PRP Records

Probable Primes Top 10000

(212140 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 (> 30000) Who ? When ?
52512^267612-196580560Lelio R Paula07/2013
52522^267553+409780542Lelio R Paula07/2013
52537^95276-880518Robert Price01/2014
5254(15185*2^267457-1)/4782980513Lelio R Paula04/2015
52556^103467+16380513Lelio R Paula12/2015
5256(7*10^80490+143)/380491Robert Price04/2016
525786^41597-85^4159780470Robert Price04/2015
525813^72237+3080468Lelio R Paula11/2015
525917^65389+1480458Lelio R Paula11/2015
5260423^30634+30634^42380456Norbert Schneider05/2017
52612^267232+10580445Lelio R Paula05/2012
526211^77237-307200080435Enzo Doria01/2013
52632^267116-45995980410Enzo Doria06/2015
526438715!2+880406Robert Price01/2015
5265(2^267017+1)/380380H.&R. Lifchitz09/2000
52662^266968-4580366Lelio R Paula05/2012
526720^61768-6380363Lelio R Paula01/2016
52682^266920-11296780351Enzo Doria06/2014
52698*10^80342+8780343Robert Price10/2017
527012^74428-1380322Lelio R Paula11/2015
52712^266680+2780279Lelio R Paula05/2012
52722^266630-13180264Lelio R Paula05/2012
52732^266598+7681980254Enzo Doria05/2016
52742^266587+188063380251Enzo Doria10/2016
52752^266541-11004980237Enzo Doria04/2014
527638635!2-880222Robert Price06/2015
52773^168111+168111^3-180210Robert Price04/2014
52782^266443+51380208Lelio R Paula07/2013
5279(26*10^80200+61)/380201Robert Price06/2017
52802^266412-10991380199Enzo Doria04/2014
5281(10223*2^266417+1)/4509180199Lelio R Paula06/2014
528213^71988+6680191Lelio R Paula11/2015
528311^77002-432080190Enzo Doria01/2013
528418^63879-1380186Lelio R Paula11/2015
52852^266368-11229580185Enzo Doria06/2014
5286(3^168050+5)/102145480175Lelio R Paula10/2012
5287(22*10^80167+41)/980168Robert Price02/2015
5288(34*10^80162-43)/980163Ray Chandler12/2010
5290(38*10^80150-11)/980151Robert Price05/2015
5289(598*10^80149-31)/980151Robert Price02/2017
529119^62678-8080150Lelio R Paula12/2015
529210^80139+3234380140Patrick De Geest02/2011
529310^80139-980139Alexander Gramolin01/2011
52943^167955-10680135Lelio R Paula12/2015
5295(197*10^80089-11)/380091Robert Price10/2017
52962^265998+7555980074Enzo Doria04/2016
52972^265969-10980180065Enzo Doria04/2014
52982^265888-11275780041Enzo Doria06/2014
52992^265809+170180017Lelio R Paula07/2013
5300gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
53013^167687-10480008Lelio R Paula02/2015
530211^76826-579080007Enzo Doria01/2013
530310^80000+8573180001Patrick De Geest10/2009
530410^80000-716980000Patrick De Geest09/2009
530510^79999+2239980000Patrick De Geest09/2009
530610^79999-7487379999Patrick De Geest09/2009
53073^167668+5879998Lelio R Paula02/2015
5308155^36506-279961Lelio R Paula10/2017
53092^265612+425779958Lelio R Paula07/2013
53105*3^167577+479956Lelio R Paula06/2014
5311(9179*2^265593-1)/979955Lelio R Paula04/2015
53126^102723-4379935Lelio R Paula04/2015
531311^76748-336079925Enzo Doria12/2012
5314(13*2^265498-1)/18711979919Lelio R Paula02/2014
53152^265399-10985579894Enzo Doria04/2014
5316(20^61403-1)/1979886Paul Bourdelais03/2010
531718^63635+5979880Lelio R Paula02/2015
5318(11*10^79867-107)/379868Robert Price11/2016
53193^167375+8079859Lelio R Paula02/2015
53205^114240-1448679851Enzo Doria02/2013
532149^47238+4879842Norbert Schneider07/2014
53222^265212-377979837Yves Minet04/2017
532391^40746+40746^9179824Norbert Schneider12/2014
5324(68*10^79813-257)/979814Robert Price06/2017
5325(5*2^265118-1)/6179808Lelio R Paula02/2014
53262^265074+2842579796Lelio R Paula07/2013
53272^265072+118579795Lelio R Paula07/2013
5328p(16682)#/2-12879771Robert Price05/2017
53293^167167-3479759Robert Price11/2013
533012^73906+2979758Lelio R Paula02/2015
53312^264934+25579754Lelio R Paula07/2013
53324*10^79729-8779730Robert Price03/2017
53332^264846-11170179727Enzo Doria05/2014
53342^264831-11204179723Enzo Doria06/2014
53352^264816-45579718Yves Minet03/2012
5336(55*10^79711+89)/979712Robert Price09/2017
533747^47667-4679704Theodore Burton02/2007
533813^71547+9679700Lelio R Paula03/2015
53392^264752-11288379699Enzo Doria06/2014
53402^264732+13379693Lelio R Paula05/2012
53418*3^167010+779685Lelio R Paula06/2014
534242^49087-4179681Norbert Schneider06/2014
5343(26*10^79678-119)/379679Robert Price07/2016
53442^264683-2179678Lelio R Paula05/2012
53457^94279+1879675Lelio R Paula02/2015
53462^264655-12779670Lelio R Paula02/2012
53472^264597-45904379652Enzo Doria05/2015
5348(21*2^264566+1)/579643Lelio R Paula10/2012
53492^264536+187002179634Enzo Doria05/2016
5350(17*2^264512-1)/35979625Lelio R Paula02/2014
53512^264477-10978379616Enzo Doria04/2014
535218^63419-133379609Enzo Doria03/2013
535313^71451-3679593Lelio R Paula03/2015
5354(2^264410-5)/12800260912179585Lelio R Paula10/2012
535519^62234+9079582Lelio R Paula03/2015
535612^73714+4979551Lelio R Paula02/2015
5357(3*2^264184-1)/143333979522Lelio R Paula02/2014
53582^264103-11253179503Enzo Doria06/2014
535919^62170+7879501Lelio R Paula03/2015
536011^76340-258079500Enzo Doria12/2012
5361(23*10^79492-11)/379493Robert Price10/2015
5362((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
53632^264060-11213379490Enzo Doria06/2014
5364((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
53659^83298+6^83298-2^8329879487Mike Oakes08/2010
536618^63319+3579483Lelio R Paula02/2015
536738303!2+25679461Robert Price01/2015
5368(29*10^79445+61)/979446Robert Price04/2015
53692^263902-19579443Lelio R Paula05/2012
53703^166499-11269679441Enzo Doria06/2014
537111^76279-276079437Enzo Doria12/2012
53726^102077-2579432Lelio R Paula03/2015
53732^263852-101779428Lelio R Paula07/2013
53742^263842-3379425Lelio R Paula05/2012
537512^73584-5579411Lelio R Paula02/2015
53762^263772-18579404Lelio R Paula05/2012
5377(15^67489+1)/1679373Paul Bourdelais03/2010
53782^263664+1501579371Lelio R Paula07/2013
537910^79362+3^7936379363Mike Oakes06/2010
5380Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
53813^166262+4479328Lelio R Paula02/2015
53824*10^79327-6379328Robert Price12/2016
53832^263486+51379318Lelio R Paula07/2013
53842^263448-51950979306Paul Bourdelais03/2013
538521^59971-20^5997179295Robert Price05/2012
53862^263372+12379283Lelio R Paula05/2012
538717^64429+8479277Lelio R Paula03/2015
538811^76124-1143079275Enzo Doria12/2012
5389(206*10^79268-17)/979270Robert Price03/2017
539013^71157+1879265Lelio R Paula03/2015
53912^263297+6583579261Lelio R Paula07/2013
539219^61980-1879258Theodore Burton12/2005
53932*10^79242+9379243Robert Price07/2016
5394(88^40751-1)/8779238Paul Bourdelais08/2017
5395(103*29^54179-39)/479233Curtis Bright05/2015
53969^83024-83024^979226Norbert Schneider08/2017
539717^64382-2679219Lelio R Paula03/2015
53987^93733-7479214Lelio R Paula02/2015
539915^67352+3879213Lelio R Paula02/2015
54002^263135-11023579212Enzo Doria05/2014
54012^263044+425779185Lelio R Paula07/2013
54032^263032+8751779181Yves Minet11/2010
54026^101755+9579181Lelio R Paula03/2015
54044^131497-3^13149779170Jean-Louis Charton05/2004
54055*7^93674+879165Lelio R Paula10/2014
5406lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
5407260^32768+179^3276879134Serge Batalov03/2018
540811^75978-4279123Lelio R Paula02/2015
54098*5^113180+979111Lelio R Paula10/2014
5410(6883*2^262741-1)/483579094Lelio R Paula04/2015
5411(9*2^262745+1)/13779093Lelio R Paula10/2012
541212^73285+8579088Lelio R Paula02/2015
541319^61840+5279079Lelio R Paula03/2015
5414(10^79067+77)/379067Robert Price01/2017
5415(1017*2^262640-1)/1155779062Lelio R Paula04/2015
541610^79040+13794979041Patrick De Geest02/2016
541810^79040-100729779040Robert Price02/2015
541710^79040-7742779040Patrick De Geest02/2016
54192^262551-1729579036Lelio R Paula07/2013
54203^165597+34079010Lelio R Paula02/2015
5421(23*2^262435+1)/5579001Lelio R Paula10/2012
542211^75860-210079001Enzo Doria12/2012
54238*7^93463+978987Lelio R Paula10/2014
542467^43240-278960Lelio R Paula09/2013
54251000001^13159-1000000^1315978953Jean-Louis Charton10/2003
54262^262199-11028778930Enzo Doria05/2014
5427(19*2^262180-1)/17778924Lelio R Paula02/2014
5428(3^165403+4)/778917Lelio R Paula10/2012
54302^21068*(2^241076+1)-178914Makoto Morimoto03/2014
54312^29258*(2^232886+1)-178914Makoto Morimoto03/2014
54292^262144+1853178914Makoto Morimoto12/2015
5432(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
5433(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
543414^68837+7578897Lelio R Paula02/2015
5435106^38949+10578884Norbert Schneider12/2016
5436(70^42737+1)/7178853Paul Bourdelais08/2017
5437(25*2^261917-1)/2092778842Lelio R Paula02/2014
54382^261881-185971378835Enzo Doria03/2016
54392^261874+191578832Lelio R Paula07/2013
54402^261856+9876533178827Jason Earls01/2009
5441(5*2^261857-1)/2050127778821Lelio R Paula02/2014
54422^261724+9269178787Tony Prest / Never Odd Or Even03/2014
54432^261724+28511178787Tony Prest / Never Odd Or Even04/2014
54442^261724+29371378787Tony Prest / Never Odd Or Even04/2014
5445(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
54462^261724+57297178787Tony Prest / Never Odd Or Even05/2014
5447(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
5448(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
5449(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
5450(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
5451(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
5452(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
5453(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
5454(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
5455(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
5456(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
5457(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
5458(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
5459(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
5460(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
5461(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
5462(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
5463(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
5464(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
5465(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
5466(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
5467(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
5468(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
5469(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
5470(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
5471(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
5472(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
5473(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
5474(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
5475(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
5476(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
5477(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
5478(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
5479(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
5480(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
5481(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
5482(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
5483(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
5484(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
5485(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
5486(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
5487(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
5488(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
5489(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
5490(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
5491(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
5492(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
5493(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
5494(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
5495(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
5496(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
5497(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
5498(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
5499(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
5500(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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