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 ?
8001(2^280405+746)/284411Stefano Morozzi01/2020
8003(19*10^84409-61)/384410Robert Price04/2017
800220862^11119+11119^2086284410Hans Havermann07/2020
80042^280388+11784406Lelio R Paula08/2012
80052^280389-56653384406Paul Bourdelais03/2013
800623423^4008+4008^2342384392Hans Havermann07/2020
8007(2^280340+3322)/284391Stefano Morozzi01/2020
8008(141584^16384+1)/6553784390Syoichiro Yamada06/2008
8009(1897^25741-1)/189684378Serge Batalov08/2020
8011119^40652+11884376Norbert Schneider09/2018
8010(2^280291+2274)/284376Stefano Morozzi01/2020
80122^280240-17384361Lelio R Paula08/2012
8013(184*10^84348-1)/384350Robert Price02/2017
801421068^10083+10083^2106884348Hans Havermann07/2020
80154*10^84346+9384347Robert Price01/2017
80167*2^280156-584337Lelio R Paula08/2014
8017(8760^21391-1)/875984331Serge Batalov08/2020
80188*7^99782-384327Lelio R Paula10/2014
80192^280116+13384324Lelio R Paula08/2012
80202^280118+5461584324Lelio R Paula09/2013
8021(509203*2^280090-1)/384321Lelio R Paula04/2015
80226^108354+4784316Lelio R Paula12/2015
8023(2^280069+462)/284309Stefano Morozzi01/2020
802420657^12058+12058^2065784307Hans Havermann07/2020
802510^84305+14196384306Patrick De Geest07/2013
802610^84305-5784305Robert Price05/2011
80279^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
802875843!4-3284295Robert Price11/2019
80293^176648-11280484283Enzo Doria06/2014
80306^108310+11584282Lelio R Paula12/2015
8031(11*2^279968-1)/584280Lelio R Paula02/2014
80326^108288-1664384265Enzo Doria02/2013
80332^279917-5869584264Lelio R Paula08/2013
803465^46477+3684259Lelio R Paula01/2016
8035(2^279883+3230)/284253Stefano Morozzi01/2020
8036(2^279876+1422)/284251Stefano Morozzi01/2020
80372^279866-190784249Yves Minet05/2013
803823140^4373+4373^2314084248Hans Havermann07/2020
803919736^18567+18567^1973684248Hans Havermann07/2020
8041(3^176580-5)/2807684246Lelio R Paula12/2012
8040(p(17530)#+4)/284246Robert Price09/2017
8042(2*10^84239+1)/384239Serge Batalov07/2009
804418^67103-4184233Lelio R Paula11/2015
804320^64743-4384233Lelio R Paula01/2016
8045(2^279807+2454)/284230Stefano Morozzi01/2020
804619717^18672+18672^1971784216Hans Havermann07/2020
8047(2^279754+3574)/284215Stefano Morozzi01/2020
8048143^39070+39070^14384209Serge Batalov05/2014
804911^80857-540084204Enzo Doria01/2013
8050(2^279642+3130)/284181Stefano Morozzi01/2020
8051(13*10^84179+161)/384180Robert Price04/2017
80522^279634-11040584179Enzo Doria05/2014
8053(74*10^84170+313)/984171Robert Price11/2017
80542^279582-101784163Lelio R Paula08/2013
8055(22*10^84159-19)/384160Robert Price02/2017
8056p(17513)#/2+51284156Robert Price05/2017
8057(19*10^84144-43)/384145Robert Price10/2017
8058(9*2^279507-1)/13784139Lelio R Paula02/2014
805911^80792-81084137Enzo Doria11/2012
8060(97*10^84134-1)/384136Serge Batalov12/2014
8061p(17507)#/2+3284125Robert Price12/2016
8062(1750^25939-1)/174984118Serge Batalov08/2020
806321485^8224+8224^2148584116Hans Havermann04/2017
80643^176294-34084114Lelio R Paula12/2015
8065(3^176287+4)/219184107Lelio R Paula12/2012
80662^279388-71984105Yves Minet05/2012
8067(22699*2^279378+1)/22184104Lelio R Paula06/2014
8068(28*10^84095-67)/384096Robert Price10/2020
8069(2^279343+578)/284091Stefano Morozzi01/2020
80702^279332-11044784088Enzo Doria05/2014
80712^279320+784084Lelio R Paula06/2012
8072127^39966-284081Lelio R Paula10/2017
8073(2^279299+2490)/284078Stefano Morozzi01/2020
8074(2^279301+1694)/284078Stefano Morozzi01/2020
8075(2^279285+962)/284073Stefano Morozzi01/2020
8076(2^279269+1122)/284069Stefano Morozzi01/2020
8077(11*2^279240-1)/9584059Lelio R Paula02/2014
80782^279218-11134784053Enzo Doria05/2014
807935^54435+284052Lelio R Paula05/2013
8080(2^279176+2998)/284041Stefano Morozzi01/2020
8081(31*2^279191-1)/1251152384040Lelio R Paula02/2014
808220996^10059+10059^2099684038Hans Havermann05/2017
808397*10^84033-384035Robert Price01/2017
8084(2^279153+1326)/284034Stefano Morozzi01/2020
8085(2^279155+3534)/284034Stefano Morozzi01/2020
808621234^9067+9067^2123484033Hans Havermann05/2017
8087(134569^16384+1)/284033Richard Fischer06/2018
8088(5858^22303-1)/585784029Serge Batalov08/2020
80892^279095-10971784016Enzo Doria04/2014
8090(2^279054+1438)/284004Stefano Morozzi01/2020
809110^83997+55559783998Patrick De Geest02/2021
809210^83997-4000183997Robert Price01/2021
809314^73282-9983991Lelio R Paula11/2015
809421457^8200+8200^2145783979Hans Havermann06/2017
809589*10^83976-783978Robert Price03/2017
80962^278955+17383974Lelio R Paula06/2012
8097(7*2^278851+1)/3983942Lelio R Paula12/2012
8098(9913*2^278844-1)/4080383940Lelio R Paula04/2015
80995^120076-1484683930Enzo Doria02/2013
8100(85*10^83921-1)/383923Robert Price07/2017
8101(2^278770-3)/2383917Lelio R Paula12/2012
8102(10^83916+449)/983916Serge Batalov12/2014
81042^278715+9983902Lelio R Paula06/2012
8103(132109^16384+1)/283902Richard Fischer05/2018
810540235!2-2^4023583899Robert Price09/2015
81062^278698-17183897Lelio R Paula06/2012
8107(19*10^83894-43)/383895Robert Price10/2017
81086^107802+2583887Lelio R Paula12/2015
81098*10^83880+3983881Robert Price01/2017
8110(58*10^83878+23)/983879Robert Price09/2015
81117^99244-9083871Lelio R Paula10/2015
8112(2^278601+1674)/283867Stefano Morozzi01/2020
81132^278554+425783854Lelio R Paula08/2013
81142^278504-10961983839Enzo Doria04/2014
81152^278499+187043383837Enzo Doria05/2016
8116(2^278487+570)/283833Stefano Morozzi01/2020
8117105^41475+10483829Norbert Schneider11/2016
811815^71276-6883828Lelio R Paula11/2015
81192^278464-21641383827Enzo Doria04/2013
8120(2^278440+1602)/283819Stefano Morozzi01/2020
8121(76*10^83816-211)/983817Robert Price10/2017
8122(2^278429+1950)/283816Stefano Morozzi01/2020
8123(2^278428+1750)/283815Stefano Morozzi01/2020
8124(8*10^83811-101)/383812Robert Price10/2017
81252^278400+4075583807Lelio R Paula08/2013
8126(2^278394+3718)/283805Stefano Morozzi01/2020
8127(2^278388+3586)/283803Stefano Morozzi01/2020
8128(9*2^278381-1)/783802Lelio R Paula02/2014
81293*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
813019551^19268+19268^1955183773Hans Havermann05/2017
813120625^11522+11522^2062583770Hans Havermann05/2017
8132(44*10^83768-791)/983769Robert Price10/2017
8133(87^43189+1)/8883764Paul Bourdelais08/2017
81342^278235-4983758Lelio R Paula06/2012
813523543^3610+3610^2354383755Hans Havermann05/2017
813718^66711-9183741Lelio R Paula11/2015
81364*10^83740-8983741Robert Price08/2017
8138(3*2^278172-1)/1183738Lelio R Paula02/2014
8139(15*29^57251+2561)/2883724Curtis Bright05/2015
81404*7^99059-983716Lelio R Paula10/2014
8141(2^278128-3)/12684472414983714Lelio R Paula12/2012
81422^278077+186721183710Enzo Doria03/2016
8143(85*10^83708+203)/983709Robert Price09/2020
81442^278059-2783705Lelio R Paula06/2012
8145214^35917+35917^21483702Norbert Schneider12/2014
8146(23*10^83693+7)/383694Robert Price10/2015
814785^43375-283689Lelio R Paula09/2013
81485*3^175360+483669Lelio R Paula07/2014
8149(23^61441-1)/2283665Robert Price01/2012
815020091^14596+14596^2009183664Hans Havermann03/2017
81512^277907-11062983659Enzo Doria05/2014
815219522^19283+19283^1952283656Hans Havermann04/2017
8153(2^277881+2570)/283651Stefano Morozzi01/2020
81548*5^119664-383643Lelio R Paula10/2014
81558*3^175299-783640Lelio R Paula07/2014
8156(26*10^83638-413)/983639Robert Price10/2017
8157(197*10^83636+7)/383638Robert Price12/2020
81583^175250+2283616Robert Price12/2013
816011^80285+3083609Lelio R Paula10/2015
815926870^1293+1293^2687083609Hans Havermann03/2017
8161(6730^21841-1)/672983604Serge Batalov08/2020
8162(2828^24223-1)/282783602Serge Batalov08/2020
81632^277691+187442383594Enzo Doria06/2016
816413^75022-6083571Lelio R Paula11/2015
8165(2^277593+2622)/283564Stefano Morozzi01/2020
816614^72905-5183559Lelio R Paula11/2015
8167(17*2^277565-1)/54383554Lelio R Paula02/2014
81685^119532-1283550Lelio R Paula10/2015
81696^107358-1625383541Enzo Doria02/2013
81702^277478-46021183530Enzo Doria06/2015
8171(2^277474+814)/283528Stefano Morozzi01/2020
8172(22*10^83525-7)/383526Erik Branger09/2014
8173(30^56543+1)/3183520Robert Price07/2013
81742^277417-46078383511Paul Bourdelais04/2013
8175(2^277404+3582)/283507Stefano Morozzi01/2020
8176(22699*2^277387+1)/21983504Lelio R Paula06/2014
8177(31*2^277383-1)/24783500Lelio R Paula02/2014
817821368^8085+8085^2136883500Hans Havermann04/2017
8179(2^277353+3750)/283492Stefano Morozzi01/2020
8180(2^277348+3538)/283490Stefano Morozzi01/2020
8181(9*2^277342+1)/1383489Lelio R Paula12/2012
81825^119439-6683485Lelio R Paula10/2015
8183(14*10^83471-101)/383472Robert Price04/2017
81845*6^107263+783468Lelio R Paula10/2014
8185(64*10^83461-1)/983462Serge Batalov11/2010
81862^277244-17570983459Hans Havermann10/2018
8187(2^277230+1450)/283455Stefano Morozzi01/2020
8188(2^277232+3658)/283455Stefano Morozzi01/2020
818917^67796-9283420Lelio R Paula11/2015
81902^277106-11005783418Enzo Doria04/2014
81916^107200-1983418Lelio R Paula12/2015
819211^80096-183083412Enzo Doria12/2012
81933^174801+5683402Lelio R Paula12/2015
81942^277033-11197383396Enzo Doria05/2014
8195120^40105-11983386Norbert Schneider09/2018
8196(2^276992+2046)/283383Stefano Morozzi01/2020
8197(2^276990+474)/283382Stefano Morozzi01/2020
819820519^11572+11572^2051983378Hans Havermann03/2017
819920850^9971+9971^2085083374Hans Havermann03/2017
82026^107122-1886383358Enzo Doria03/2013
8200(2^276908+2322)/283358Stefano Morozzi01/2020
8201(2^276910+2734)/283358Stefano Morozzi01/2020
82034*10^83354-8983355Robert Price08/2017
82043^174697-3483352Robert Price11/2013
8206(9787*2^276855-1)/234583343Lelio R Paula04/2015
8205(2^276860+1678)/283343Stefano Morozzi01/2020
8207(2^276841+3354)/283338Stefano Morozzi01/2020
82092^276825+7522783333Enzo Doria04/2016
820834*10^83331-983333Robert Price06/2020
82105^119214+8483328Lelio R Paula10/2015
82112^276803-15983327Lelio R Paula06/2012
8212(3*2^276753-1)/2583311Lelio R Paula02/2014
82137*10^83297-3983298Robert Price07/2020
8214114^40495+40495^11483295Norbert Schneider12/2014
821539967!2+102483282Robert Price02/2015
8216(1894^25411-1)/189383279Serge Batalov08/2020
82182^276641+5783278Lelio R Paula06/2012
821935^53934-341483278Enzo Doria03/2013
821721777^6670+6670^2177783278Hans Havermann06/2020
8220(2^276655+78557)/36542583276Lelio R Paula12/2012
82212^276615-403583270Lelio R Paula08/2013
82222^276588+115583262Lelio R Paula08/2013
82232^276587-93783261Yves Minet10/2009
82242^276584-11318383261Enzo Doria07/2014
8225(2^276592-1017)/1384373983256Lelio R Paula12/2012
82262^276547-10959183249Enzo Doria04/2014
822713^74733-3283249Lelio R Paula11/2015
82282^276523-258783242Yves Minet07/2014
822918^66311-4383239Lelio R Paula11/2015
823011^79919-153083228Enzo Doria12/2012
82312^276468-10974583226Enzo Doria04/2014
82322^276462+538583224Lelio R Paula08/2013
82333*10^83219-1783220Robert Price03/2021
8234(9787*2^276422-1)/383215Lelio R Paula04/2015
82362^276391-1583202Lelio R Paula06/2012
8235(4*10^83201+173)/383202Robert Price01/2017
8237(259*10^83186-1)/383188Robert Price12/2020
8238(2^276327+534)/283183Stefano Morozzi01/2020
82392^276316-10965583180Enzo Doria04/2014
82402^276305-11206383177Enzo Doria06/2014
8241(2^276296+3406)/283174Stefano Morozzi01/2020
8242(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
8243(2^276277+3254)/283168Stefano Morozzi01/2020
824474913!4-283161Robert Price07/2017
8245(3023^23893-1)/302283155Serge Batalov08/2020
82462^276227-183720783153Enzo Doria05/2015
8248(2^276227+3)/783152Lelio R Paula12/2012
8247(2^276229+12)/2883152Stefano Morozzi03/2020
8249(2^276205+1190)/283146Stefano Morozzi01/2020
82502^276184-6338983140Paul Bourdelais02/2012


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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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