PRP Records

Probable Primes Top 10000

(271019 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 ?
77512^266598+7681980254Enzo Doria05/2016
775224463^1908+1908^2446380253Hans Havermann01/2020
77532^266587+188063380251Enzo Doria10/2016
7754(2^266570+3942)/280246Stefano Morozzi01/2020
77552^266541-11004980237Enzo Doria04/2014
775638635!2-880222Robert Price06/2015
7757(2^266465+986)/280214Stefano Morozzi01/2020
77583^168111+168111^3-180210Robert Price04/2014
7759(2^266447+758)/280209Stefano Morozzi01/2020
77602^266443+51380208Lelio R Paula07/2013
7761(26*10^80200+61)/380201Robert Price06/2017
77622^266412-10991380199Enzo Doria04/2014
7763(10223*2^266417+1)/4509180199Lelio R Paula06/2014
77642^266413-469380199Yves Minet05/2019
7765(13737^19381-1)/1373680193Serge Batalov08/2020
776613^71988+6680191Lelio R Paula11/2015
776711^77002-432080190Enzo Doria01/2013
776819839^11012+11012^1983980187Hans Havermann03/2020
777018^63879-1380186Lelio R Paula11/2015
7769(2^266371+1814)/280186Stefano Morozzi01/2020
77712^266368-11229580185Enzo Doria06/2014
777219217^14880+14880^1921780185Hans Havermann03/2020
7773(3^168050+5)/102145480175Lelio R Paula10/2012
7774(2^266324+1386)/280172Stefano Morozzi01/2020
7775(22*10^80167+41)/980168Robert Price02/2015
7776(2^266308+1618)/280167Stefano Morozzi01/2020
7777(34*10^80162-43)/980163Ray Chandler12/2010
7778(2^266276+762)/280157Stefano Morozzi01/2020
7780(38*10^80150-11)/980151Robert Price05/2015
7779(598*10^80149-31)/980151Robert Price02/2017
778119^62678-8080150Lelio R Paula12/2015
7782(559^29173-1)/55880148Serge Batalov08/2020
778310^80139+3234380140Patrick De Geest02/2011
778410^80139-980139Alexander Gramolin01/2011
77853^167955-10680135Lelio R Paula12/2015
778620545^7944+7944^2054580127Hans Havermann04/2020
778718876^17569+17569^1887680124Hans Havermann03/2020
7788(2^266137+3782)/280115Stefano Morozzi01/2020
7789(2^266121+3846)/280111Stefano Morozzi01/2020
779022752^3313+3313^2275280093Hans Havermann03/2020
7791(197*10^80089-11)/380091Robert Price10/2017
77922^265998+7555980074Enzo Doria04/2016
7793(2^265999+3290)/280074Stefano Morozzi01/2020
77942^265969-10980180065Enzo Doria04/2014
7795(2^265956+3378)/280061Stefano Morozzi01/2020
77962^265888-11275780041Enzo Doria06/2014
7797(24847^18211-1)/2484680038Serge Batalov08/2020
77982^265809+170180017Lelio R Paula07/2013
7799gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
780019807^10954+10954^1980780012Hans Havermann04/2020
78013^167687-10480008Lelio R Paula02/2015
780211^76826-579080007Enzo Doria01/2013
780310^80000+8573180001Patrick De Geest10/2009
780410^80000-716980000Patrick De Geest09/2009
780510^79999+2239980000Patrick De Geest09/2009
780610^79999-7487379999Patrick De Geest09/2009
78073^167668+5879998Lelio R Paula02/2015
7808(2^265728+3742)/279992Stefano Morozzi01/2020
780918780^18137+18137^1878079976Hans Havermann04/2020
781019190^14709+14709^1919079976Hans Havermann04/2020
7811155^36506-279961Lelio R Paula10/2017
7812(2^265621+3882)/279960Stefano Morozzi01/2020
78142^265612+425779958Lelio R Paula07/2013
7813(2^265613+1470)/279958Stefano Morozzi01/2020
78155*3^167577+479956Lelio R Paula06/2014
7816(9179*2^265593-1)/979955Lelio R Paula04/2015
78176^102723-4379935Lelio R Paula04/2015
781821052^6261+6261^2105279927Hans Havermann03/2020
781911^76748-336079925Enzo Doria12/2012
782019430^12981+12981^1943079922Hans Havermann03/2020
7821(2^265490+870)/279921Stefano Morozzi01/2020
7822(13*2^265498-1)/18711979919Lelio R Paula02/2014
7823(2^265438+3978)/279905Stefano Morozzi01/2020
7824(2^265409+1250)/279896Stefano Morozzi01/2020
78252^265399-10985579894Enzo Doria04/2014
7826(2^265380+3930)/279888Stefano Morozzi01/2020
7827(20^61403-1)/1979886Paul Bourdelais03/2010
7828(2^265368+2970)/279884Stefano Morozzi01/2020
782918^63635+5979880Lelio R Paula02/2015
7830(11*10^79867-107)/379868Robert Price11/2016
78313^167375+8079859Lelio R Paula02/2015
78325^114240-1448679851Enzo Doria02/2013
783349^47238+4879842Norbert Schneider07/2014
78342^265212-377979837Yves Minet04/2017
7835(2^265201+2790)/279834Stefano Morozzi01/2020
783691^40746+40746^9179824Norbert Schneider12/2014
7837(68*10^79813-257)/979814Robert Price06/2017
7838(13063^19391-1)/1306279811Serge Batalov08/2020
7839(5*2^265118-1)/6179808Lelio R Paula02/2014
7840(2^265102+1462)/279804Stefano Morozzi01/2020
78412^265074+2842579796Lelio R Paula07/2013
78422^265072+118579795Lelio R Paula07/2013
7844p(16682)#/2-12879771Robert Price05/2017
7843(2^264994+1714)/279771Stefano Morozzi01/2020
78463^167167-3479759Robert Price11/2013
7845(2^264952+3258)/279759Stefano Morozzi01/2020
784712^73906+2979758Lelio R Paula02/2015
78482^264934+25579754Lelio R Paula07/2013
78494*10^79729-8779730Robert Price03/2017
78502^264846-11170179727Enzo Doria05/2014
78512^264831-11204179723Enzo Doria06/2014
78522^264816-45579718Yves Minet03/2012
7853(55*10^79711+89)/979712Robert Price09/2017
785447^47667-4679704Theodore Burton02/2007
785513^71547+9679700Lelio R Paula03/2015
78562^264752-11288379699Enzo Doria06/2014
7857(2^264748+1978)/279697Stefano Morozzi01/2020
78582^264732+13379693Lelio R Paula05/2012
78598*3^167010+779685Lelio R Paula06/2014
786042^49087-4179681Norbert Schneider06/2014
7861(26*10^79678-119)/379679Robert Price07/2016
78622^264683-2179678Lelio R Paula05/2012
78637^94279+1879675Lelio R Paula02/2015
78652^264655-12779670Lelio R Paula02/2012
7864(2^264658+3102)/279670Stefano Morozzi01/2020
7866(2^264637+1682)/279664Stefano Morozzi01/2020
78672^264597-45904379652Enzo Doria05/2015
7868(21*2^264566+1)/579643Lelio R Paula10/2012
78692^264536+187002179634Enzo Doria05/2016
7870(17*2^264512-1)/35979625Lelio R Paula02/2014
787119957^9762+9762^1995779620Hans Havermann03/2020
78722^264477-10978379616Enzo Doria04/2014
787318^63419-133379609Enzo Doria03/2013
787413^71451-3679593Lelio R Paula03/2015
787523314^2593+2593^2331479590Hans Havermann03/2020
7876(2^264410-5)/12800260912179585Lelio R Paula10/2012
787719^62234+9079582Lelio R Paula03/2015
7878(2^264276+2866)/279555Stefano Morozzi01/2020
787912^73714+4979551Lelio R Paula02/2015
7880(2^264213+1442)/279536Stefano Morozzi01/2020
7881(3*2^264184-1)/143333979522Lelio R Paula02/2014
7882(2^264160+1590)/279520Stefano Morozzi01/2020
7883(29*10^79510-107)/379511Robert Price08/2020
7884(9363^20021-1)/936279508Serge Batalov08/2020
78852^264103-11253179503Enzo Doria06/2014
788619^62170+7879501Lelio R Paula03/2015
788711^76340-258079500Enzo Doria12/2012
7888(2^264084+858)/279497Stefano Morozzi01/2020
7889(5652^21187-1)/565179495Serge Batalov08/2020
7890(23*10^79492-11)/379493Robert Price10/2015
7891((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
78922^264060-11213379490Enzo Doria06/2014
7894((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
789320158^8775+8775^2015879488Hans Havermann02/2020
78959^83298+6^83298-2^8329879487Mike Oakes08/2010
789618^63319+3579483Lelio R Paula02/2015
7897(10011^19867-1)/1001079474Serge Batalov08/2020
78982*10^79468+7779469Robert Price08/2020
789922479^3428+3428^2247979465Hans Havermann04/2020
790038303!2+25679461Robert Price01/2015
7901(29*10^79445+61)/979446Robert Price04/2015
79022^263902-19579443Lelio R Paula05/2012
79033^166499-11269679441Enzo Doria06/2014
790411^76279-276079437Enzo Doria12/2012
790518907^15894+15894^1890779433Hans Havermann03/2020
79066^102077-2579432Lelio R Paula03/2015
79072^263852-101779428Lelio R Paula07/2013
79082^263842-3379425Lelio R Paula05/2012
7909(2^263814+3582)/279416Stefano Morozzi01/2020
791012^73584-5579411Lelio R Paula02/2015
7911(2^263783+3558)/279407Stefano Morozzi01/2020
79122^263772-18579404Lelio R Paula05/2012
7913(15^67489+1)/1679373Paul Bourdelais03/2010
79142^263664+1501579371Lelio R Paula07/2013
7915(2^263643+1206)/279365Stefano Morozzi01/2020
7916(2^263642+3082)/279364Stefano Morozzi01/2020
7917(3319^22541-1)/331879364Serge Batalov08/2020
791810^79362+3^7936379363Mike Oakes06/2010
7919(2^263591+2910)/279349Stefano Morozzi01/2020
7920(2^263589+1922)/279348Stefano Morozzi01/2020
7921Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
79223^166262+4479328Lelio R Paula02/2015
79234*10^79327-6379328Robert Price12/2016
79242^263486+51379318Lelio R Paula07/2013
7925(2^263458+1282)/279309Stefano Morozzi01/2020
7926(2^263456+1558)/279308Stefano Morozzi01/2020
79272^263448-51950979306Paul Bourdelais03/2013
7928(18926^18541-1)/1892579297Serge Batalov08/2020
792969153^16384+279296Matt Stath01/2019
793021^59971-20^5997179295Robert Price05/2012
79312^263372+12379283Lelio R Paula05/2012
7932(2^263366+1974)/279281Stefano Morozzi01/2020
793317^64429+8479277Lelio R Paula03/2015
793411^76124-1143079275Enzo Doria12/2012
793519294^12845+12845^1929479274Hans Havermann03/2020
7936(206*10^79268-17)/979270Robert Price03/2017
793713^71157+1879265Lelio R Paula03/2015
79382^263297+6583579261Lelio R Paula07/2013
793919^61980-1879258Theodore Burton12/2005
7940(2^263259+2970)/279249Stefano Morozzi01/2020
79412*10^79242+9379243Robert Price07/2016
7942(2^263226+1074)/279239Stefano Morozzi01/2020
7943(88^40751-1)/8779238Paul Bourdelais08/2017
7944(103*29^54179-39)/479233Curtis Bright05/2015
79459^83024-83024^979226Norbert Schneider08/2017
794617^64382-2679219Lelio R Paula03/2015
79477^93733-7479214Lelio R Paula02/2015
794815^67352+3879213Lelio R Paula02/2015
79492^263135-11023579212Enzo Doria05/2014
7950(2^263080+3658)/279195Stefano Morozzi01/2020
79512^263044+425779185Lelio R Paula07/2013
7952(2^263039+3554)/279183Stefano Morozzi01/2020
79542^263032+8751779181Yves Minet11/2010
79536^101755+9579181Lelio R Paula03/2015
7955(2^263010+1738)/279174Stefano Morozzi01/2020
79564^131497-3^13149779170Jean-Louis Charton05/2004
79575*7^93674+879165Lelio R Paula10/2014
7958(2^262939+1326)/279153Stefano Morozzi01/2020
7959(2^262941+926)/279153Stefano Morozzi01/2020
7960lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
7961260^32768+179^3276879134Serge Batalov03/2018
796211^75978-4279123Lelio R Paula02/2015
79638*5^113180+979111Lelio R Paula10/2014
7964(2^262757+3222)/279098Stefano Morozzi01/2020
7965(6883*2^262741-1)/483579094Lelio R Paula04/2015
7966(9*2^262745+1)/13779093Lelio R Paula10/2012
796712^73285+8579088Lelio R Paula02/2015
796819^61840+5279079Lelio R Paula03/2015
7970(10^79067+77)/379067Robert Price01/2017
7969(2^262655+678)/279067Stefano Morozzi01/2020
7971(1017*2^262640-1)/1155779062Lelio R Paula04/2015
7972(2^262634+1674)/279061Stefano Morozzi01/2020
797310^79040+13794979041Patrick De Geest02/2016
797510^79040-100729779040Robert Price02/2015
797410^79040-7742779040Patrick De Geest02/2016
79762^262551-1729579036Lelio R Paula07/2013
7977(22973^18121-1)/2297279026Serge Batalov08/2020
79783^165597+34079010Lelio R Paula02/2015
797919620^10633+10633^1962079003Hans Havermann02/2020
7980(23*2^262435+1)/5579001Lelio R Paula10/2012
798111^75860-210079001Enzo Doria12/2012
79828*7^93463+978987Lelio R Paula10/2014
7983(2^262376+3942)/278983Stefano Morozzi01/2020
798467^43240-278960Lelio R Paula09/2013
79851000001^13159-1000000^1315978953Jean-Louis Charton10/2003
7986(2^262263+3410)/278949Stefano Morozzi01/2020
79872^262199-11028778930Enzo Doria05/2014
7988(19*2^262180-1)/17778924Lelio R Paula02/2014
7989(3^165403+4)/778917Lelio R Paula10/2012
79902^21068*(2^241076+1)-178914Makoto Morimoto03/2014
79912^29258*(2^232886+1)-178914Makoto Morimoto03/2014
79932^262144+1853178914Makoto Morimoto12/2015
79922^262144-23142578914Matthias Baur03/2020
7994(2^262137+1730)/278911Stefano Morozzi01/2020
7995(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
7996(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
799714^68837+7578897Lelio R Paula02/2015
7998(2^262055+1806)/278887Stefano Morozzi01/2020
7999(20450^18301-1)/2044978886Serge Batalov08/2020
8000(2^262049+1406)/278885Stefano Morozzi01/2020


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 15:45 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!