PRP Records

Probable Primes Top 10000

(259919 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 ?
67512^266630-13180264Lelio R Paula05/2012
6752(2^266627+1278)/280263Stefano Morozzi01/2020
67532^266598+7681980254Enzo Doria05/2016
675424463^1908+1908^2446380253Hans Havermann01/2020
67552^266587+188063380251Enzo Doria10/2016
6756(2^266570+3942)/280246Stefano Morozzi01/2020
67572^266541-11004980237Enzo Doria04/2014
675838635!2-880222Robert Price06/2015
6759(2^266465+986)/280214Stefano Morozzi01/2020
67603^168111+168111^3-180210Robert Price04/2014
6761(2^266447+758)/280209Stefano Morozzi01/2020
67622^266443+51380208Lelio R Paula07/2013
6763(26*10^80200+61)/380201Robert Price06/2017
67652^266412-10991380199Enzo Doria04/2014
6766(10223*2^266417+1)/4509180199Lelio R Paula06/2014
67642^266413-469380199Yves Minet05/2019
676713^71988+6680191Lelio R Paula11/2015
676811^77002-432080190Enzo Doria01/2013
676918^63879-1380186Lelio R Paula11/2015
6770(2^266371+1814)/280186Stefano Morozzi01/2020
67722^266368-11229580185Enzo Doria06/2014
677119217^14880+14880^1921780185Hans Havermann03/2020
6773(3^168050+5)/102145480175Lelio R Paula10/2012
6774(2^266324+1386)/280172Stefano Morozzi01/2020
6775(22*10^80167+41)/980168Robert Price02/2015
6776(2^266308+1618)/280167Stefano Morozzi01/2020
6777(34*10^80162-43)/980163Ray Chandler12/2010
6778(2^266276+762)/280157Stefano Morozzi01/2020
6779(38*10^80150-11)/980151Robert Price05/2015
6780(598*10^80149-31)/980151Robert Price02/2017
678119^62678-8080150Lelio R Paula12/2015
678210^80139+3234380140Patrick De Geest02/2011
678310^80139-980139Alexander Gramolin01/2011
67843^167955-10680135Lelio R Paula12/2015
6785(2^266137+3782)/280115Stefano Morozzi01/2020
6786(2^266121+3846)/280111Stefano Morozzi01/2020
6787(197*10^80089-11)/380091Robert Price10/2017
67892^265998+7555980074Enzo Doria04/2016
6788(2^265999+3290)/280074Stefano Morozzi01/2020
67902^265969-10980180065Enzo Doria04/2014
6791(2^265956+3378)/280061Stefano Morozzi01/2020
67922^265888-11275780041Enzo Doria06/2014
67932^265809+170180017Lelio R Paula07/2013
6794gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
67953^167687-10480008Lelio R Paula02/2015
679611^76826-579080007Enzo Doria01/2013
679710^80000+8573180001Patrick De Geest10/2009
679810^80000-716980000Patrick De Geest09/2009
679910^79999+2239980000Patrick De Geest09/2009
680010^79999-7487379999Patrick De Geest09/2009
68013^167668+5879998Lelio R Paula02/2015
6802(2^265728+3742)/279992Stefano Morozzi01/2020
6803155^36506-279961Lelio R Paula10/2017
6804(2^265621+3882)/279960Stefano Morozzi01/2020
68062^265612+425779958Lelio R Paula07/2013
6805(2^265613+1470)/279958Stefano Morozzi01/2020
68075*3^167577+479956Lelio R Paula06/2014
6808(9179*2^265593-1)/979955Lelio R Paula04/2015
68096^102723-4379935Lelio R Paula04/2015
681011^76748-336079925Enzo Doria12/2012
681119430^12981+12981^1943079922Hans Havermann03/2020
6812(2^265490+870)/279921Stefano Morozzi01/2020
6813(13*2^265498-1)/18711979919Lelio R Paula02/2014
6814(2^265438+3978)/279905Stefano Morozzi01/2020
6815(2^265409+1250)/279896Stefano Morozzi01/2020
68162^265399-10985579894Enzo Doria04/2014
6817(2^265380+3930)/279888Stefano Morozzi01/2020
6818(20^61403-1)/1979886Paul Bourdelais03/2010
6819(2^265368+2970)/279884Stefano Morozzi01/2020
682018^63635+5979880Lelio R Paula02/2015
6821(11*10^79867-107)/379868Robert Price11/2016
68223^167375+8079859Lelio R Paula02/2015
68235^114240-1448679851Enzo Doria02/2013
682449^47238+4879842Norbert Schneider07/2014
68252^265212-377979837Yves Minet04/2017
6826(2^265201+2790)/279834Stefano Morozzi01/2020
682791^40746+40746^9179824Norbert Schneider12/2014
6828(68*10^79813-257)/979814Robert Price06/2017
6829(5*2^265118-1)/6179808Lelio R Paula02/2014
6830(2^265102+1462)/279804Stefano Morozzi01/2020
68312^265074+2842579796Lelio R Paula07/2013
68322^265072+118579795Lelio R Paula07/2013
6834p(16682)#/2-12879771Robert Price05/2017
6833(2^264994+1714)/279771Stefano Morozzi01/2020
68363^167167-3479759Robert Price11/2013
6835(2^264952+3258)/279759Stefano Morozzi01/2020
683712^73906+2979758Lelio R Paula02/2015
68382^264934+25579754Lelio R Paula07/2013
68394*10^79729-8779730Robert Price03/2017
68402^264846-11170179727Enzo Doria05/2014
68412^264831-11204179723Enzo Doria06/2014
68422^264816-45579718Yves Minet03/2012
6843(55*10^79711+89)/979712Robert Price09/2017
684447^47667-4679704Theodore Burton02/2007
684513^71547+9679700Lelio R Paula03/2015
68462^264752-11288379699Enzo Doria06/2014
6847(2^264748+1978)/279697Stefano Morozzi01/2020
68482^264732+13379693Lelio R Paula05/2012
68498*3^167010+779685Lelio R Paula06/2014
685042^49087-4179681Norbert Schneider06/2014
6851(26*10^79678-119)/379679Robert Price07/2016
68522^264683-2179678Lelio R Paula05/2012
68537^94279+1879675Lelio R Paula02/2015
68552^264655-12779670Lelio R Paula02/2012
6854(2^264658+3102)/279670Stefano Morozzi01/2020
6856(2^264637+1682)/279664Stefano Morozzi01/2020
68572^264597-45904379652Enzo Doria05/2015
6858(21*2^264566+1)/579643Lelio R Paula10/2012
68592^264536+187002179634Enzo Doria05/2016
6860(17*2^264512-1)/35979625Lelio R Paula02/2014
68612^264477-10978379616Enzo Doria04/2014
686218^63419-133379609Enzo Doria03/2013
686313^71451-3679593Lelio R Paula03/2015
686423314^2593+2593^2331479590Hans Havermann03/2020
6865(2^264410-5)/12800260912179585Lelio R Paula10/2012
686619^62234+9079582Lelio R Paula03/2015
6867(2^264276+2866)/279555Stefano Morozzi01/2020
686812^73714+4979551Lelio R Paula02/2015
6869(2^264213+1442)/279536Stefano Morozzi01/2020
6870(3*2^264184-1)/143333979522Lelio R Paula02/2014
6871(2^264160+1590)/279520Stefano Morozzi01/2020
68722^264103-11253179503Enzo Doria06/2014
687319^62170+7879501Lelio R Paula03/2015
687411^76340-258079500Enzo Doria12/2012
6875(2^264084+858)/279497Stefano Morozzi01/2020
6876(23*10^79492-11)/379493Robert Price10/2015
6877((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
68782^264060-11213379490Enzo Doria06/2014
6879((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
688020158^8775+8775^2015879488Hans Havermann02/2020
68819^83298+6^83298-2^8329879487Mike Oakes08/2010
688218^63319+3579483Lelio R Paula02/2015
688338303!2+25679461Robert Price01/2015
6884(29*10^79445+61)/979446Robert Price04/2015
68852^263902-19579443Lelio R Paula05/2012
68863^166499-11269679441Enzo Doria06/2014
688711^76279-276079437Enzo Doria12/2012
688818907^15894+15894^1890779433Hans Havermann03/2020
68896^102077-2579432Lelio R Paula03/2015
68902^263852-101779428Lelio R Paula07/2013
68912^263842-3379425Lelio R Paula05/2012
6892(2^263814+3582)/279416Stefano Morozzi01/2020
689312^73584-5579411Lelio R Paula02/2015
6894(2^263783+3558)/279407Stefano Morozzi01/2020
68952^263772-18579404Lelio R Paula05/2012
6896(15^67489+1)/1679373Paul Bourdelais03/2010
68972^263664+1501579371Lelio R Paula07/2013
6898(2^263643+1206)/279365Stefano Morozzi01/2020
6899(2^263642+3082)/279364Stefano Morozzi01/2020
690010^79362+3^7936379363Mike Oakes06/2010
6901(2^263591+2910)/279349Stefano Morozzi01/2020
6902(2^263589+1922)/279348Stefano Morozzi01/2020
6903Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
69043^166262+4479328Lelio R Paula02/2015
69054*10^79327-6379328Robert Price12/2016
69062^263486+51379318Lelio R Paula07/2013
6907(2^263458+1282)/279309Stefano Morozzi01/2020
6908(2^263456+1558)/279308Stefano Morozzi01/2020
69092^263448-51950979306Paul Bourdelais03/2013
691069153^16384+279296Matt Stath01/2019
691121^59971-20^5997179295Robert Price05/2012
69122^263372+12379283Lelio R Paula05/2012
6913(2^263366+1974)/279281Stefano Morozzi01/2020
691417^64429+8479277Lelio R Paula03/2015
691511^76124-1143079275Enzo Doria12/2012
691619294^12845+12845^1929479274Hans Havermann03/2020
6917(206*10^79268-17)/979270Robert Price03/2017
691813^71157+1879265Lelio R Paula03/2015
69192^263297+6583579261Lelio R Paula07/2013
692019^61980-1879258Theodore Burton12/2005
6921(2^263259+2970)/279249Stefano Morozzi01/2020
69222*10^79242+9379243Robert Price07/2016
6923(2^263226+1074)/279239Stefano Morozzi01/2020
6924(88^40751-1)/8779238Paul Bourdelais08/2017
6925(103*29^54179-39)/479233Curtis Bright05/2015
69269^83024-83024^979226Norbert Schneider08/2017
692717^64382-2679219Lelio R Paula03/2015
69287^93733-7479214Lelio R Paula02/2015
692915^67352+3879213Lelio R Paula02/2015
69302^263135-11023579212Enzo Doria05/2014
6931(2^263080+3658)/279195Stefano Morozzi01/2020
69322^263044+425779185Lelio R Paula07/2013
6933(2^263039+3554)/279183Stefano Morozzi01/2020
69352^263032+8751779181Yves Minet11/2010
69346^101755+9579181Lelio R Paula03/2015
6936(2^263010+1738)/279174Stefano Morozzi01/2020
69374^131497-3^13149779170Jean-Louis Charton05/2004
69385*7^93674+879165Lelio R Paula10/2014
6939(2^262939+1326)/279153Stefano Morozzi01/2020
6940(2^262941+926)/279153Stefano Morozzi01/2020
6941lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
6942260^32768+179^3276879134Serge Batalov03/2018
694311^75978-4279123Lelio R Paula02/2015
69448*5^113180+979111Lelio R Paula10/2014
6945(2^262757+3222)/279098Stefano Morozzi01/2020
6946(6883*2^262741-1)/483579094Lelio R Paula04/2015
6947(9*2^262745+1)/13779093Lelio R Paula10/2012
694812^73285+8579088Lelio R Paula02/2015
694919^61840+5279079Lelio R Paula03/2015
6951(10^79067+77)/379067Robert Price01/2017
6950(2^262655+678)/279067Stefano Morozzi01/2020
6952(1017*2^262640-1)/1155779062Lelio R Paula04/2015
6953(2^262634+1674)/279061Stefano Morozzi01/2020
695410^79040+13794979041Patrick De Geest02/2016
695610^79040-100729779040Robert Price02/2015
695510^79040-7742779040Patrick De Geest02/2016
69572^262551-1729579036Lelio R Paula07/2013
69583^165597+34079010Lelio R Paula02/2015
695919620^10633+10633^1962079003Hans Havermann02/2020
6960(23*2^262435+1)/5579001Lelio R Paula10/2012
696111^75860-210079001Enzo Doria12/2012
69628*7^93463+978987Lelio R Paula10/2014
6963(2^262376+3942)/278983Stefano Morozzi01/2020
696467^43240-278960Lelio R Paula09/2013
69651000001^13159-1000000^1315978953Jean-Louis Charton10/2003
6966(2^262263+3410)/278949Stefano Morozzi01/2020
69672^262199-11028778930Enzo Doria05/2014
6968(19*2^262180-1)/17778924Lelio R Paula02/2014
6969(3^165403+4)/778917Lelio R Paula10/2012
69702^21068*(2^241076+1)-178914Makoto Morimoto03/2014
69712^29258*(2^232886+1)-178914Makoto Morimoto03/2014
69732^262144+1853178914Makoto Morimoto12/2015
69722^262144-23142578914Matthias Baur03/2020
6974(2^262137+1730)/278911Stefano Morozzi01/2020
6975(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
6976(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
697714^68837+7578897Lelio R Paula02/2015
6978(2^262055+1806)/278887Stefano Morozzi01/2020
6979(2^262049+1406)/278885Stefano Morozzi01/2020
6980106^38949+10578884Norbert Schneider12/2016
6981(2^262010+3778)/278873Stefano Morozzi01/2020
698218683^16636+16636^1868378862Hans Havermann03/2020
6983(2^261964+1450)/278859Stefano Morozzi01/2020
698423288^2433+2433^2328878857Hans Havermann03/2020
6985(70^42737+1)/7178853Paul Bourdelais08/2017
6986(2^261919+2474)/278846Stefano Morozzi01/2020
6987(25*2^261917-1)/2092778842Lelio R Paula02/2014
69882^261881-185971378835Enzo Doria03/2016
69902^261874+191578832Lelio R Paula07/2013
6989(2^261872+1582)/278832Stefano Morozzi01/2020
69912^261856+9876533178827Jason Earls01/2009
6992(5*2^261857-1)/2050127778821Lelio R Paula02/2014
699324586^1605+1605^2458678810Hans Havermann02/2020
6994(2^261786+3538)/278806Stefano Morozzi01/2020
6995(2^261780+2290)/278804Stefano Morozzi01/2020
69962^261724+9269178787Tony Prest / Never Odd Or Even03/2014
69972^261724+28511178787Tony Prest / Never Odd Or Even04/2014
69982^261724+29371378787Tony Prest / Never Odd Or Even04/2014
6999(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
70002^261724+57297178787Tony Prest / Never Odd Or Even05/2014


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!