PRP Records

Probable Primes Top 10000

(252402 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 ?
525119522^19283+19283^1952283656Hans Havermann04/2017
52528*5^119664-383643Lelio R Paula10/2014
52538*3^175299-783640Lelio R Paula07/2014
5254(26*10^83638-413)/983639Robert Price10/2017
52553^175250+2283616Robert Price12/2013
525711^80285+3083609Lelio R Paula10/2015
525626870^1293+1293^2687083609Hans Havermann03/2017
52582^277691+187442383594Enzo Doria06/2016
525913^75022-6083571Lelio R Paula11/2015
526014^72905-5183559Lelio R Paula11/2015
5261(17*2^277565-1)/54383554Lelio R Paula02/2014
52625^119532-1283550Lelio R Paula10/2015
52636^107358-1625383541Enzo Doria02/2013
52642^277478-46021183530Enzo Doria06/2015
5265(22*10^83525-7)/383526Erik Branger09/2014
5266(30^56543+1)/3183520Robert Price07/2013
52672^277417-46078383511Paul Bourdelais04/2013
5268(22699*2^277387+1)/21983504Lelio R Paula06/2014
5269(31*2^277383-1)/24783500Lelio R Paula02/2014
527021368^8085+8085^2136883500Hans Havermann04/2017
5271(9*2^277342+1)/1383489Lelio R Paula12/2012
52725^119439-6683485Lelio R Paula10/2015
5273(14*10^83471-101)/383472Robert Price04/2017
52745*6^107263+783468Lelio R Paula10/2014
5275(64*10^83461-1)/983462Serge Batalov11/2010
52762^277244-17570983459Hans Havermann10/2018
527717^67796-9283420Lelio R Paula11/2015
52782^277106-11005783418Enzo Doria04/2014
52796^107200-1983418Lelio R Paula12/2015
528011^80096-183083412Enzo Doria12/2012
52813^174801+5683402Lelio R Paula12/2015
52822^277033-11197383396Enzo Doria05/2014
5283120^40105-11983386Norbert Schneider09/2018
528420519^11572+11572^2051983378Hans Havermann03/2017
528520850^9971+9971^2085083374Hans Havermann03/2017
52866^107122-1886383358Enzo Doria03/2013
52874*10^83354-8983355Robert Price08/2017
52883^174697-3483352Robert Price11/2013
5289(9787*2^276855-1)/234583343Lelio R Paula04/2015
52902^276825+7522783333Enzo Doria04/2016
52915^119214+8483328Lelio R Paula10/2015
52922^276803-15983327Lelio R Paula06/2012
5293(3*2^276753-1)/2583311Lelio R Paula02/2014
5294114^40495+40495^11483295Norbert Schneider12/2014
529539967!2+102483282Robert Price02/2015
52972^276641+5783278Lelio R Paula06/2012
529635^53934-341483278Enzo Doria03/2013
5298(2^276655+78557)/36542583276Lelio R Paula12/2012
52992^276615-403583270Lelio R Paula08/2013
53002^276588+115583262Lelio R Paula08/2013
53022^276587-93783261Yves Minet10/2009
53012^276584-11318383261Enzo Doria07/2014
5303(2^276592-1017)/1384373983256Lelio R Paula12/2012
53042^276547-10959183249Enzo Doria04/2014
530513^74733-3283249Lelio R Paula11/2015
53062^276523-258783242Yves Minet07/2014
530718^66311-4383239Lelio R Paula11/2015
530811^79919-153083228Enzo Doria12/2012
53092^276468-10974583226Enzo Doria04/2014
53102^276462+538583224Lelio R Paula08/2013
5311(9787*2^276422-1)/383215Lelio R Paula04/2015
53122^276391-1583202Lelio R Paula06/2012
5313(4*10^83201+173)/383202Robert Price01/2017
53142^276316-10965583180Enzo Doria04/2014
53152^276305-11206383177Enzo Doria06/2014
5316(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
531774913!4-283161Robert Price07/2017
53182^276227-183720783153Enzo Doria05/2015
5319(2^276227+3)/783152Lelio R Paula12/2012
53202^276184-6338983140Paul Bourdelais02/2012
53212^276066-11160383105Enzo Doria05/2014
5322(2^276028-3)*6-783094Gilbert Mozzo09/2016
5323(2^275897+9)/115383051Lelio R Paula12/2012
53242^275879-10980783048Enzo Doria04/2014
5326F(397379)83047Henri Lifchitz08/2003
5325U(397379)83047Serge Batalov03/2015
53273^174040-1483039Robert Price08/2013
5328(86*10^83038-221)/983039Robert Price06/2017
53292^275841-688383037Lelio R Paula07/2011
53303^174002-14083021Lelio R Paula12/2015
53316^106681+7783014Lelio R Paula12/2015
5332187^36539-283011Lelio R Paula10/2017
533311^79701-315083001Enzo Doria12/2012
5334(55459*2^275657+1)/2182985Lelio R Paula06/2014
5335(7*10^82960-457)/982960Robert Price09/2017
53362^275535-685582945Lelio R Paula08/2013
53383^173828-1482938Robert Price08/2013
53372^275512-10967782938Enzo Doria04/2014
53392^275446-11004582918Enzo Doria04/2014
5340(2^275473+47)/2952609744782916Lelio R Paula12/2012
53413^173755-1482903Robert Price08/2013
5342(182*10^82898+43)/982900Robert Price11/2017
53432^275363-11230982893Enzo Doria06/2014
534461^46427-6082888Norbert Schneider10/2014
53453*10^82880-7^8288082881Mike Oakes02/2010
53472^275290+9019582871Lelio R Paula07/2013
5346(35*10^82870-71)/982871Robert Price05/2015
53482^275270-185962182865Enzo Doria03/2016
53492^275259+8182862Henri Lifchitz01/2007
5350(113703^16384+1)/282834Richard Fischer04/2018
53517^98003+98003^7+182823Robert Price05/2014
535210^82790+12604382791Patrick De Geest07/2013
535310^82790-4782790Robert Price05/2011
53542^274985-11266382779Enzo Doria06/2014
53552^274935+1501582764Lelio R Paula07/2013
5356(17*2^274922+1)/382761Lelio R Paula12/2012
5357(43*10^82752-61)/982753Robert Price06/2015
5358(3*2^274862+1)/102782740Lelio R Paula12/2012
5359(31*2^274848-1)/406582736Lelio R Paula02/2014
5360(4^137405+23)/382726Robert Price02/2017
53612^274791-11049182721Enzo Doria05/2014
5362(11*2^274776-1)/9582715Lelio R Paula02/2014
5363(47*10^82706-119)/982707Robert Price09/2017
53642^274704-11139582695Enzo Doria05/2014
53652^274686-391182689Yves Minet04/2017
5366(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
5367(3^173263-5)/1449882664Lelio R Paula12/2012
53682^274511-6487582637Lelio R Paula08/2013
536912^76572-8382636Lelio R Paula11/2015
53703^173191-2^17319182634Mike Oakes02/2004
537114^72072-1582604Lelio R Paula11/2015
5372(55459*2^274339+1)/382589Lelio R Paula06/2014
53732^274351+12382588Lelio R Paula06/2012
5374(1017*2^274339-1)/351582584Lelio R Paula04/2015
53756^106086+11382551Lelio R Paula12/2015
5376(17*10^82540-377)/982541Robert Price11/2017
53772^274093-5869582511Lelio R Paula07/2013
53787*10^82509-4782510Robert Price02/2017
53792^274081-655582507Lelio R Paula07/2013
53812^274074-274074+182505Robert Price10/2014
538214^71985+4782505Lelio R Paula11/2015
53805*10^82504+2182505Robert Price01/2017
53836^106014-13982495Lelio R Paula12/2015
5384(2^274046+47)/75382494Lelio R Paula12/2012
53852^274008-183809982485Enzo Doria05/2015
53862^273981-11002982477Enzo Doria04/2014
538719^64490-3082467Lelio R Paula12/2015
53882^273785+1171582418Lelio R Paula07/2013
53898*10^82417+5182418Robert Price05/2017
539011^79133-1082409Theodore Burton11/2005
539191^42063+9082404Norbert Schneider01/2016
53922^273662-6382381Lelio R Paula06/2012
53932^273661+25582381Lelio R Paula07/2013
5394(62*10^82377-17)/982378Robert Price09/2015
53952^273608+52428782365Paul Underwood08/2018
53968*10^82360-5182361Robert Price10/2017
5397(79*10^82347-1)/382349Robert Price11/2017
5398(11*10^82323+91)/382323Robert Price02/2017
5399(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
5400(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
540115^69984+3282308Lelio R Paula11/2015
54029*6^105746+782288Lelio R Paula10/2014
540389^42211-8882286Norbert Schneider01/2016
5404gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
5405(19*10^82270-43)/382271Robert Price10/2017
54062^273282-11024182267Enzo Doria05/2014
5407(13^73849+4^73849)/1782263Robert Price05/2013
540910^82254+9^(82254+1)82255Robert Price08/2016
540810^82254+45777382255Patrick De Geest12/2016
541010^82254-9960982254Patrick De Geest12/2016
5411(754*10^82250-7)/982252Robert Price11/2017
541218^65524+1382251Lelio R Paula11/2015
54132^273206-10782244Lelio R Paula06/2012
54142^273193-45914582240Enzo Doria05/2015
54162^273126+3693782220Yves Minet06/2010
541539505!2+12882220Robert Price03/2015
54172^273053-11211182198Enzo Doria06/2014
54182^273016+118582187Lelio R Paula07/2013
5419(2^273008+3)/782183Lelio R Paula12/2012
54205^117554-1538682167Enzo Doria02/2013
5421(38*10^82161+403)/982162Robert Price11/2017
54222^272907-11143982154Enzo Doria05/2014
5423(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
54242^272875-6982144Lelio R Paula06/2012
54257^97197+482141Robert Price01/2014
5426(4*6^105554+1)/582137Serge Batalov10/2014
54276^105531-10982120Lelio R Paula12/2015
54282^272766-6582111Lelio R Paula06/2012
542919^64205-7882103Lelio R Paula12/2015
54302^272702+186997982092Enzo Doria05/2016
5431(29*2^272687-1)/982088Lelio R Paula02/2014
5432(5*10^82085-119)/382086Robert Price04/2016
54332^272660-11004982079Enzo Doria04/2014
54346^105474+6782075Lelio R Paula12/2015
54352^272637+8287582072Lelio R Paula07/2013
54362^272587-3182057Lelio R Paula06/2012
5437(41*10^82044-59)/982045Robert Price10/2017
54388*5^117368+982038Lelio R Paula10/2014
5439(101525^16384+1)/13107482023Lelio R Paula11/2011
54404*5^117343-782020Lelio R Paula10/2014
5441(265*10^81990+17)/381992Robert Price05/2016
54423^171843+1081990Robert Price10/2013
5443(7*10^81985+107)/381986Robert Price02/2017
5444(3*2^272356+1)/17716381983Lelio R Paula12/2012
54452^272296-11114981970Enzo Doria05/2014
5446(9*2^272243-1)/781954Lelio R Paula02/2014
54472^272177-11122381934Enzo Doria05/2014
5448(151009^15817+1)/15101081912Faysal YAtim06/2017
5449(16*10^81896-19)/381897Robert Price03/2016
5450(2^271922+78557)/6381855Lelio R Paula12/2012
5451(10^81848+77)/381848Robert Price01/2017
5452(24737*2^271883+1)/375781846Lelio R Paula06/2014
545310^81778+3981779Robert Price03/2011
545410^81778-17199981778Patrick De Geest07/2013
5455(14*10^81767-11)/381768Erik Branger09/2014
54562^271541+186841781742Enzo Doria04/2016
5457(2^271549-1)/23874968248781734Jens K. Andersen02/2009
54582^271484-16781725Lelio R Paula06/2012
5459(8*10^81709-611)/981709Robert Price11/2017
54602^271382+1290981695Lelio R Paula07/2013
546149^48334+4881694Norbert Schneider07/2014
54627^96668+4881694Lelio R Paula10/2015
546311^78435-141081682Enzo Doria12/2012
54645*10^81653+981654Dmitry Domanov11/2010
5465(2^271211-1)/61396149515981631Jens K. Andersen02/2009
54663^171068+5281621Lelio R Paula12/2015
54672^271115-11040781614Enzo Doria05/2014
54682^271111-11063581613Enzo Doria05/2014
54692^271098-11181609Lelio R Paula06/2012
5470(77*10^81606+13)/981607Robert Price10/2015
54712^271064-279020981599Enzo Doria03/2016
5472(13*2^271053-1)/309581593Lelio R Paula02/2014
54732^271040-5781592Lelio R Paula06/2012
5474(14*10^81585+73)/381586Robert Price04/2016
5475127^38779+12681584Norbert Schneider02/2015
547618^64966-4381551Lelio R Paula11/2015
5477(2^270840+47)/59181529Lelio R Paula12/2012
547820^62654+8781515Lelio R Paula01/2016
5479(19*10^81488+191)/381489Robert Price01/2017
54808*10^81487+2181488Robert Price02/2017
5481(73*10^81485+107)/981486Robert Price08/2016
5482536^29847+29847^53681458Norbert Schneider03/2017
54838*7^96378+981450Lelio R Paula10/2014
54842^270546-11034581443Enzo Doria05/2014
548513^73105-6081435Lelio R Paula11/2015
548644^49524+4381391Norbert Schneider06/2014
5487(3*2^270368-1)/1381389Lelio R Paula02/2014
5488(10^81363+719)/981363Serge Batalov12/2014
5489(10^81353+449)/981353Serge Batalov12/2014
549014^70978-8981350Lelio R Paula11/2015
549111^78108-204081342Enzo Doria12/2012
54923^170400-5881302Lelio R Paula12/2015
5493(17*10^81300-131)/381301Robert Price12/2017
549410^81297+3699181298Patrick De Geest06/2013
549510^81297-5781297Robert Price05/2011
54962^270055-11304781295Enzo Doria07/2014
549718^64759-5581291Lelio R Paula11/2015
5498(2^269987+1)/381274H.&R. Lifchitz10/2000
5499(31^54493-1)/3081268Alexander Zhirkov10/2010
5500(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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