PRP Records

Probable Primes Top 10000

(280932 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 ?
8751(197*10^80089-11)/380091Robert Price10/2017
87522^265998+7555980074Enzo Doria04/2016
8753(2^265999+3290)/280074Stefano Morozzi01/2020
87542^265969-10980180065Enzo Doria04/2014
8755(2^265956+3378)/280061Stefano Morozzi01/2020
8756(185*10^80051-11)/380053Robert Price10/2020
87572^265888-11275780041Enzo Doria06/2014
8758(24847^18211-1)/2484680038Serge Batalov08/2020
87592^265809+170180017Lelio R Paula07/2013
8760gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
876119807^10954+10954^1980780012Hans Havermann04/2020
87623^167687-10480008Lelio R Paula02/2015
876311^76826-579080007Enzo Doria01/2013
876410^80000+8573180001Patrick De Geest10/2009
876510^80000-716980000Patrick De Geest09/2009
876610^79999+2239980000Patrick De Geest09/2009
876710^79999-7487379999Patrick De Geest09/2009
87683^167668+5879998Lelio R Paula02/2015
8769(59*10^79995+391)/979996Robert Price03/2021
8770(2^265728+3742)/279992Stefano Morozzi01/2020
877118780^18137+18137^1878079976Hans Havermann04/2020
877219190^14709+14709^1919079976Hans Havermann04/2020
8773155^36506-279961Lelio R Paula10/2017
8774(2^265621+3882)/279960Stefano Morozzi01/2020
87762^265612+425779958Lelio R Paula07/2013
8775(2^265613+1470)/279958Stefano Morozzi01/2020
87775*3^167577+479956Lelio R Paula06/2014
8778(9179*2^265593-1)/979955Lelio R Paula04/2015
87796^102723-4379935Lelio R Paula04/2015
878021052^6261+6261^2105279927Hans Havermann03/2020
878111^76748-336079925Enzo Doria12/2012
878219430^12981+12981^1943079922Hans Havermann03/2020
8783(2^265490+870)/279921Stefano Morozzi01/2020
8784(13*2^265498-1)/18711979919Lelio R Paula02/2014
8785(2^265438+3978)/279905Stefano Morozzi01/2020
8786(2^265409+1250)/279896Stefano Morozzi01/2020
87872^265399-10985579894Enzo Doria04/2014
8788(2^265380+3930)/279888Stefano Morozzi01/2020
8789(20^61403-1)/1979886Paul Bourdelais03/2010
8790(2^265368+2970)/279884Stefano Morozzi01/2020
879118^63635+5979880Lelio R Paula02/2015
8792(11*10^79867-107)/379868Robert Price11/2016
87933^167375+8079859Lelio R Paula02/2015
87945^114240-1448679851Enzo Doria02/2013
879549^47238+4879842Norbert Schneider07/2014
87962^265212-377979837Yves Minet04/2017
8797(2^265201+2790)/279834Stefano Morozzi01/2020
879891^40746+40746^9179824Norbert Schneider12/2014
8799(68*10^79813-257)/979814Robert Price06/2017
8800(13063^19391-1)/1306279811Serge Batalov08/2020
8801(5*2^265118-1)/6179808Lelio R Paula02/2014
8802(2^265102+1462)/279804Stefano Morozzi01/2020
88032^265074+2842579796Lelio R Paula07/2013
88042^265072+118579795Lelio R Paula07/2013
8806p(16682)#/2-12879771Robert Price05/2017
8805(2^264994+1714)/279771Stefano Morozzi01/2020
88083^167167-3479759Robert Price11/2013
8807(2^264952+3258)/279759Stefano Morozzi01/2020
880912^73906+2979758Lelio R Paula02/2015
88102^264934+25579754Lelio R Paula07/2013
88114*10^79729-8779730Robert Price03/2017
88122^264846-11170179727Enzo Doria05/2014
88132^264831-11204179723Enzo Doria06/2014
88142^264816-45579718Yves Minet03/2012
8815(55*10^79711+89)/979712Robert Price09/2017
881647^47667-4679704Theodore Burton02/2007
881713^71547+9679700Lelio R Paula03/2015
88182^264752-11288379699Enzo Doria06/2014
8819(2^264748+1978)/279697Stefano Morozzi01/2020
8820(185*10^79694-11)/379696Robert Price10/2020
88212^264732+13379693Lelio R Paula05/2012
88228*3^167010+779685Lelio R Paula06/2014
882342^49087-4179681Norbert Schneider06/2014
8824(26*10^79678-119)/379679Robert Price07/2016
88252^264683-2179678Lelio R Paula05/2012
88267^94279+1879675Lelio R Paula02/2015
88282^264655-12779670Lelio R Paula02/2012
8827(2^264658+3102)/279670Stefano Morozzi01/2020
8829(2^264637+1682)/279664Stefano Morozzi01/2020
88302^264597-45904379652Enzo Doria05/2015
8831(21*2^264566+1)/579643Lelio R Paula10/2012
88322^264536+187002179634Enzo Doria05/2016
8833(17*2^264512-1)/35979625Lelio R Paula02/2014
883419957^9762+9762^1995779620Hans Havermann03/2020
88352^264477-10978379616Enzo Doria04/2014
883618^63419-133379609Enzo Doria03/2013
883713^71451-3679593Lelio R Paula03/2015
883823314^2593+2593^2331479590Hans Havermann03/2020
8839(2^264410-5)/12800260912179585Lelio R Paula10/2012
884019^62234+9079582Lelio R Paula03/2015
8841(2^264276+2866)/279555Stefano Morozzi01/2020
884212^73714+4979551Lelio R Paula02/2015
8843(2^264213+1442)/279536Stefano Morozzi01/2020
8844(3*2^264184-1)/143333979522Lelio R Paula02/2014
8845(2^264160+1590)/279520Stefano Morozzi01/2020
8846(29*10^79510-107)/379511Robert Price08/2020
8847(9363^20021-1)/936279508Serge Batalov08/2020
88482^264103-11253179503Enzo Doria06/2014
884919^62170+7879501Lelio R Paula03/2015
8850((10^(4*19875)-1)/9999)*18880+179501Matt Stath01/2021
885111^76340-258079500Enzo Doria12/2012
8852(2^264084+858)/279497Stefano Morozzi01/2020
8853(5652^21187-1)/565179495Serge Batalov08/2020
8854(23*10^79492-11)/379493Robert Price10/2015
8855((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
88562^264060-11213379490Enzo Doria06/2014
8857((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
885820158^8775+8775^2015879488Hans Havermann02/2020
88599^83298+6^83298-2^8329879487Mike Oakes08/2010
886018^63319+3579483Lelio R Paula02/2015
8861(10011^19867-1)/1001079474Serge Batalov08/2020
88622*10^79468+7779469Robert Price08/2020
886322479^3428+3428^2247979465Hans Havermann04/2020
886438303!2+25679461Robert Price01/2015
8865(29*10^79445+61)/979446Robert Price04/2015
88662^263902-19579443Lelio R Paula05/2012
88673^166499-11269679441Enzo Doria06/2014
886811^76279-276079437Enzo Doria12/2012
886918907^15894+15894^1890779433Hans Havermann03/2020
88706^102077-2579432Lelio R Paula03/2015
88712^263852-101779428Lelio R Paula07/2013
88722^263842-3379425Lelio R Paula05/2012
8873(2^263814+3582)/279416Stefano Morozzi01/2020
887412^73584-5579411Lelio R Paula02/2015
8875(2^263783+3558)/279407Stefano Morozzi01/2020
88762^263772-18579404Lelio R Paula05/2012
8877(15^67489+1)/1679373Paul Bourdelais03/2010
88782^263664+1501579371Lelio R Paula07/2013
8879(2^263643+1206)/279365Stefano Morozzi01/2020
8880(2^263642+3082)/279364Stefano Morozzi01/2020
8881(3319^22541-1)/331879364Serge Batalov08/2020
888210^79362+3^7936379363Mike Oakes06/2010
8883(2^263591+2910)/279349Stefano Morozzi01/2020
8884(2^263589+1922)/279348Stefano Morozzi01/2020
8885Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
88863^166262+4479328Lelio R Paula02/2015
88874*10^79327-6379328Robert Price12/2016
88882^263486+51379318Lelio R Paula07/2013
8889(2^263458+1282)/279309Stefano Morozzi01/2020
8890(2^263456+1558)/279308Stefano Morozzi01/2020
88912^263448-51950979306Paul Bourdelais03/2013
8892(18926^18541-1)/1892579297Serge Batalov08/2020
889369153^16384+279296Matt Stath01/2019
889421^59971-20^5997179295Robert Price05/2012
88952^263372+12379283Lelio R Paula05/2012
8896(2^263366+1974)/279281Stefano Morozzi01/2020
889717^64429+8479277Lelio R Paula03/2015
889811^76124-1143079275Enzo Doria12/2012
889919294^12845+12845^1929479274Hans Havermann03/2020
8900(206*10^79268-17)/979270Robert Price03/2017
890113^71157+1879265Lelio R Paula03/2015
89022^263297+6583579261Lelio R Paula07/2013
890319^61980-1879258Theodore Burton12/2005
8904(2^263259+2970)/279249Stefano Morozzi01/2020
89052*10^79242+9379243Robert Price07/2016
8906(2^263226+1074)/279239Stefano Morozzi01/2020
8907(88^40751-1)/8779238Paul Bourdelais08/2017
8908(103*29^54179-39)/479233Curtis Bright05/2015
89099^83024-83024^979226Norbert Schneider08/2017
891017^64382-2679219Lelio R Paula03/2015
89117^93733-7479214Lelio R Paula02/2015
891215^67352+3879213Lelio R Paula02/2015
89132^263135-11023579212Enzo Doria05/2014
8914(2^263080+3658)/279195Stefano Morozzi01/2020
89152^263044+425779185Lelio R Paula07/2013
8916(2^263039+3554)/279183Stefano Morozzi01/2020
89182^263032+8751779181Yves Minet11/2010
89176^101755+9579181Lelio R Paula03/2015
8919(2^263010+1738)/279174Stefano Morozzi01/2020
89204^131497-3^13149779170Jean-Louis Charton05/2004
89215*7^93674+879165Lelio R Paula10/2014
8922(2^262939+1326)/279153Stefano Morozzi01/2020
8923(2^262941+926)/279153Stefano Morozzi01/2020
8924lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
8925260^32768+179^3276879134Serge Batalov03/2018
892611^75978-4279123Lelio R Paula02/2015
89278*5^113180+979111Lelio R Paula10/2014
8928(2^262757+3222)/279098Stefano Morozzi01/2020
8929(6883*2^262741-1)/483579094Lelio R Paula04/2015
8930(9*2^262745+1)/13779093Lelio R Paula10/2012
893112^73285+8579088Lelio R Paula02/2015
893219^61840+5279079Lelio R Paula03/2015
8934(10^79067+77)/379067Robert Price01/2017
8933(2^262655+678)/279067Stefano Morozzi01/2020
8935(1017*2^262640-1)/1155779062Lelio R Paula04/2015
8936(2^262634+1674)/279061Stefano Morozzi01/2020
893710^79040+13794979041Patrick De Geest02/2016
893910^79040-100729779040Robert Price02/2015
893810^79040-7742779040Patrick De Geest02/2016
89402^262551-1729579036Lelio R Paula07/2013
8941(22973^18121-1)/2297279026Serge Batalov08/2020
89423^165597+34079010Lelio R Paula02/2015
894319620^10633+10633^1962079003Hans Havermann02/2020
8944(23*2^262435+1)/5579001Lelio R Paula10/2012
894511^75860-210079001Enzo Doria12/2012
89468*7^93463+978987Lelio R Paula10/2014
8947(2^262376+3942)/278983Stefano Morozzi01/2020
894867^43240-278960Lelio R Paula09/2013
89491000001^13159-1000000^1315978953Jean-Louis Charton10/2003
8950(2^262263+3410)/278949Stefano Morozzi01/2020
89512^262199-11028778930Enzo Doria05/2014
8952(19*2^262180-1)/17778924Lelio R Paula02/2014
8953(3^165403+4)/778917Lelio R Paula10/2012
89542^21068*(2^241076+1)-178914Makoto Morimoto03/2014
89552^29258*(2^232886+1)-178914Makoto Morimoto03/2014
89572^262144+1853178914Makoto Morimoto12/2015
89562^262144-23142578914Matthias Baur03/2020
8958(2^262137+1730)/278911Stefano Morozzi01/2020
8959(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
8960(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
896114^68837+7578897Lelio R Paula02/2015
8962(2^262055+1806)/278887Stefano Morozzi01/2020
8963(20450^18301-1)/2044978886Serge Batalov08/2020
8964(2^262049+1406)/278885Stefano Morozzi01/2020
8965106^38949+10578884Norbert Schneider12/2016
8966(2^262010+3778)/278873Stefano Morozzi01/2020
8967(14*10^78863-191)/378864Robert Price10/2020
896818683^16636+16636^1868378862Hans Havermann03/2020
8969(2^261964+1450)/278859Stefano Morozzi01/2020
897023288^2433+2433^2328878857Hans Havermann03/2020
8971(70^42737+1)/7178853Paul Bourdelais08/2017
8972(2^261919+2474)/278846Stefano Morozzi01/2020
8973(25*2^261917-1)/2092778842Lelio R Paula02/2014
89742^261881-185971378835Enzo Doria03/2016
89762^261874+191578832Lelio R Paula07/2013
8975(2^261872+1582)/278832Stefano Morozzi01/2020
89772^261856+9876533178827Jason Earls01/2009
8978(5*2^261857-1)/2050127778821Lelio R Paula02/2014
8979(10493^19603-1)/1049278818Serge Batalov08/2020
898024586^1605+1605^2458678810Hans Havermann02/2020
8981(2^261786+3538)/278806Stefano Morozzi01/2020
8982(2^261780+2290)/278804Stefano Morozzi01/2020
89832^261724+9269178787Tony Prest / Never Odd Or Even03/2014
89842^261724+28511178787Tony Prest / Never Odd Or Even04/2014
89852^261724+29371378787Tony Prest / Never Odd Or Even04/2014
8986(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
89872^261724+57297178787Tony Prest / Never Odd Or Even05/2014
8988(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
8989(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
8990(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
8991(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
8992(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
8993(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
8994(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
8995(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
8996(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
899719473^11110+11110^1947378783Hans Havermann04/2020
8998(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
8999(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
9000(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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