PRP Records

Probable Primes Top 10000

(288949 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 ?
925111^80096-183083412Enzo Doria12/2012
92523^174801+5683402Lelio R Paula12/2015
92532^277033-11197383396Enzo Doria05/2014
9254120^40105-11983386Norbert Schneider09/2018
9255(2^276992+2046)/283383Stefano Morozzi01/2020
9256(2^276990+474)/283382Stefano Morozzi01/2020
925720519^11572+11572^2051983378Hans Havermann03/2017
925820850^9971+9971^2085083374Hans Havermann03/2017
92616^107122-1886383358Enzo Doria03/2013
9259(2^276908+2322)/283358Stefano Morozzi01/2020
9260(2^276910+2734)/283358Stefano Morozzi01/2020
92624*10^83354-8983355Robert Price08/2017
92633^174697-3483352Robert Price11/2013
9264(9787*2^276855-1)/234583343Lelio R Paula04/2015
9265(2^276860+1678)/283343Stefano Morozzi01/2020
9266(2^276841+3354)/283338Stefano Morozzi01/2020
92682^276825+7522783333Enzo Doria04/2016
926734*10^83331-983333Robert Price06/2020
92695^119214+8483328Lelio R Paula10/2015
92702^276803-15983327Lelio R Paula06/2012
9271(13*10^83313+137)/383314Robert Price06/2021
9272(3*2^276753-1)/2583311Lelio R Paula02/2014
92737*10^83297-3983298Robert Price07/2020
9274114^40495+40495^11483295Norbert Schneider12/2014
927539967!2+102483282Robert Price02/2015
9276(1894^25411-1)/189383279Serge Batalov08/2020
92782^276641+5783278Lelio R Paula06/2012
927935^53934-341483278Enzo Doria03/2013
927721777^6670+6670^2177783278Hans Havermann06/2020
9280(2^276655+78557)/36542583276Lelio R Paula12/2012
92812^276615-403583270Lelio R Paula08/2013
92822^276588+115583262Lelio R Paula08/2013
92832^276587-93783261Yves Minet10/2009
92842^276584-11318383261Enzo Doria07/2014
9285(2^276592-1017)/1384373983256Lelio R Paula12/2012
92862^276547-10959183249Enzo Doria04/2014
928713^74733-3283249Lelio R Paula11/2015
92882^276523-258783242Yves Minet07/2014
928918^66311-4383239Lelio R Paula11/2015
929011^79919-153083228Enzo Doria12/2012
92912^276468-10974583226Enzo Doria04/2014
92922^276462+538583224Lelio R Paula08/2013
92933*10^83219-1783220Robert Price03/2021
9294(9787*2^276422-1)/383215Lelio R Paula04/2015
92962^276391-1583202Lelio R Paula06/2012
9295(4*10^83201+173)/383202Robert Price01/2017
9297(259*10^83186-1)/383188Robert Price12/2020
9298(2^276327+534)/283183Stefano Morozzi01/2020
92992^276316-10965583180Enzo Doria04/2014
93002^276305-11206383177Enzo Doria06/2014
9301(2^276296+3406)/283174Stefano Morozzi01/2020
9302(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
9303(2^276277+3254)/283168Stefano Morozzi01/2020
930474913!4-283161Robert Price07/2017
9305(3023^23893-1)/302283155Serge Batalov08/2020
93062^276227-183720783153Enzo Doria05/2015
9307(2^276227+3)/783152Lelio R Paula12/2012
9308(2^276229+12)/2883152Stefano Morozzi03/2020
9309(2^276205+1190)/283146Stefano Morozzi01/2020
93102^276184-6338983140Paul Bourdelais02/2012
9311(2^276165+2046)/283134Stefano Morozzi01/2020
9312(2^276105+1274)/283116Stefano Morozzi01/2020
93132^276066-11160383105Enzo Doria05/2014
931419438^18837+18837^1943883098Hans Havermann07/2020
9315(431^31543-1)/43083097Serge Batalov08/2020
9316(2^276028-3)*6-783094Gilbert Mozzo09/2016
9317(85*10^83080-139)/983081Robert Price08/2021
9318(26*10^83067+79)/383068Robert Price09/2020
93192^275926-469183063Yves Minet05/2019
9320(2^275919+1386)/283060Stefano Morozzi01/2020
9321(2^275897+9)/115383051Lelio R Paula12/2012
93222^275879-10980783048Enzo Doria04/2014
9324F(397379)83047Henri Lifchitz08/2003
9323U(397379)83047Serge Batalov03/2015
93253^174040-1483039Robert Price08/2013
9326(86*10^83038-221)/983039Robert Price06/2017
932721632^6897+6897^2163283038Hans Havermann05/2020
93282^275841-688383037Lelio R Paula07/2011
932919610^17127+17127^1961083023Hans Havermann06/2020
93303^174002-14083021Lelio R Paula12/2015
93316^106681+7783014Lelio R Paula12/2015
9332187^36539-283011Lelio R Paula10/2017
93331036^27529+27529^103683010Norbert Schneider03/2020
933411^79701-315083001Enzo Doria12/2012
9335(2^275721+1554)/283000Stefano Morozzi01/2020
9336(2^275704+1858)/282995Stefano Morozzi01/2020
9337(2^275696+1726)/282993Stefano Morozzi01/2020
9338(22*10^82988-43)/382989Robert Price10/2021
9339(55459*2^275657+1)/2182985Lelio R Paula06/2014
9340(7*10^82960-457)/982960Robert Price09/2017
93412^275535-685582945Lelio R Paula08/2013
93423^173828-1482938Robert Price08/2013
93432^275512-10967782938Enzo Doria04/2014
9344(2^275450+1698)/282919Stefano Morozzi01/2020
93452^275446-11004582918Enzo Doria04/2014
9346(2^275473+47)/2952609744782916Lelio R Paula12/2012
93473*10^82914-8382915Robert Price02/2021
93483^173755-1482903Robert Price08/2013
9349(182*10^82898+43)/982900Robert Price11/2017
9350(86*10^82897+103)/982898Robert Price12/2021
93512^275363-11230982893Enzo Doria06/2014
935261^46427-6082888Norbert Schneider10/2014
93533*10^82880-7^8288082881Mike Oakes02/2010
93542^275290+9019582871Lelio R Paula07/2013
9355(35*10^82870-71)/982871Robert Price05/2015
93562^275270-185962182865Enzo Doria03/2016
93572^275259+8182862Henri Lifchitz01/2007
935821436^7335+7335^2143682859Hans Havermann05/2020
9359(2^275247+1590)/282858Stefano Morozzi01/2020
936022515^4784+4784^2251582851Hans Havermann05/2020
93616*10^82842-3182843Robert Price07/2020
9362(10013^20707-1)/1001282836Serge Batalov08/2020
9363(113703^16384+1)/282834Richard Fischer04/2018
9364(2^275146+954)/282827Stefano Morozzi01/2020
93657^98003+98003^7+182823Robert Price05/2014
9366(2^275101+3566)/282814Stefano Morozzi01/2020
9367(2^275050+3150)/282798Stefano Morozzi01/2020
9368(2^275044+2482)/282797Stefano Morozzi01/2020
936910^82790+12604382791Patrick De Geest07/2013
937010^82790-4782790Robert Price05/2011
937120762^9711+9711^2076282784Hans Havermann05/2020
93722^274985-11266382779Enzo Doria06/2014
93732^274935+1501582764Lelio R Paula07/2013
9374(17*2^274922+1)/382761Lelio R Paula12/2012
9375[(55^5)^9511-(22434^2)^9511]/1982759Richard Fischer11/2019
9376(43*10^82752-61)/982753Robert Price06/2015
9377(3*2^274862+1)/102782740Lelio R Paula12/2012
9378(2^274851+3126)/282739Stefano Morozzi01/2020
9379(31*2^274848-1)/406582736Lelio R Paula02/2014
9380(4^137405+23)/382726Robert Price02/2017
9381(2^274798+414)/282723Stefano Morozzi01/2020
93822^274791-11049182721Enzo Doria05/2014
9383(11*2^274776-1)/9582715Lelio R Paula02/2014
9384(47*10^82706-119)/982707Robert Price09/2017
93852^274704-11139582695Enzo Doria05/2014
93862^274686-391182689Yves Minet04/2017
9387(1629^25741-1)/162882675Serge Batalov08/2020
938821474^7075+7075^2147482670Hans Havermann06/2020
9389(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
9390(3^173263-5)/1449882664Lelio R Paula12/2012
939120488^10815+10815^2048882650Hans Havermann07/2020
9392(2^274554+894)/282649Stefano Morozzi01/2020
93942^274511-6487582637Lelio R Paula08/2013
9393(2^274512+1222)/282637Stefano Morozzi01/2020
939512^76572-8382636Lelio R Paula11/2015
93963^173191-2^17319182634Mike Oakes02/2004
9397(2^274500+2970)/282633Stefano Morozzi01/2020
939820507^10698+10698^2050782629Hans Havermann07/2020
93992^274464-23831982622Harrison Mesh10/2021
9400(2^274429+3726)/282612Stefano Morozzi01/2020
940114^72072-1582604Lelio R Paula11/2015
9402(2^274374+2950)/282595Stefano Morozzi01/2020
9403(55459*2^274339+1)/382589Lelio R Paula06/2014
94042^274351+12382588Lelio R Paula06/2012
9405(1017*2^274339-1)/351582584Lelio R Paula04/2015
940621208^7833+7833^2120882583Hans Havermann07/2020
9407(2^274248+750)/282557Stefano Morozzi01/2020
9408(2^274240+822)/282555Stefano Morozzi01/2020
94096^106086+11382551Lelio R Paula12/2015
9410(17*10^82540-377)/982541Robert Price11/2017
9411(3470^23311-1)/346982526Serge Batalov08/2020
9412(7*10^82517+173)/982517Robert Price01/2022
94132^274093-5869582511Lelio R Paula07/2013
94147*10^82509-4782510Robert Price02/2017
94152^274081-655582507Lelio R Paula07/2013
94172^274074-274074+182505Robert Price10/2014
941814^71985+4782505Lelio R Paula11/2015
94165*10^82504+2182505Robert Price01/2017
9419(2^274062+498)/282501Stefano Morozzi01/2020
94206^106014-13982495Lelio R Paula12/2015
9421(2^274046+47)/75382494Lelio R Paula12/2012
94222^274008-183809982485Enzo Doria05/2015
94232^273981-11002982477Enzo Doria04/2014
942419^64490-3082467Lelio R Paula12/2015
9425(2^273864+3150)/282441Stefano Morozzi01/2020
942621328^7333+7333^2132882439Hans Havermann07/2020
942720829^9070+9070^2082982434Hans Havermann07/2020
94292^273785+1171582418Lelio R Paula07/2013
94308*10^82417+5182418Robert Price05/2017
9428(2^273786+2242)/282418Stefano Morozzi01/2020
943111^79133-1082409Theodore Burton11/2005
9432(2^273752+1882)/282408Stefano Morozzi01/2020
943391^42063+9082404Norbert Schneider01/2016
943410140^20567-20567^1014082393Norbert Schneider11/2021
94362^273662-6382381Lelio R Paula06/2012
94352^273661+25582381Lelio R Paula07/2013
9437(62*10^82377-17)/982378Robert Price09/2015
94382^273608+52428782365Paul Underwood08/2018
94398*10^82360-5182361Robert Price10/2017
9440(79*10^82347-1)/382349Robert Price11/2017
9441(11*10^82323+91)/382323Robert Price02/2017
9442(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
9443(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
944415^69984+3282308Lelio R Paula11/2015
94459*6^105746+782288Lelio R Paula10/2014
944689^42211-8882286Norbert Schneider01/2016
9447gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
944820596^9883+9883^2059682279Hans Havermann06/2020
9449(19*10^82270-43)/382271Robert Price10/2017
94502^273282-11024182267Enzo Doria05/2014
9451(2^273277+3746)/282265Stefano Morozzi01/2020
9452(13^73849+4^73849)/1782263Robert Price05/2013
945410^82254+9^(82254+1)82255Robert Price08/2016
945310^82254+45777382255Patrick De Geest12/2016
945510^82254-9960982254Patrick De Geest12/2016
9456(754*10^82250-7)/982252Robert Price11/2017
945718^65524+1382251Lelio R Paula11/2015
94582^273206-10782244Lelio R Paula06/2012
94592^273193-45914582240Enzo Doria05/2015
94612^273126+3693782220Yves Minet06/2010
946039505!2+12882220Robert Price03/2015
9462(2^273090+2214)/282208Stefano Morozzi01/2020
94632^273053-11211182198Enzo Doria06/2014
9464(2^273052+3138)/282197Stefano Morozzi01/2020
94652^273016+118582187Lelio R Paula07/2013
9466(2^273008+3)/782183Lelio R Paula12/2012
9467(2^272992+2230)/282179Stefano Morozzi01/2020
94695^117554-1538682167Enzo Doria02/2013
946821158^7647+7647^2115882167Hans Havermann06/2020
947020194^11715+11715^2019482165Hans Havermann06/2020
9471(38*10^82161+403)/982162Robert Price11/2017
94722^272907-11143982154Enzo Doria05/2014
9473(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
94742^272875-6982144Lelio R Paula06/2012
9475(3997^22807-1)/399682142Serge Batalov08/2020
94767^97197+482141Robert Price01/2014
9477(4*6^105554+1)/582137Serge Batalov10/2014
94782^272826-443382129Yves Minet03/2019
94796^105531-10982120Lelio R Paula12/2015
94802^272766-6582111Lelio R Paula06/2012
948119^64205-7882103Lelio R Paula12/2015
94822^272702+186997982092Enzo Doria05/2016
9483(29*2^272687-1)/982088Lelio R Paula02/2014
9484(5*10^82085-119)/382086Robert Price04/2016
9485(2^272665+1334)/282081Stefano Morozzi01/2020
94862^272660-11004982079Enzo Doria04/2014
94876^105474+6782075Lelio R Paula12/2015
94882^272637+8287582072Lelio R Paula07/2013
9489(6330^21589-1)/632982065Serge Batalov08/2020
94902^272587-3182057Lelio R Paula06/2012
9491(1969^24907-1)/196882047Serge Batalov08/2020
9493(41*10^82044-59)/982045Robert Price10/2017
949292*10^82043-982045Robert Price12/2021
94948*5^117368+982038Lelio R Paula10/2014
9495(101525^16384+1)/13107482023Lelio R Paula11/2011
94964*5^117343-782020Lelio R Paula10/2014
9497(2^272381+506)/281995Stefano Morozzi01/2020
9498(265*10^81990+17)/381992Robert Price05/2016
94993^171843+1081990Robert Price10/2013
9500(2^272361+3762)/281989Stefano Morozzi01/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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