PRP Records

Probable Primes Top 10000

(255244 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 ?
6251(38*10^80150-11)/980151Robert Price05/2015
6252(598*10^80149-31)/980151Robert Price02/2017
625319^62678-8080150Lelio R Paula12/2015
625410^80139+3234380140Patrick De Geest02/2011
625510^80139-980139Alexander Gramolin01/2011
62563^167955-10680135Lelio R Paula12/2015
6257(197*10^80089-11)/380091Robert Price10/2017
62582^265998+7555980074Enzo Doria04/2016
62592^265969-10980180065Enzo Doria04/2014
62602^265888-11275780041Enzo Doria06/2014
62612^265809+170180017Lelio R Paula07/2013
6262gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
62633^167687-10480008Lelio R Paula02/2015
626411^76826-579080007Enzo Doria01/2013
626510^80000+8573180001Patrick De Geest10/2009
626610^80000-716980000Patrick De Geest09/2009
626710^79999+2239980000Patrick De Geest09/2009
626810^79999-7487379999Patrick De Geest09/2009
62693^167668+5879998Lelio R Paula02/2015
6270155^36506-279961Lelio R Paula10/2017
62712^265612+425779958Lelio R Paula07/2013
62725*3^167577+479956Lelio R Paula06/2014
6273(9179*2^265593-1)/979955Lelio R Paula04/2015
62746^102723-4379935Lelio R Paula04/2015
627511^76748-336079925Enzo Doria12/2012
6276(13*2^265498-1)/18711979919Lelio R Paula02/2014
62772^265399-10985579894Enzo Doria04/2014
6278(20^61403-1)/1979886Paul Bourdelais03/2010
627918^63635+5979880Lelio R Paula02/2015
6280(11*10^79867-107)/379868Robert Price11/2016
62813^167375+8079859Lelio R Paula02/2015
62825^114240-1448679851Enzo Doria02/2013
628349^47238+4879842Norbert Schneider07/2014
62842^265212-377979837Yves Minet04/2017
628591^40746+40746^9179824Norbert Schneider12/2014
6286(68*10^79813-257)/979814Robert Price06/2017
6287(5*2^265118-1)/6179808Lelio R Paula02/2014
62882^265074+2842579796Lelio R Paula07/2013
62892^265072+118579795Lelio R Paula07/2013
6290p(16682)#/2-12879771Robert Price05/2017
62913^167167-3479759Robert Price11/2013
629212^73906+2979758Lelio R Paula02/2015
62932^264934+25579754Lelio R Paula07/2013
62944*10^79729-8779730Robert Price03/2017
62952^264846-11170179727Enzo Doria05/2014
62962^264831-11204179723Enzo Doria06/2014
62972^264816-45579718Yves Minet03/2012
6298(55*10^79711+89)/979712Robert Price09/2017
629947^47667-4679704Theodore Burton02/2007
630013^71547+9679700Lelio R Paula03/2015
63012^264752-11288379699Enzo Doria06/2014
63022^264732+13379693Lelio R Paula05/2012
63038*3^167010+779685Lelio R Paula06/2014
630442^49087-4179681Norbert Schneider06/2014
6305(26*10^79678-119)/379679Robert Price07/2016
63062^264683-2179678Lelio R Paula05/2012
63077^94279+1879675Lelio R Paula02/2015
63082^264655-12779670Lelio R Paula02/2012
63092^264597-45904379652Enzo Doria05/2015
6310(21*2^264566+1)/579643Lelio R Paula10/2012
63112^264536+187002179634Enzo Doria05/2016
6312(17*2^264512-1)/35979625Lelio R Paula02/2014
63132^264477-10978379616Enzo Doria04/2014
631418^63419-133379609Enzo Doria03/2013
631513^71451-3679593Lelio R Paula03/2015
6316(2^264410-5)/12800260912179585Lelio R Paula10/2012
631719^62234+9079582Lelio R Paula03/2015
631812^73714+4979551Lelio R Paula02/2015
6319(3*2^264184-1)/143333979522Lelio R Paula02/2014
63202^264103-11253179503Enzo Doria06/2014
632119^62170+7879501Lelio R Paula03/2015
632211^76340-258079500Enzo Doria12/2012
6323(23*10^79492-11)/379493Robert Price10/2015
6324((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
63252^264060-11213379490Enzo Doria06/2014
6326((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
63279^83298+6^83298-2^8329879487Mike Oakes08/2010
632818^63319+3579483Lelio R Paula02/2015
632938303!2+25679461Robert Price01/2015
6330(29*10^79445+61)/979446Robert Price04/2015
63312^263902-19579443Lelio R Paula05/2012
63323^166499-11269679441Enzo Doria06/2014
633311^76279-276079437Enzo Doria12/2012
63346^102077-2579432Lelio R Paula03/2015
63352^263852-101779428Lelio R Paula07/2013
63362^263842-3379425Lelio R Paula05/2012
633712^73584-5579411Lelio R Paula02/2015
63382^263772-18579404Lelio R Paula05/2012
6339(15^67489+1)/1679373Paul Bourdelais03/2010
63402^263664+1501579371Lelio R Paula07/2013
634110^79362+3^7936379363Mike Oakes06/2010
6342Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
63433^166262+4479328Lelio R Paula02/2015
63444*10^79327-6379328Robert Price12/2016
63452^263486+51379318Lelio R Paula07/2013
63462^263448-51950979306Paul Bourdelais03/2013
634769153^16384+279296Matt Stath01/2019
634821^59971-20^5997179295Robert Price05/2012
63492^263372+12379283Lelio R Paula05/2012
635017^64429+8479277Lelio R Paula03/2015
635111^76124-1143079275Enzo Doria12/2012
6352(206*10^79268-17)/979270Robert Price03/2017
635313^71157+1879265Lelio R Paula03/2015
63542^263297+6583579261Lelio R Paula07/2013
635519^61980-1879258Theodore Burton12/2005
63562*10^79242+9379243Robert Price07/2016
6357(88^40751-1)/8779238Paul Bourdelais08/2017
6358(103*29^54179-39)/479233Curtis Bright05/2015
63599^83024-83024^979226Norbert Schneider08/2017
636017^64382-2679219Lelio R Paula03/2015
63617^93733-7479214Lelio R Paula02/2015
636215^67352+3879213Lelio R Paula02/2015
63632^263135-11023579212Enzo Doria05/2014
63642^263044+425779185Lelio R Paula07/2013
63652^263032+8751779181Yves Minet11/2010
63666^101755+9579181Lelio R Paula03/2015
63674^131497-3^13149779170Jean-Louis Charton05/2004
63685*7^93674+879165Lelio R Paula10/2014
6369lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
6370260^32768+179^3276879134Serge Batalov03/2018
637111^75978-4279123Lelio R Paula02/2015
63728*5^113180+979111Lelio R Paula10/2014
6373(6883*2^262741-1)/483579094Lelio R Paula04/2015
6374(9*2^262745+1)/13779093Lelio R Paula10/2012
637512^73285+8579088Lelio R Paula02/2015
637619^61840+5279079Lelio R Paula03/2015
6377(10^79067+77)/379067Robert Price01/2017
6378(1017*2^262640-1)/1155779062Lelio R Paula04/2015
637910^79040+13794979041Patrick De Geest02/2016
638110^79040-100729779040Robert Price02/2015
638010^79040-7742779040Patrick De Geest02/2016
63822^262551-1729579036Lelio R Paula07/2013
63833^165597+34079010Lelio R Paula02/2015
6384(23*2^262435+1)/5579001Lelio R Paula10/2012
638511^75860-210079001Enzo Doria12/2012
63868*7^93463+978987Lelio R Paula10/2014
638767^43240-278960Lelio R Paula09/2013
63881000001^13159-1000000^1315978953Jean-Louis Charton10/2003
63892^262199-11028778930Enzo Doria05/2014
6390(19*2^262180-1)/17778924Lelio R Paula02/2014
6391(3^165403+4)/778917Lelio R Paula10/2012
63922^21068*(2^241076+1)-178914Makoto Morimoto03/2014
63932^29258*(2^232886+1)-178914Makoto Morimoto03/2014
63942^262144+1853178914Makoto Morimoto12/2015
6395(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
6396(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
639714^68837+7578897Lelio R Paula02/2015
6398106^38949+10578884Norbert Schneider12/2016
6399(70^42737+1)/7178853Paul Bourdelais08/2017
6400(25*2^261917-1)/2092778842Lelio R Paula02/2014
64012^261881-185971378835Enzo Doria03/2016
64022^261874+191578832Lelio R Paula07/2013
64032^261856+9876533178827Jason Earls01/2009
6404(5*2^261857-1)/2050127778821Lelio R Paula02/2014
64052^261724+9269178787Tony Prest / Never Odd Or Even03/2014
64062^261724+28511178787Tony Prest / Never Odd Or Even04/2014
64072^261724+29371378787Tony Prest / Never Odd Or Even04/2014
6408(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
64092^261724+57297178787Tony Prest / Never Odd Or Even05/2014
6410(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
6411(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
6412(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
6413(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
6414(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
6415(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
6416(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
6417(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
6418(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
6419(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
6420(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
6421(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
6422(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
6423(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
6424(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
6425(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
6426(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
6427(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
6428(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
6429(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
6430(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
6431(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
6432(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
6433(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
6434(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
6435(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
6436(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
6437(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
6438(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
6439(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
6440(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
6441(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
6442(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
6443(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
6444(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
6445(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
6446(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
6447(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
6448(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
6449(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
6450(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
6451(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
6452(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
6453(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
6454(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
6455(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
6456(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
6457(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
6458(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
6459(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
6460(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
6461(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
6462(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
6464(23*2^261642+1)/9378762Lelio R Paula10/2012
6463(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
6465(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
6466(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
646771293!4-478759Robert Price11/2019
6468(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
64692^261507-228778722Yves Minet04/2009
64708*10^78717+3978718Robert Price01/2017
6471(78557*2^261440+1)/378706Lelio R Paula06/2014
64726^101128-1643378693Enzo Doria02/2013
647320^60482+9978689Lelio R Paula03/2015
64742^261348-11063378674Enzo Doria05/2014
6475191^34487+278666Lelio R Paula05/2013
64762^261305-11013978661Enzo Doria04/2014
6477(82*10^78635-1)/978636Robert Price12/2014
647810^78632+8178633Robert Price03/2011
647910^78632-40269378632Patrick De Geest07/2013
64803*10^78631+1778632Robert Price03/2017
64812^261174-391178622Yves Minet04/2017
64822^261167+7484378620Enzo Doria04/2016
6483L(376121)+F(376122)78605Henri Lifchitz01/2007
648414^68580-2978602Lelio R Paula02/2015
6485(73*10^78576-1)/978577Robert Price01/2015
6486(17*2^261026-1)/4045178574Lelio R Paula02/2014
64872^261001-19578570Lelio R Paula05/2012
64885*2^260950+978555Lelio R Paula06/2014
64892^260931-760578549Lelio R Paula07/2013
649015^66778-3278538Lelio R Paula02/2015
6491(11*2^260896-1)/24578537Lelio R Paula02/2014
649230^53166+2978533Norbert Schneider03/2017
6493lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
64947*3^164574-278523Lelio R Paula06/2014
64952^260830-11213378518Enzo Doria06/2014
649613^70486+4278518Lelio R Paula03/2015
649711^75386-708078507Enzo Doria01/2013
6498(86^40583-1)/8578506Paul Bourdelais08/2017
64995*10^78504+1178505Robert Price08/2019
65002^260711-5869578482Lelio R Paula07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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