PRP Records

Probable Primes Top 10000

(173006 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 (> 30000) Who ? When ?
4501(2^276028-3)*6-783094Gilbert Mozzo09/2016
4502(2^275897+9)/115383051Lelio R Paula12/2012
45032^275879-10980783048Enzo Doria04/2014
4505F(397379)83047Henri Lifchitz08/2003
4504U(397379)83047Serge Batalov03/2015
45063^174040-1483039Robert Price08/2013
45072^275841-688383037Lelio R Paula07/2011
45083^174002-14083021Lelio R Paula12/2015
45096^106681+7783014Lelio R Paula12/2015
451011^79701-315083001Enzo Doria12/2012
4511(55459*2^275657+1)/2182985Lelio R Paula06/2014
45122^275535-685582945Lelio R Paula08/2013
45143^173828-1482938Robert Price08/2013
45132^275512-10967782938Enzo Doria04/2014
45152^275446-11004582918Enzo Doria04/2014
4516(2^275473+47)/2952609744782916Lelio R Paula12/2012
45173^173755-1482903Robert Price08/2013
45182^275363-11230982893Enzo Doria06/2014
451961^46427-6082888Norbert Schneider10/2014
45203*10^82880-7^8288082881Mike Oakes02/2010
45222^275290+9019582871Lelio R Paula07/2013
4521(35*10^82870-71)/982871Robert Price05/2015
45232^275270-185962182865Enzo Doria03/2016
45242^275259+8182862Henri Lifchitz01/2007
45257^98003+98003^7+182823Robert Price05/2014
452610^82790+12604382791Patrick De Geest07/2013
452710^82790-4782790Robert Price05/2011
45282^274985-11266382779Enzo Doria06/2014
45292^274935+1501582764Lelio R Paula07/2013
4530(17*2^274922+1)/382761Lelio R Paula12/2012
4531(43*10^82752-61)/982753Robert Price06/2015
4532(3*2^274862+1)/102782740Lelio R Paula12/2012
4533(31*2^274848-1)/406582736Lelio R Paula02/2014
4534(4^137405+23)/382726Robert Price02/2017
45352^274791-11049182721Enzo Doria05/2014
4536(11*2^274776-1)/9582715Lelio R Paula02/2014
45372^274704-11139582695Enzo Doria05/2014
45382^274686-391182689Yves Minet04/2017
4539(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
4540(3^173263-5)/1449882664Lelio R Paula12/2012
45412^274511-6487582637Lelio R Paula08/2013
454212^76572-8382636Lelio R Paula11/2015
45433^173191-2^17319182634Mike Oakes02/2004
454414^72072-1582604Lelio R Paula11/2015
4545(55459*2^274339+1)/382589Lelio R Paula06/2014
45462^274351+12382588Lelio R Paula06/2012
4547(1017*2^274339-1)/351582584Lelio R Paula04/2015
45486^106086+11382551Lelio R Paula12/2015
45492^274093-5869582511Lelio R Paula07/2013
45507*10^82509-4782510Robert Price02/2017
45512^274081-655582507Lelio R Paula07/2013
45532^274074-274074+182505Robert Price10/2014
455414^71985+4782505Lelio R Paula11/2015
45525*10^82504+2182505Robert Price01/2017
45556^106014-13982495Lelio R Paula12/2015
4556(2^274046+47)/75382494Lelio R Paula12/2012
45572^274008-183809982485Enzo Doria05/2015
45582^273981-11002982477Enzo Doria04/2014
455919^64490-3082467Lelio R Paula12/2015
45612^273785+1171582418Lelio R Paula07/2013
45608*10^82417+5182418Robert Price05/2017
456211^79133-1082409Theodore Burton11/2005
456391^42063+9082404Norbert Schneider01/2016
45652^273662-6382381Lelio R Paula06/2012
45642^273661+25582381Lelio R Paula07/2013
4566(62*10^82377-17)/982378Robert Price09/2015
4567(11*10^82323+91)/382323Robert Price02/2017
456815^69984+3282308Lelio R Paula11/2015
45699*6^105746+782288Lelio R Paula10/2014
457089^42211-8882286Norbert Schneider01/2016
4571gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
45722^273282-11024182267Enzo Doria05/2014
4573(13^73849+4^73849)/1782263Robert Price05/2013
457510^82254+9^(82254+1)82255Robert Price08/2016
457410^82254+45777382255Patrick De Geest12/2016
457610^82254-9960982254Patrick De Geest12/2016
457718^65524+1382251Lelio R Paula11/2015
45782^273206-10782244Lelio R Paula06/2012
45792^273193-45914582240Enzo Doria05/2015
45812^273126+3693782220Yves Minet06/2010
458039505!2+12882220Robert Price03/2015
45822^273053-11211182198Enzo Doria06/2014
45832^273016+118582187Lelio R Paula07/2013
4584(2^273008+3)/782183Lelio R Paula12/2012
45855^117554-1538682167Enzo Doria02/2013
45862^272907-11143982154Enzo Doria05/2014
4587(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
45882^272875-6982144Lelio R Paula06/2012
45897^97197+482141Robert Price01/2014
4590(4*6^105554+1)/582137Serge Batalov10/2014
45916^105531-10982120Lelio R Paula12/2015
45922^272766-6582111Lelio R Paula06/2012
459319^64205-7882103Lelio R Paula12/2015
45942^272702+186997982092Enzo Doria05/2016
4595(29*2^272687-1)/982088Lelio R Paula02/2014
4596(5*10^82085-119)/382086Robert Price04/2016
45972^272660-11004982079Enzo Doria04/2014
45986^105474+6782075Lelio R Paula12/2015
45992^272637+8287582072Lelio R Paula07/2013
46002^272587-3182057Lelio R Paula06/2012
46018*5^117368+982038Lelio R Paula10/2014
4602(101525^16384+1)/13107482023Lelio R Paula11/2011
46034*5^117343-782020Lelio R Paula10/2014
4604(265*10^81990+17)/381992Robert Price05/2016
46053^171843+1081990Robert Price10/2013
4606(7*10^81985+107)/381986Robert Price02/2017
4607(3*2^272356+1)/17716381983Lelio R Paula12/2012
46082^272296-11114981970Enzo Doria05/2014
4609(9*2^272243-1)/781954Lelio R Paula02/2014
46102^272177-11122381934Enzo Doria05/2014
4611(16*10^81896-19)/381897Robert Price03/2016
4612(2^271922+78557)/6381855Lelio R Paula12/2012
4613(10^81848+77)/381848Robert Price01/2017
4614(24737*2^271883+1)/375781846Lelio R Paula06/2014
461510^81778+3981779Robert Price03/2011
461610^81778-17199981778Patrick De Geest07/2013
4617(14*10^81767-11)/381768Erik Branger09/2014
46182^271541+186841781742Enzo Doria04/2016
4619(2^271549-1)/23874968248781734Jens K. Andersen02/2009
46202^271484-16781725Lelio R Paula06/2012
46212^271382+1290981695Lelio R Paula07/2013
462249^48334+4881694Norbert Schneider07/2014
46237^96668+4881694Lelio R Paula10/2015
462411^78435-141081682Enzo Doria12/2012
46255*10^81653+981654Dmitry Domanov11/2010
4626(2^271211-1)/61396149515981631Jens K. Andersen02/2009
46273^171068+5281621Lelio R Paula12/2015
46282^271115-11040781614Enzo Doria05/2014
46292^271111-11063581613Enzo Doria05/2014
46302^271098-11181609Lelio R Paula06/2012
4631(77*10^81606+13)/981607Robert Price10/2015
46322^271064-279020981599Enzo Doria03/2016
4633(13*2^271053-1)/309581593Lelio R Paula02/2014
46342^271040-5781592Lelio R Paula06/2012
4635(14*10^81585+73)/381586Robert Price04/2016
4636127^38779+12681584Norbert Schneider02/2015
463718^64966-4381551Lelio R Paula11/2015
4638(2^270840+47)/59181529Lelio R Paula12/2012
463920^62654+8781515Lelio R Paula01/2016
4640(19*10^81488+191)/381489Robert Price01/2017
46418*10^81487+2181488Robert Price02/2017
4642(73*10^81485+107)/981486Robert Price08/2016
4643536^29847+29847^53681458Norbert Schneider03/2017
46448*7^96378+981450Lelio R Paula10/2014
46452^270546-11034581443Enzo Doria05/2014
464613^73105-6081435Lelio R Paula11/2015
464744^49524+4381391Norbert Schneider06/2014
4648(3*2^270368-1)/1381389Lelio R Paula02/2014
4649(10^81363+719)/981363Serge Batalov12/2014
4650(10^81353+449)/981353Serge Batalov12/2014
465114^70978-8981350Lelio R Paula11/2015
465211^78108-204081342Enzo Doria12/2012
46533^170400-5881302Lelio R Paula12/2015
465410^81297+3699181298Patrick De Geest06/2013
465510^81297-5781297Robert Price05/2011
46562^270055-11304781295Enzo Doria07/2014
465718^64759-5581291Lelio R Paula11/2015
4658(2^269987+1)/381274H.&R. Lifchitz10/2000
4659(31^54493-1)/3081268Alexander Zhirkov10/2010
4660(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
4661(2^269816+7)/42490181218Lelio R Paula12/2012
4662(23*10^81214+1)/381215Serge Batalov06/2009
4663(17*2^269720+1)/30381193Lelio R Paula07/2012
466456^46441-55^4644181188Robert Price10/2013
46652^269664+17781177Lelio R Paula06/2012
4666(13*2^269665-1)/18581177Lelio R Paula02/2014
46672^269539-11224981140Enzo Doria06/2014
4668((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
4669(2^269495-5)/981126Lelio R Paula12/2012
46702^269490-362381125Yves Minet10/2009
4671(55459*2^269444+1)/3581114Lelio R Paula06/2014
4672(2^269417+78557)/525781099Lelio R Paula12/2012
46734*5^116011-781089Lelio R Paula10/2014
46747*10^81058+7981059Robert Price02/2017
46752^269236-10990781049Enzo Doria04/2014
4676(8*10^81029-11)/381030Erik Branger03/2014
46773*10^81021+781022Erik Branger11/2013
46786^104115+10381018Lelio R Paula12/2015
46792^269120+186915181014Enzo Doria05/2016
46805^115901+1281012Lelio R Paula10/2015
4681(2^269083-9)/32036980997Lelio R Paula12/2012
468217^65810-2080976Lelio R Paula11/2015
468320^62236-2380971Lelio R Paula01/2016
46842^268974-11218180970Enzo Doria06/2014
4686L(387433)80969Renaud Lifchitz11/2003
4685V(387433)80969Serge Batalov03/2015
4687(2^268955-509203)/580963Lelio R Paula12/2012
4688(87398^16384+1)/6553780957Lelio R Paula11/2011
4689329^32160+32160^32980954Norbert Schneider11/2014
46902^268859-15980935Lelio R Paula05/2012
4691(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
46922^268827+577580925Lelio R Paula07/2013
46932^268824-11025580925Enzo Doria05/2014
46942^268798-186832180917Enzo Doria04/2016
46952^268753-11462180903Enzo Doria05/2015
46962^268743+160580900Lelio R Paula07/2013
46976^103954-13980892Lelio R Paula12/2015
469810^80883+4980884Robert Price03/2011
469910^80883-8032780883Patrick De Geest07/2013
47006^103937+12180879Lelio R Paula12/2015
4701(26*10^80875-119)/380876Robert Price07/2016
4702(22699*2^268657+1)/635180875Lelio R Paula06/2014
47032^268581-86968810580851Lelio R Paula05/2016
4704(11*2^268521-1)/380834Lelio R Paula02/2014
47052^268516-24980832Yves Minet02/2012
47062^268500+1609580827Lelio R Paula07/2013
47073^169402+10080826Lelio R Paula12/2015
47089^84698+8^(84698-1)80823Robert Price03/2016
47092^268472-10973980819Enzo Doria04/2014
4710(9*2^268454+1)/3780813Lelio R Paula12/2012
4711(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
4712134^37987-133^3798780803Jean-Louis Charton12/2005
471315^68702-7680800Lelio R Paula11/2015
47142^268408+780799Lelio R Paula05/2012
47152^268375+14180789Lelio R Paula05/2012
471612^74856-4780784Lelio R Paula11/2015
47176^103770-10780749Lelio R Paula12/2015
47193^169224-6280741Lelio R Paula12/2015
4718p(16866)#/2+6480741Robert Price03/2017
47205^115502-7280733Lelio R Paula10/2015
47212^268079-192780700Yves Minet10/2009
47222^268028+11780685Lelio R Paula05/2012
4723121^38738+12080683Norbert Schneider01/2015
4724(3^169097-8)/83580677Lelio R Paula12/2012
47252^267918+6780652Lelio R Paula05/2012
4726(302*10^80638+13)/980640Robert Price01/2017
47273^169004+266080636Lelio R Paula12/2015
47282^267860-11285980634Enzo Doria06/2014
47292^267828-11070580625Enzo Doria05/2014
47302^267743+1270580599Lelio R Paula07/2013
4731(22*10^80595+23)/980596Robert Price03/2015
47322^267674-5180578Lelio R Paula05/2012
4733(86*10^80571-41)/980572Robert Price11/2015
47342^267612-196580560Lelio R Paula07/2013
47352^267553+409780542Lelio R Paula07/2013
47367^95276-880518Robert Price01/2014
4737(15185*2^267457-1)/4782980513Lelio R Paula04/2015
47386^103467+16380513Lelio R Paula12/2015
4739(7*10^80490+143)/380491Robert Price04/2016
474086^41597-85^4159780470Robert Price04/2015
474113^72237+3080468Lelio R Paula11/2015
474217^65389+1480458Lelio R Paula11/2015
47432^267232+10580445Lelio R Paula05/2012
474411^77237-307200080435Enzo Doria01/2013
47452^267116-45995980410Enzo Doria06/2015
474638715!2+880406Robert Price01/2015
4747(2^267017+1)/380380H.&R. Lifchitz09/2000
47482^266968-4580366Lelio R Paula05/2012
474920^61768-6380363Lelio R Paula01/2016
47502^266920-11296780351Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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