PRP Records

Probable Primes Top 10000

(253466 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 ?
72512^235793-11255570981Enzo Doria06/2014
725249936!3-3^4993670981Robert Price08/2015
72532^235787-7879570979Lelio R Paula05/2012
7254Perrin(581132)70970Eric W. Weisstein02/2011
725514^61913-9770961Lelio R Paula01/2015
72562^235720+1632170959Yves Minet03/2010
72572^235718+1609570959Lelio R Paula05/2012
7258163841#+34993370957Nicolas PALAU11/2016
72592^235710+770956Lelio R Paula02/2012
7260(175^31627+1)/17670939Eric Chen10/2017
72612^235635-11208770934Enzo Doria06/2014
7262153^32467+15270931Norbert Schneider11/2018
72642^235575-196570916Lelio R Paula05/2012
72636^91133+10170916Lelio R Paula01/2015
7265(21181*2^235505+1)/370898Lelio R Paula06/2014
7266(14*10^70896+211)/970897Robert Price11/2017
72675^101425+8470894Lelio R Paula07/2014
7268177^31536+270893Lelio R Paula05/2013
726943*71^38292+470891Serge Batalov03/2016
7270(29*2^235506-1)/11202978570888Lelio R Paula01/2014
727111^68045-153070862Enzo Doria12/2012
72725*10^70858+2170859Robert Price01/2017
72742^235326+370841Donovan Johnson02/2006
727334523!2+470841Robert Price02/2015
7275(31*2^235307+1)/370836Lelio R Paula06/2012
72762^235308+13570835Lelio R Paula02/2012
7277r(35414,90)*1000+91170831Patrick De Geest07/2004
72782^235274+15970825Lelio R Paula02/2012
72793^148409+7070810Lelio R Paula11/2014
7280(19*10^70794+17)/970795Robert Price03/2015
72812^235108-23270970775Paul Bourdelais03/2013
7282(2^235099-2^117550+1)/57077211/2006
728319^55325-670748Lelio R Paula08/2014
7284257^29356+29356^25770746Norbert Schneider10/2014
728522*10^70729+370731Robert Price10/2017
72862^234956+1171570729Lelio R Paula05/2012
7287(7*10^70727-43)/970727Robert Price10/2014
72882^234890-3034170709Enzo Doria11/2012
728917^57461+1470703Lelio R Paula01/2015
7290(9179*2^234834-1)/570696Lelio R Paula04/2015
72912*10^70688+5170689Robert Price10/2017
7292123^33822-12270685Norbert Schneider01/2015
72937*10^70680-9970681Robert Price11/2017
7294(21*2^234772-1)/209570672Lelio R Paula01/2014
7295(29*2^234686-1)/2114570645Lelio R Paula01/2014
7296(15*2^234688-1)/527814170643Lelio R Paula01/2014
72982^234655-6770639Lelio R Paula02/2012
7297(79*10^70638-61)/970639Robert Price10/2015
72992^234652-17370638Lelio R Paula02/2012
73002^234618-364570628Lelio R Paula05/2012
7301(2^234610-5)/1970624Lelio R Paula05/2012
73024*5^101038+970624Lelio R Paula10/2014
73032^234603+7196370623Enzo Doria04/2016
73042^234600-11312970622Enzo Doria07/2014
73052^234586+970618Lelio R Paula02/2012
73063^148008+2670618Robert Price11/2013
7307(7*10^70616-151)/970616Robert Price09/2017
730865^38947+3270608Lelio R Paula01/2016
7309(2^234488-3)/1170587Lelio R Paula05/2012
7310(3*2^234451+1)/3570576Lelio R Paula08/2012
7311Phi(159495,10)70560Maksym Voznyy09/2015
73122^234383-403570557Lelio R Paula05/2012
73132^234315-11124170536Enzo Doria05/2014
731414^61526+9770517Lelio R Paula01/2015
7315(3*2^234170+1)/1370492Lelio R Paula08/2012
731651^41281-50^4128170491Robert Price02/2013
73172^234141-11212370484Enzo Doria06/2014
73182^234139+1228570483Lelio R Paula04/2012
73192^234133-316370482Yves Minet04/2009
73202^234115+8370476Lelio R Paula02/2012
73212^234114-159570476Lelio R Paula05/2012
732224^51061-23^5106170475Robert Price07/2012
732319471^16428-270467Faysal YAtim09/2005
73247^83381+1270466Robert Price01/2014
73252^234067-11142770462Enzo Doria05/2014
7326(266*10^70457+1)/370459Robert Price02/2016
7327(31*2^234041-1)/9770453Lelio R Paula01/2014
73282^234026+1290970449Lelio R Paula04/2012
73292^233965-1970431Lelio R Paula02/2012
7330(5*2^233932-1)/17970419Lelio R Paula01/2014
73312^233908-1710970414Enzo Doria05/2013
7332695^24772+24772^69570402Norbert Schneider09/2016
73333*5^100719-270401Lelio R Paula10/2014
73342^233829-11135570390Enzo Doria05/2014
7335(19775^16384+1)/270388Henri Lifchitz03/2007
73367*3^147519+870386Lelio R Paula04/2014
7337141^32749-270385Lelio R Paula10/2017
73385*7^83265+270368Lelio R Paula10/2014
7339(23*10^70363+97)/370364Robert Price02/2017
7340(23*2^233749-1)/3532570363Lelio R Paula01/2014
73425^100652-1391670353Enzo Doria02/2013
734145^42555-270353Lelio R Paula08/2013
73432^233661-6170339Lelio R Paula02/2012
73442^233523-11224970298Enzo Doria06/2014
73455*3^147324-870293Lelio R Paula04/2014
73462^233488-1306570287Enzo Doria11/2012
7347(3^147322+8)/4285170286Lelio R Paula06/2012
7348(22*10^70259+161)/370260Robert Price02/2017
73502^233388+46570257Lelio R Paula11/2012
734914^61299+5970257Lelio R Paula01/2015
73512^233383+9406570256Lelio R Paula04/2012
735249471!3-656170253Robert Price11/2015
73537^83121+6^(83121-1)70246Robert Price03/2016
7354(197*10^70241-11)/370243Robert Price10/2017
735523*10^70240-770242Robert Price03/2016
7356(71*10^70227-53)/970228Robert Price10/2015
735710815^17408+17408^1081570225Norbert Schneider05/2019
7358(2^233247-9)/1770214Lelio R Paula05/2012
7359(11^67421-2^67421)/970211Robert Price01/2013
7360(23*10^70209-41)/970210Robert Price03/2015
7361(29*10^70194-11)/970195Robert Price04/2015
73623^147109+19670189Lelio R Paula05/2014
7363(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
73649^73538+8^(73538+1)70174Robert Price06/2016
73652*5^100391+770171Lelio R Paula10/2014
736699^35156-270159Lelio R Paula08/2013
7367(68*10^70148+7)/370150Robert Price03/2016
736811^67360-603070149Enzo Doria01/2013
7369(35*10^70130-377)/970131Robert Price12/2017
737049391!3+3^4939170128Robert Price09/2015
7371(229*10^70122-1)/370124Robert Price12/2016
73727^82975-9270123Lelio R Paula07/2014
737365^38670+5870106Lelio R Paula01/2016
7374105^34684+34684^10570103Serge Batalov05/2014
7375134^32955-13370099Norbert Schneider03/2015
73772^232836-22790370091Enzo Doria12/2012
73762^232837-185917370091Enzo Doria03/2016
73783*2^232820+570087Lelio R Paula04/2014
73802^232799+9019570080Lelio R Paula02/2013
73792^232799-11223770080Enzo Doria06/2014
73812^232759+26214570068Lelio R Paula04/2012
73823*2^232750+770066Lelio R Paula04/2014
738312^64918-1170059Lelio R Paula01/2015
73847^82899-1270058Lelio R Paula09/2013
7385(22*10^70051-13)/970052Robert Price03/2015
7386(2^232685-7)/251462570039Lelio R Paula04/2012
738718^55786-536370027Enzo Doria03/2013
7388(2^(77537*3+1)+243)/770023Kevin Acres11/2013
73892^232602+16970021Lelio R Paula02/2012
7390(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
73912^232580+7213370014Enzo Doria04/2016
73924*6^89958-770002Lelio R Paula09/2014
739310^70000+8048770001Milton L. Brown05/2006
739410^69999+13485770000Patrick De Geest02/2007
739810^70000-927370000Patrick De Geest08/2009
7397(79*10^69999-7)/970000Robert Price01/2015
7399((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
7395(2^756839/10^36014)%10^7000070000Michael Vang12/2016
7396(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
740010^69999-8825169999Patrick De Geest08/2009
74012^232507+108969992Lelio R Paula04/2012
7402(17*2^232445+1)/569974Lelio R Paula08/2012
7403(529^25693+1)/53069972Richard Fischer12/2017
74047^82778+4869956Lelio R Paula09/2013
74057*2^232381+369955Lelio R Paula04/2014
74062^232362-11054169948Enzo Doria05/2014
74072^232326-11239169938Enzo Doria06/2014
74083^146575+23669935Lelio R Paula09/2013
740930^47341-2969929Norbert Schneider02/2014
74105^100040-6869925Lelio R Paula09/2013
74119946^17491+17491^994669923Norbert Schneider07/2019
7412(35*10^69866-593)/969867Robert Price08/2017
74132^232045-1729569853Lelio R Paula04/2012
7414(2^231987+78557)/9569834Lelio R Paula05/2012
74152^231955+7424369826Yves Minet03/2011
74162^231946-1587369823Enzo Doria04/2013
741718^55618+9569816Lelio R Paula09/2013
74186^89712+5^(89712-1)69810Robert Price02/2016
74192^231870+13569800Lelio R Paula02/2012
7420(23*2^231827-1)/417969785Lelio R Paula01/2014
74212^231778+5461569773Lelio R Paula04/2012
7422(19*2^231780+1)/23569772Lelio R Paula08/2012
742314^60866+2769761Lelio R Paula09/2013
742413^62619-4469755Lelio R Paula09/2013
7425(2^231715-509203)/3569752Lelio R Paula05/2012
74262^231711-11046769752Enzo Doria05/2014
7427(19^54547+18^54547)/3769751Robert Price08/2013
7428(23*2^231697-1)/4569748Lelio R Paula01/2014
74292^231696-186149969748Enzo Doria03/2016
74302^231684-14769744Lelio R Paula02/2012
7431(23*2^231686-1)/118369743Lelio R Paula01/2014
74322^231591-47739769716Paul Bourdelais03/2013
743311^66916-42069686Enzo Doria08/2012
74345^99680-1370669674Enzo Doria02/2013
7435(8*10^69674-53)/969674Robert Price11/2014
7436(44*10^69663-413)/969664Robert Price10/2017
7437(77*10^69656-23)/969657Robert Price10/2015
74386^89509+13169652Lelio R Paula09/2013
7439(78557*2^231349+1)/3569647Lelio R Paula06/2014
7440(11*10^69645+19)/369646Robert Price03/2016
744111^66875-2869644Lelio R Paula09/2013
74422^231347+7148369643Enzo Doria04/2016
7443(14^60763+3^60763)/1769641Robert Price04/2013
7444(4*10^69626+173)/369627Robert Price01/2017
74452^231289+25569625Lelio R Paula04/2012
74462^231234-11291369609Enzo Doria06/2014
7447(265*10^69602-7)/369604Robert Price07/2016
74482^231182-11284169593Enzo Doria06/2014
7449(15*2^231129+1)/2369577Lelio R Paula08/2012
74503^145806-2869568Lelio R Paula09/2013
7451(265*10^69554-7)/369556Robert Price07/2016
74522^231052-11315969554Enzo Doria07/2014
7453(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
745411^66784-869549Lelio R Paula09/2013
7455Phi(104409,10)/229699969546Maksym Voznyy07/2015
74562^231016-11052369543Enzo Doria05/2014
74572^231014+57729457569543Lelio R Paula02/2016
745814^60658+6769522Lelio R Paula09/2013
74595^99418+3669491Lelio R Paula06/2013
74607^82203-3069470Lelio R Paula09/2013
7461(63^38609-1)/6269469Paul Bourdelais08/2017
74625^99359-2^9936069449Mike Oakes12/2010
7463(29*2^230684+1)/139569442Lelio R Paula08/2012
7464(19*10^69424+77)/369425Robert Price08/2016
746519^54287-9669420Lelio R Paula09/2013
74662^230541+5890569400Lelio R Paula04/2012
74672^230506+1270569390Lelio R Paula02/2013
74688*6^89156-569378Lelio R Paula09/2014
74692^230438-11134769369Enzo Doria05/2014
74702^230428-9969366Lelio R Paula02/2012
7471(62^38699+1)/6369362Paul Bourdelais08/2017
74723*10^69354+1769355Robert Price03/2017
7473(493*10^69340-7)/969342Robert Price07/2016
7474(41*10^69321+373)/969322Robert Price04/2017
74756^89072+5369312Lelio R Paula09/2013
7476155^31639+269300Lelio R Paula05/2013
74773*7^81965-469269Lelio R Paula09/2014
7478(16*10^69265+41)/369266Robert Price10/2017
7479(86*10^69260-77)/969261Robert Price05/2016
74809*5^99087+469260Lelio R Paula09/2014
74813^145145+266069252Lelio R Paula09/2013
748311^66492-114069245Enzo Doria11/2012
74825*3^145129-469245Lelio R Paula04/2014
74847*3^145126+869244Lelio R Paula04/2014
748511^66480-237069232Enzo Doria12/2012
74862^229962-6569226Lelio R Paula02/2012
74872^229958-11073369225Enzo Doria05/2014
7488V(332407)69225Serge Batalov03/2015
74896^88959+769224Lelio R Paula09/2013
749015^58855-9469219Lelio R Paula09/2013
7491159773#-p(159773)69212Henri Lifchitz12/2018
7492(2^229838+47)/1208169185Lelio R Paula04/2012
74933^144952+9869160Lelio R Paula09/2013
74945^98941-7269157Lelio R Paula06/2013
7495(17*2^229604-1)/22969117Lelio R Paula01/2014
74962^229585-106369112Yves Minet11/2012
7497(13*2^229567-1)/1969107Lelio R Paula01/2014
7498(13*2^229393-1)/569055Lelio R Paula01/2014
7499(53*10^69050-17)/969051Robert Price09/2015
7500(43*10^69048+47)/969049Robert Price12/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2019 14:10 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!