PRP Records

Probable Primes Top 10000

(271023 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 ?
9501(2^235099-2^117550+1)/57077211/2006
950219^55325-670748Lelio R Paula08/2014
9503257^29356+29356^25770746Norbert Schneider10/2014
950422*10^70729+370731Robert Price10/2017
95052^234956+1171570729Lelio R Paula05/2012
9506(7*10^70727-43)/970727Robert Price10/2014
9507(2^234897+3906)/270711Stefano Morozzi01/2020
95082^234890-3034170709Enzo Doria11/2012
950917^57461+1470703Lelio R Paula01/2015
951018281^7366+7366^1828170697Hans Havermann09/2019
9511(9179*2^234834-1)/570696Lelio R Paula04/2015
95122*10^70688+5170689Robert Price10/2017
9513123^33822-12270685Norbert Schneider01/2015
95147*10^70680-9970681Robert Price11/2017
9515(2^234784+3646)/270677Stefano Morozzi01/2020
9516(21*2^234772-1)/209570672Lelio R Paula01/2014
9517(2^234762+1498)/270671Stefano Morozzi01/2020
9518(24355^16111-1)/2435470668Serge Batalov08/2020
9519(2^234723+3690)/270659Stefano Morozzi01/2020
9520(2^234718+3798)/270657Stefano Morozzi01/2020
9521(2^234680+2902)/270646Stefano Morozzi01/2020
9522(29*2^234686-1)/2114570645Lelio R Paula01/2014
9523(15*2^234688-1)/527814170643Lelio R Paula01/2014
95252^234655-6770639Lelio R Paula02/2012
9524(79*10^70638-61)/970639Robert Price10/2015
95262^234652-17370638Lelio R Paula02/2012
95272^234618-364570628Lelio R Paula05/2012
9528(2^234610-5)/1970624Lelio R Paula05/2012
95294*5^101038+970624Lelio R Paula10/2014
95302^234603+7196370623Enzo Doria04/2016
95312^234600-11312970622Enzo Doria07/2014
9532(2^234601+1446)/270622Stefano Morozzi01/2020
95332^234586+970618Lelio R Paula02/2012
95343^148008+2670618Robert Price11/2013
9535(7*10^70616-151)/970616Robert Price09/2017
953665^38947+3270608Lelio R Paula01/2016
9537(2^234517+2750)/270597Stefano Morozzi01/2020
953818363^6988+6988^1836370594Hans Havermann10/2019
9539(2^234488-3)/1170587Lelio R Paula05/2012
9540(3*2^234451+1)/3570576Lelio R Paula08/2012
9541(8848^17881-1)/884770570Serge Batalov08/2020
9542Phi(159495,10)70560Maksym Voznyy09/2015
95432^234383-403570557Lelio R Paula05/2012
9544(2^234364+3618)/270551Stefano Morozzi01/2020
9545(2^234333+3482)/270541Stefano Morozzi01/2020
95462^234315-11124170536Enzo Doria05/2014
954714^61526+9770517Lelio R Paula01/2015
954814742^16915+16915^1474270512Norbert Schneider10/2019
9549(2^234203+3306)/270502Stefano Morozzi01/2020
9550(3*2^234170+1)/1370492Lelio R Paula08/2012
955151^41281-50^4128170491Robert Price02/2013
95522^234141-11212370484Enzo Doria06/2014
95532^234139+1228570483Lelio R Paula04/2012
95542^234133-316370482Yves Minet04/2009
95552^234115+8370476Lelio R Paula02/2012
95562^234114-159570476Lelio R Paula05/2012
955724^51061-23^5106170475Robert Price07/2012
9558(2^234099+2538)/270471Stefano Morozzi01/2020
955919471^16428-270467Faysal YAtim09/2005
95607^83381+1270466Robert Price01/2014
9561(2^234080+3922)/270465Stefano Morozzi01/2020
95622^234067-11142770462Enzo Doria05/2014
9563(266*10^70457+1)/370459Robert Price02/2016
9564(31*2^234041-1)/9770453Lelio R Paula01/2014
9565(2^234030+642)/270450Stefano Morozzi01/2020
95662^234026+1290970449Lelio R Paula04/2012
9567(2^234021+3510)/270448Stefano Morozzi01/2020
95682^233965-1970431Lelio R Paula02/2012
9569(11152^17401-1)/1115170424Serge Batalov08/2020
9570(5*2^233932-1)/17970419Lelio R Paula01/2014
95712^233908-1710970414Enzo Doria05/2013
9572695^24772+24772^69570402Norbert Schneider09/2016
95733*5^100719-270401Lelio R Paula10/2014
9574(2^233862+1878)/270400Stefano Morozzi01/2020
9575(2^233843+3330)/270394Stefano Morozzi01/2020
95762^233829-11135570390Enzo Doria05/2014
9577(19775^16384+1)/270388Henri Lifchitz03/2007
95787*3^147519+870386Lelio R Paula04/2014
9579141^32749-270385Lelio R Paula10/2017
95805*7^83265+270368Lelio R Paula10/2014
9581(23*10^70363+97)/370364Robert Price02/2017
9582(23*2^233749-1)/3532570363Lelio R Paula01/2014
95835^100652-1391670353Enzo Doria02/2013
958445^42555-270353Lelio R Paula08/2013
9585(3084^20161-1)/308370341Serge Batalov08/2020
95862^233661-6170339Lelio R Paula02/2012
9587(2^233641+1014)/270333Stefano Morozzi01/2020
9588(2^233614+1074)/270325Stefano Morozzi01/2020
9589(2^233592+2986)/270318Stefano Morozzi01/2020
95902^233523-11224970298Enzo Doria06/2014
95915*3^147324-870293Lelio R Paula04/2014
95922^233488-1306570287Enzo Doria11/2012
9593(3^147322+8)/4285170286Lelio R Paula06/2012
9594(13301^17041-1)/1330070271Serge Batalov08/2020
9595(22*10^70259+161)/370260Robert Price02/2017
95972^233388+46570257Lelio R Paula11/2012
959614^61299+5970257Lelio R Paula01/2015
95982^233383+9406570256Lelio R Paula04/2012
959949471!3-656170253Robert Price11/2015
96007^83121+6^(83121-1)70246Robert Price03/2016
9601(197*10^70241-11)/370243Robert Price10/2017
960223*10^70240-770242Robert Price03/2016
9603(2^233301+2730)/270231Stefano Morozzi01/2020
9604(71*10^70227-53)/970228Robert Price10/2015
960519825^3486+3486^1982570227Hans Havermann10/2019
960610815^17408+17408^1081570225Norbert Schneider05/2019
9607(2^233247-9)/1770214Lelio R Paula05/2012
9608(11^67421-2^67421)/970211Robert Price01/2013
9609(23*10^70209-41)/970210Robert Price03/2015
9610(29*10^70194-11)/970195Robert Price04/2015
96113^147109+19670189Lelio R Paula05/2014
9612(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
96139^73538+8^(73538+1)70174Robert Price06/2016
96142*5^100391+770171Lelio R Paula10/2014
961599^35156-270159Lelio R Paula08/2013
9616(68*10^70148+7)/370150Robert Price03/2016
961711^67360-603070149Enzo Doria01/2013
9618(35*10^70130-377)/970131Robert Price12/2017
961949391!3+3^4939170128Robert Price09/2015
9620(229*10^70122-1)/370124Robert Price12/2016
96217^82975-9270123Lelio R Paula07/2014
9622(19099^16381-1)/1909870123Serge Batalov08/2020
962320294^2853+2853^2029470122Hans Havermann10/2019
962465^38670+5870106Lelio R Paula01/2016
9625105^34684+34684^10570103Serge Batalov05/2014
962618597^5882+5882^1859770102Hans Havermann10/2019
9627134^32955-13370099Norbert Schneider03/2015
96302^232836-22790370091Enzo Doria12/2012
96292^232837-185917370091Enzo Doria03/2016
962817778^8761+8761^1777870091Hans Havermann10/2019
96313*2^232820+570087Lelio R Paula04/2014
96332^232799+9019570080Lelio R Paula02/2013
96322^232799-11223770080Enzo Doria06/2014
963417894^8247+8247^1789470079Hans Havermann09/2019
9635(2^232766+954)/270070Stefano Morozzi01/2020
96362^232759+26214570068Lelio R Paula04/2012
963716817^14670+14670^1681770067Hans Havermann09/2019
96383*2^232750+770066Lelio R Paula04/2014
9639(7019^18217-1)/701870064Serge Batalov08/2020
9640(3330^19891-1)/332970062Serge Batalov08/2020
964112^64918-1170059Lelio R Paula01/2015
96427^82899-1270058Lelio R Paula09/2013
9643(22*10^70051-13)/970052Robert Price03/2015
964416428^16615-16615^1642870042Norbert Schneider11/2019
9645(2^232685-7)/251462570039Lelio R Paula04/2012
9646(2^232653+1494)/270036Stefano Morozzi01/2020
964718^55786-536370027Enzo Doria03/2013
9648(2^(77537*3+1)+243)/770023Kevin Acres11/2013
96492^232602+16970021Lelio R Paula02/2012
9650(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
96512^232580+7213370014Enzo Doria04/2016
9652(4095^19381-1)/409470006Serge Batalov08/2020
96534*6^89958-770002Lelio R Paula09/2014
965410^70000+8048770001Milton L. Brown05/2006
965510^69999+13485770000Patrick De Geest02/2007
965610^70000-927370000Patrick De Geest08/2009
9657(79*10^69999-7)/970000Robert Price01/2015
9658((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
9659(2^756839/10^36014)%10^7000070000Michael Vang12/2016
9660(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
966110^69999-8825169999Patrick De Geest08/2009
96622^232507+108969992Lelio R Paula04/2012
9663(2^232506+498)/269991Stefano Morozzi01/2020
9664(17*2^232445+1)/569974Lelio R Paula08/2012
9665(529^25693+1)/53069972Richard Fischer12/2017
9666(2^232416+498)/269964Stefano Morozzi01/2020
9667(2^232410+2794)/269963Stefano Morozzi01/2020
96687^82778+4869956Lelio R Paula09/2013
96707*2^232381+369955Lelio R Paula04/2014
966919305^4204+4204^1930569955Hans Havermann10/2019
96712^232362-11054169948Enzo Doria05/2014
967219442^3957+3957^1944269940Hans Havermann09/2019
96732^232326-11239169938Enzo Doria06/2014
96743^146575+23669935Lelio R Paula09/2013
967530^47341-2969929Norbert Schneider02/2014
9676(2^232294+1218)/269928Stefano Morozzi01/2020
96775^100040-6869925Lelio R Paula09/2013
96789946^17491+17491^994669923Norbert Schneider07/2019
967916351^16592-16592^1635169912Norbert Schneider11/2019
9680(2^232139+3746)/269881Stefano Morozzi01/2020
9681(2^232132+2566)/269879Stefano Morozzi01/2020
9682(35*10^69866-593)/969867Robert Price08/2017
96832^232045-1729569853Lelio R Paula04/2012
9684(2^231987+78557)/9569834Lelio R Paula05/2012
96852^231955+7424369826Yves Minet03/2011
9686(2^231949+3290)/269824Stefano Morozzi01/2020
96872^231946-1587369823Enzo Doria04/2013
968818^55618+9569816Lelio R Paula09/2013
96896^89712+5^(89712-1)69810Robert Price02/2016
9690(2^231876+670)/269802Stefano Morozzi01/2020
96912^231870+13569800Lelio R Paula02/2012
9692(23*2^231827-1)/417969785Lelio R Paula01/2014
96932^231778+5461569773Lelio R Paula04/2012
9694(19*2^231780+1)/23569772Lelio R Paula08/2012
9695(2^231775+2430)/269771Stefano Morozzi01/2020
9696(381^27031-1)/38069763Serge Batalov08/2020
969714^60866+2769761Lelio R Paula09/2013
969813^62619-4469755Lelio R Paula09/2013
9699(2^231715-509203)/3569752Lelio R Paula05/2012
97002^231711-11046769752Enzo Doria05/2014
9702(19^54547+18^54547)/3769751Robert Price08/2013
9701(2^231707+998)/269751Stefano Morozzi01/2020
9703(3823^19471-1)/382269750Serge Batalov08/2020
9704(23*2^231697-1)/4569748Lelio R Paula01/2014
97052^231696-186149969748Enzo Doria03/2016
97062^231684-14769744Lelio R Paula02/2012
9707(23*2^231686-1)/118369743Lelio R Paula01/2014
97084*10^69723-9369724Robert Price07/2020
97092^231591-47739769716Paul Bourdelais03/2013
971016916^13209+13209^1691669709Hans Havermann09/2019
971116568^16095+16095^1656869697Hans Havermann09/2019
971211^66916-42069686Enzo Doria08/2012
97135^99680-1370669674Enzo Doria02/2013
9714(8*10^69674-53)/969674Robert Price11/2014
9715(44*10^69663-413)/969664Robert Price10/2017
971618950^4743+4743^1895069662Hans Havermann10/2019
9717(77*10^69656-23)/969657Robert Price10/2015
9718(2^231385+3710)/269654Stefano Morozzi01/2020
97196^89509+13169652Lelio R Paula09/2013
9720(2^231364+3030)/269648Stefano Morozzi01/2020
9721(78557*2^231349+1)/3569647Lelio R Paula06/2014
9722(11*10^69645+19)/369646Robert Price03/2016
972311^66875-2869644Lelio R Paula09/2013
97242^231347+7148369643Enzo Doria04/2016
9725(14^60763+3^60763)/1769641Robert Price04/2013
9726(2^231340+3126)/269640Stefano Morozzi01/2020
9727(4*10^69626+173)/369627Robert Price01/2017
97282^231289+25569625Lelio R Paula04/2012
9729(7155^18061-1)/715469615Serge Batalov08/2020
973019794^3287+3287^1979469612Hans Havermann09/2019
97312^231234-11291369609Enzo Doria06/2014
9732(265*10^69602-7)/369604Robert Price07/2016
97332^231182-11284169593Enzo Doria06/2014
9734(15*2^231129+1)/2369577Lelio R Paula08/2012
97353^145806-2869568Lelio R Paula09/2013
9736(265*10^69554-7)/369556Robert Price07/2016
97372^231052-11315969554Enzo Doria07/2014
9738(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
973911^66784-869549Lelio R Paula09/2013
9740Phi(104409,10)/229699969546Maksym Voznyy07/2015
9741(2^231023+1758)/269545Stefano Morozzi01/2020
97422^231016-11052369543Enzo Doria05/2014
97432^231014+57729457569543Lelio R Paula02/2016
9744(2^230982+970)/269533Stefano Morozzi01/2020
974514^60658+6769522Lelio R Paula09/2013
9746(2^230898+2422)/269507Stefano Morozzi01/2020
97475^99418+3669491Lelio R Paula06/2013
9748(5596^18541-1)/559569486Serge Batalov08/2020
97497^82203-3069470Lelio R Paula09/2013
9750(63^38609-1)/6269469Paul Bourdelais08/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 00:02 (Time in France)

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