PRP Records

Probable Primes Top 10000

(277054 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 ?
825119807^10954+10954^1980780012Hans Havermann04/2020
82523^167687-10480008Lelio R Paula02/2015
825311^76826-579080007Enzo Doria01/2013
825410^80000+8573180001Patrick De Geest10/2009
825510^80000-716980000Patrick De Geest09/2009
825610^79999+2239980000Patrick De Geest09/2009
825710^79999-7487379999Patrick De Geest09/2009
82583^167668+5879998Lelio R Paula02/2015
8259(2^265728+3742)/279992Stefano Morozzi01/2020
826018780^18137+18137^1878079976Hans Havermann04/2020
826119190^14709+14709^1919079976Hans Havermann04/2020
8262155^36506-279961Lelio R Paula10/2017
8263(2^265621+3882)/279960Stefano Morozzi01/2020
82652^265612+425779958Lelio R Paula07/2013
8264(2^265613+1470)/279958Stefano Morozzi01/2020
82665*3^167577+479956Lelio R Paula06/2014
8267(9179*2^265593-1)/979955Lelio R Paula04/2015
82686^102723-4379935Lelio R Paula04/2015
826921052^6261+6261^2105279927Hans Havermann03/2020
827011^76748-336079925Enzo Doria12/2012
827119430^12981+12981^1943079922Hans Havermann03/2020
8272(2^265490+870)/279921Stefano Morozzi01/2020
8273(13*2^265498-1)/18711979919Lelio R Paula02/2014
8274(2^265438+3978)/279905Stefano Morozzi01/2020
8275(2^265409+1250)/279896Stefano Morozzi01/2020
82762^265399-10985579894Enzo Doria04/2014
8277(2^265380+3930)/279888Stefano Morozzi01/2020
8278(20^61403-1)/1979886Paul Bourdelais03/2010
8279(2^265368+2970)/279884Stefano Morozzi01/2020
828018^63635+5979880Lelio R Paula02/2015
8281(11*10^79867-107)/379868Robert Price11/2016
82823^167375+8079859Lelio R Paula02/2015
82835^114240-1448679851Enzo Doria02/2013
828449^47238+4879842Norbert Schneider07/2014
82852^265212-377979837Yves Minet04/2017
8286(2^265201+2790)/279834Stefano Morozzi01/2020
828791^40746+40746^9179824Norbert Schneider12/2014
8288(68*10^79813-257)/979814Robert Price06/2017
8289(13063^19391-1)/1306279811Serge Batalov08/2020
8290(5*2^265118-1)/6179808Lelio R Paula02/2014
8291(2^265102+1462)/279804Stefano Morozzi01/2020
82922^265074+2842579796Lelio R Paula07/2013
82932^265072+118579795Lelio R Paula07/2013
8295p(16682)#/2-12879771Robert Price05/2017
8294(2^264994+1714)/279771Stefano Morozzi01/2020
82973^167167-3479759Robert Price11/2013
8296(2^264952+3258)/279759Stefano Morozzi01/2020
829812^73906+2979758Lelio R Paula02/2015
82992^264934+25579754Lelio R Paula07/2013
83004*10^79729-8779730Robert Price03/2017
83012^264846-11170179727Enzo Doria05/2014
83022^264831-11204179723Enzo Doria06/2014
83032^264816-45579718Yves Minet03/2012
8304(55*10^79711+89)/979712Robert Price09/2017
830547^47667-4679704Theodore Burton02/2007
830613^71547+9679700Lelio R Paula03/2015
83072^264752-11288379699Enzo Doria06/2014
8308(2^264748+1978)/279697Stefano Morozzi01/2020
8309(185*10^79694-11)/379696Robert Price10/2020
83102^264732+13379693Lelio R Paula05/2012
83118*3^167010+779685Lelio R Paula06/2014
831242^49087-4179681Norbert Schneider06/2014
8313(26*10^79678-119)/379679Robert Price07/2016
83142^264683-2179678Lelio R Paula05/2012
83157^94279+1879675Lelio R Paula02/2015
83172^264655-12779670Lelio R Paula02/2012
8316(2^264658+3102)/279670Stefano Morozzi01/2020
8318(2^264637+1682)/279664Stefano Morozzi01/2020
83192^264597-45904379652Enzo Doria05/2015
8320(21*2^264566+1)/579643Lelio R Paula10/2012
83212^264536+187002179634Enzo Doria05/2016
8322(17*2^264512-1)/35979625Lelio R Paula02/2014
832319957^9762+9762^1995779620Hans Havermann03/2020
83242^264477-10978379616Enzo Doria04/2014
832518^63419-133379609Enzo Doria03/2013
832613^71451-3679593Lelio R Paula03/2015
832723314^2593+2593^2331479590Hans Havermann03/2020
8328(2^264410-5)/12800260912179585Lelio R Paula10/2012
832919^62234+9079582Lelio R Paula03/2015
8330(2^264276+2866)/279555Stefano Morozzi01/2020
833112^73714+4979551Lelio R Paula02/2015
8332(2^264213+1442)/279536Stefano Morozzi01/2020
8333(3*2^264184-1)/143333979522Lelio R Paula02/2014
8334(2^264160+1590)/279520Stefano Morozzi01/2020
8335(29*10^79510-107)/379511Robert Price08/2020
8336(9363^20021-1)/936279508Serge Batalov08/2020
83372^264103-11253179503Enzo Doria06/2014
833819^62170+7879501Lelio R Paula03/2015
833911^76340-258079500Enzo Doria12/2012
8340(2^264084+858)/279497Stefano Morozzi01/2020
8341(5652^21187-1)/565179495Serge Batalov08/2020
8342(23*10^79492-11)/379493Robert Price10/2015
8343((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
83442^264060-11213379490Enzo Doria06/2014
8346((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
834520158^8775+8775^2015879488Hans Havermann02/2020
83479^83298+6^83298-2^8329879487Mike Oakes08/2010
834818^63319+3579483Lelio R Paula02/2015
8349(10011^19867-1)/1001079474Serge Batalov08/2020
83502*10^79468+7779469Robert Price08/2020
835122479^3428+3428^2247979465Hans Havermann04/2020
835238303!2+25679461Robert Price01/2015
8353(29*10^79445+61)/979446Robert Price04/2015
83542^263902-19579443Lelio R Paula05/2012
83553^166499-11269679441Enzo Doria06/2014
835611^76279-276079437Enzo Doria12/2012
835718907^15894+15894^1890779433Hans Havermann03/2020
83586^102077-2579432Lelio R Paula03/2015
83592^263852-101779428Lelio R Paula07/2013
83602^263842-3379425Lelio R Paula05/2012
8361(2^263814+3582)/279416Stefano Morozzi01/2020
836212^73584-5579411Lelio R Paula02/2015
8363(2^263783+3558)/279407Stefano Morozzi01/2020
83642^263772-18579404Lelio R Paula05/2012
8365(15^67489+1)/1679373Paul Bourdelais03/2010
83662^263664+1501579371Lelio R Paula07/2013
8367(2^263643+1206)/279365Stefano Morozzi01/2020
8368(2^263642+3082)/279364Stefano Morozzi01/2020
8369(3319^22541-1)/331879364Serge Batalov08/2020
837010^79362+3^7936379363Mike Oakes06/2010
8371(2^263591+2910)/279349Stefano Morozzi01/2020
8372(2^263589+1922)/279348Stefano Morozzi01/2020
8373Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
83743^166262+4479328Lelio R Paula02/2015
83754*10^79327-6379328Robert Price12/2016
83762^263486+51379318Lelio R Paula07/2013
8377(2^263458+1282)/279309Stefano Morozzi01/2020
8378(2^263456+1558)/279308Stefano Morozzi01/2020
83792^263448-51950979306Paul Bourdelais03/2013
8380(18926^18541-1)/1892579297Serge Batalov08/2020
838169153^16384+279296Matt Stath01/2019
838221^59971-20^5997179295Robert Price05/2012
83832^263372+12379283Lelio R Paula05/2012
8384(2^263366+1974)/279281Stefano Morozzi01/2020
838517^64429+8479277Lelio R Paula03/2015
838611^76124-1143079275Enzo Doria12/2012
838719294^12845+12845^1929479274Hans Havermann03/2020
8388(206*10^79268-17)/979270Robert Price03/2017
838913^71157+1879265Lelio R Paula03/2015
83902^263297+6583579261Lelio R Paula07/2013
839119^61980-1879258Theodore Burton12/2005
8392(2^263259+2970)/279249Stefano Morozzi01/2020
83932*10^79242+9379243Robert Price07/2016
8394(2^263226+1074)/279239Stefano Morozzi01/2020
8395(88^40751-1)/8779238Paul Bourdelais08/2017
8396(103*29^54179-39)/479233Curtis Bright05/2015
83979^83024-83024^979226Norbert Schneider08/2017
839817^64382-2679219Lelio R Paula03/2015
83997^93733-7479214Lelio R Paula02/2015
840015^67352+3879213Lelio R Paula02/2015
84012^263135-11023579212Enzo Doria05/2014
8402(2^263080+3658)/279195Stefano Morozzi01/2020
84032^263044+425779185Lelio R Paula07/2013
8404(2^263039+3554)/279183Stefano Morozzi01/2020
84062^263032+8751779181Yves Minet11/2010
84056^101755+9579181Lelio R Paula03/2015
8407(2^263010+1738)/279174Stefano Morozzi01/2020
84084^131497-3^13149779170Jean-Louis Charton05/2004
84095*7^93674+879165Lelio R Paula10/2014
8410(2^262939+1326)/279153Stefano Morozzi01/2020
8411(2^262941+926)/279153Stefano Morozzi01/2020
8412lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
8413260^32768+179^3276879134Serge Batalov03/2018
841411^75978-4279123Lelio R Paula02/2015
84158*5^113180+979111Lelio R Paula10/2014
8416(2^262757+3222)/279098Stefano Morozzi01/2020
8417(6883*2^262741-1)/483579094Lelio R Paula04/2015
8418(9*2^262745+1)/13779093Lelio R Paula10/2012
841912^73285+8579088Lelio R Paula02/2015
842019^61840+5279079Lelio R Paula03/2015
8422(10^79067+77)/379067Robert Price01/2017
8421(2^262655+678)/279067Stefano Morozzi01/2020
8423(1017*2^262640-1)/1155779062Lelio R Paula04/2015
8424(2^262634+1674)/279061Stefano Morozzi01/2020
842510^79040+13794979041Patrick De Geest02/2016
842710^79040-100729779040Robert Price02/2015
842610^79040-7742779040Patrick De Geest02/2016
84282^262551-1729579036Lelio R Paula07/2013
8429(22973^18121-1)/2297279026Serge Batalov08/2020
84303^165597+34079010Lelio R Paula02/2015
843119620^10633+10633^1962079003Hans Havermann02/2020
8432(23*2^262435+1)/5579001Lelio R Paula10/2012
843311^75860-210079001Enzo Doria12/2012
84348*7^93463+978987Lelio R Paula10/2014
8435(2^262376+3942)/278983Stefano Morozzi01/2020
843667^43240-278960Lelio R Paula09/2013
84371000001^13159-1000000^1315978953Jean-Louis Charton10/2003
8438(2^262263+3410)/278949Stefano Morozzi01/2020
84392^262199-11028778930Enzo Doria05/2014
8440(19*2^262180-1)/17778924Lelio R Paula02/2014
8441(3^165403+4)/778917Lelio R Paula10/2012
84422^21068*(2^241076+1)-178914Makoto Morimoto03/2014
84432^29258*(2^232886+1)-178914Makoto Morimoto03/2014
84452^262144+1853178914Makoto Morimoto12/2015
84442^262144-23142578914Matthias Baur03/2020
8446(2^262137+1730)/278911Stefano Morozzi01/2020
8447(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
8448(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
844914^68837+7578897Lelio R Paula02/2015
8450(2^262055+1806)/278887Stefano Morozzi01/2020
8451(20450^18301-1)/2044978886Serge Batalov08/2020
8452(2^262049+1406)/278885Stefano Morozzi01/2020
8453106^38949+10578884Norbert Schneider12/2016
8454(2^262010+3778)/278873Stefano Morozzi01/2020
8455(14*10^78863-191)/378864Robert Price10/2020
845618683^16636+16636^1868378862Hans Havermann03/2020
8457(2^261964+1450)/278859Stefano Morozzi01/2020
845823288^2433+2433^2328878857Hans Havermann03/2020
8459(70^42737+1)/7178853Paul Bourdelais08/2017
8460(2^261919+2474)/278846Stefano Morozzi01/2020
8461(25*2^261917-1)/2092778842Lelio R Paula02/2014
84622^261881-185971378835Enzo Doria03/2016
84642^261874+191578832Lelio R Paula07/2013
8463(2^261872+1582)/278832Stefano Morozzi01/2020
84652^261856+9876533178827Jason Earls01/2009
8466(5*2^261857-1)/2050127778821Lelio R Paula02/2014
8467(10493^19603-1)/1049278818Serge Batalov08/2020
846824586^1605+1605^2458678810Hans Havermann02/2020
8469(2^261786+3538)/278806Stefano Morozzi01/2020
8470(2^261780+2290)/278804Stefano Morozzi01/2020
84712^261724+9269178787Tony Prest / Never Odd Or Even03/2014
84722^261724+28511178787Tony Prest / Never Odd Or Even04/2014
84732^261724+29371378787Tony Prest / Never Odd Or Even04/2014
8474(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
84752^261724+57297178787Tony Prest / Never Odd Or Even05/2014
8476(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
8477(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
8478(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
8479(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
8480(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
8481(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
8482(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
8483(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
8484(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
848519473^11110+11110^1947378783Hans Havermann04/2020
8486(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
8487(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
8488(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
8489(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
8490(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
8491(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
8492(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
8493(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
8494(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
8495(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
8496(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
8497(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
8498(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
8499(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
8500(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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