016
6736(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
673910^69999-8825169999Patrick De Geest08/2009
67402^232507+108969992Lelio R Paula04/2012
6741(17*2^232445+1)/569974Lelio R Paula08/2012
6742(529^25693+1)/53069972Richard Fischer12/2017
67437^82778+4869956Lelio R Paula09/2013
67447*2^232381+369955Lelio R Paula04/2014
67452^232362-11054169948Enzo Doria05/2014
67462^232326-11239169938Enzo Doria06/2014
67473^146575+23669935Lelio R Paula09/2013
674830^47341-2969929Norbert Schneider02/2014
67495^100040-6869925Lelio R Paula09/2013
6750(35*10^69866-593)/969867Robert Price08/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 18 2018 22:22 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!