PRP Records

Probable Primes Top 10000

(224660 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 ?
52522^274074-274074+182505Robert Price10/2014
525314^71985+4782505Lelio R Paula11/2015
52515*10^82504+2182505Robert Price01/2017
52546^106014-13982495Lelio R Paula12/2015
5255(2^274046+47)/75382494Lelio R Paula12/2012
52562^274008-183809982485Enzo Doria05/2015
52572^273981-11002982477Enzo Doria04/2014
525819^64490-3082467Lelio R Paula12/2015
52592^273785+1171582418Lelio R Paula07/2013
52608*10^82417+5182418Robert Price05/2017
526111^79133-1082409Theodore Burton11/2005
526291^42063+9082404Norbert Schneider01/2016
52632^273662-6382381Lelio R Paula06/2012
52642^273661+25582381Lelio R Paula07/2013
5265(62*10^82377-17)/982378Robert Price09/2015
52662^273608+52428782365Paul Underwood08/2018
52678*10^82360-5182361Robert Price10/2017
5268(79*10^82347-1)/382349Robert Price11/2017
5269(11*10^82323+91)/382323Robert Price02/2017
5270(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
5271(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
527215^69984+3282308Lelio R Paula11/2015
52739*6^105746+782288Lelio R Paula10/2014
527489^42211-8882286Norbert Schneider01/2016
5275gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
5276(19*10^82270-43)/382271Robert Price10/2017
52772^273282-11024182267Enzo Doria05/2014
5278(13^73849+4^73849)/1782263Robert Price05/2013
528010^82254+9^(82254+1)82255Robert Price08/2016
527910^82254+45777382255Patrick De Geest12/2016
528110^82254-9960982254Patrick De Geest12/2016
5282(754*10^82250-7)/982252Robert Price11/2017
528318^65524+1382251Lelio R Paula11/2015
52842^273206-10782244Lelio R Paula06/2012
52852^273193-45914582240Enzo Doria05/2015
52872^273126+3693782220Yves Minet06/2010
528639505!2+12882220Robert Price03/2015
52882^273053-11211182198Enzo Doria06/2014
52892^273016+118582187Lelio R Paula07/2013
5290(2^273008+3)/782183Lelio R Paula12/2012
52915^117554-1538682167Enzo Doria02/2013
5292(38*10^82161+403)/982162Robert Price11/2017
52932^272907-11143982154Enzo Doria05/2014
5294(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
52952^272875-6982144Lelio R Paula06/2012
52967^97197+482141Robert Price01/2014
5297(4*6^105554+1)/582137Serge Batalov10/2014
52986^105531-10982120Lelio R Paula12/2015
52992^272766-6582111Lelio R Paula06/2012
530019^64205-7882103Lelio R Paula12/2015
53012^272702+186997982092Enzo Doria05/2016
5302(29*2^272687-1)/982088Lelio R Paula02/2014
5303(5*10^82085-119)/382086Robert Price04/2016
53042^272660-11004982079Enzo Doria04/2014
53056^105474+6782075Lelio R Paula12/2015
53062^272637+8287582072Lelio R Paula07/2013
53072^272587-3182057Lelio R Paula06/2012
5308(41*10^82044-59)/982045Robert Price10/2017
53098*5^117368+982038Lelio R Paula10/2014
5310(101525^16384+1)/13107482023Lelio R Paula11/2011
53114*5^117343-782020Lelio R Paula10/2014
5312(265*10^81990+17)/381992Robert Price05/2016
53133^171843+1081990Robert Price10/2013
5314(7*10^81985+107)/381986Robert Price02/2017
5315(3*2^272356+1)/17716381983Lelio R Paula12/2012
53162^272296-11114981970Enzo Doria05/2014
5317(9*2^272243-1)/781954Lelio R Paula02/2014
53182^272177-11122381934Enzo Doria05/2014
5319(151009^15817+1)/15101081912Faysal YAtim06/2017
5320(16*10^81896-19)/381897Robert Price03/2016
5321(2^271922+78557)/6381855Lelio R Paula12/2012
5322(10^81848+77)/381848Robert Price01/2017
5323(24737*2^271883+1)/375781846Lelio R Paula06/2014
532410^81778+3981779Robert Price03/2011
532510^81778-17199981778Patrick De Geest07/2013
5326(14*10^81767-11)/381768Erik Branger09/2014
53272^271541+186841781742Enzo Doria04/2016
5328(2^271549-1)/23874968248781734Jens K. Andersen02/2009
53292^271484-16781725Lelio R Paula06/2012
5330(8*10^81709-611)/981709Robert Price11/2017
53312^271382+1290981695Lelio R Paula07/2013
533249^48334+4881694Norbert Schneider07/2014
53337^96668+4881694Lelio R Paula10/2015
533411^78435-141081682Enzo Doria12/2012
53355*10^81653+981654Dmitry Domanov11/2010
5336(2^271211-1)/61396149515981631Jens K. Andersen02/2009
53373^171068+5281621Lelio R Paula12/2015
53382^271115-11040781614Enzo Doria05/2014
53392^271111-11063581613Enzo Doria05/2014
53402^271098-11181609Lelio R Paula06/2012
5341(77*10^81606+13)/981607Robert Price10/2015
53422^271064-279020981599Enzo Doria03/2016
5343(13*2^271053-1)/309581593Lelio R Paula02/2014
53442^271040-5781592Lelio R Paula06/2012
5345(14*10^81585+73)/381586Robert Price04/2016
5346127^38779+12681584Norbert Schneider02/2015
534718^64966-4381551Lelio R Paula11/2015
5348(2^270840+47)/59181529Lelio R Paula12/2012
534920^62654+8781515Lelio R Paula01/2016
5350(19*10^81488+191)/381489Robert Price01/2017
53518*10^81487+2181488Robert Price02/2017
5352(73*10^81485+107)/981486Robert Price08/2016
5353536^29847+29847^53681458Norbert Schneider03/2017
53548*7^96378+981450Lelio R Paula10/2014
53552^270546-11034581443Enzo Doria05/2014
535613^73105-6081435Lelio R Paula11/2015
535744^49524+4381391Norbert Schneider06/2014
5358(3*2^270368-1)/1381389Lelio R Paula02/2014
5359(10^81363+719)/981363Serge Batalov12/2014
5360(10^81353+449)/981353Serge Batalov12/2014
536114^70978-8981350Lelio R Paula11/2015
536211^78108-204081342Enzo Doria12/2012
53633^170400-5881302Lelio R Paula12/2015
5364(17*10^81300-131)/381301Robert Price12/2017
536510^81297+3699181298Patrick De Geest06/2013
536610^81297-5781297Robert Price05/2011
53672^270055-11304781295Enzo Doria07/2014
536818^64759-5581291Lelio R Paula11/2015
5369(2^269987+1)/381274H.&R. Lifchitz10/2000
5370(31^54493-1)/3081268Alexander Zhirkov10/2010
5371(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
5372(2^269816+7)/42490181218Lelio R Paula12/2012
5373(23*10^81214+1)/381215Serge Batalov06/2009
5374(17*2^269720+1)/30381193Lelio R Paula07/2012
537556^46441-55^4644181188Robert Price10/2013
53762^269664+17781177Lelio R Paula06/2012
5377(13*2^269665-1)/18581177Lelio R Paula02/2014
53782^269539-11224981140Enzo Doria06/2014
5379((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
5380(2^269495-5)/981126Lelio R Paula12/2012
53812^269490-362381125Yves Minet10/2009
5382(55459*2^269444+1)/3581114Lelio R Paula06/2014
5383(2^269417+78557)/525781099Lelio R Paula12/2012
53844*5^116011-781089Lelio R Paula10/2014
53857*10^81058+7981059Robert Price02/2017
53862^269236-10990781049Enzo Doria04/2014
5387(8*10^81029-11)/381030Erik Branger03/2014
53883*10^81021+781022Erik Branger11/2013
53896^104115+10381018Lelio R Paula12/2015
53902^269120+186915181014Enzo Doria05/2016
53915^115901+1281012Lelio R Paula10/2015
5392(2^269083-9)/32036980997Lelio R Paula12/2012
539317^65810-2080976Lelio R Paula11/2015
539420^62236-2380971Lelio R Paula01/2016
53952^268974-11218180970Enzo Doria06/2014
5397L(387433)80969Renaud Lifchitz11/2003
5396V(387433)80969Serge Batalov03/2015
5398(2^268955-509203)/580963Lelio R Paula12/2012
5399(87398^16384+1)/6553780957Lelio R Paula11/2011
5400329^32160+32160^32980954Norbert Schneider11/2014
54012^268859-15980935Lelio R Paula05/2012
5402(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
54032^268827+577580925Lelio R Paula07/2013
54042^268824-11025580925Enzo Doria05/2014
54052^268798-186832180917Enzo Doria04/2016
54062^268753-11462180903Enzo Doria05/2015
54072^268743+160580900Lelio R Paula07/2013
54086^103954-13980892Lelio R Paula12/2015
540910^80883+4980884Robert Price03/2011
541010^80883-8032780883Patrick De Geest07/2013
54116^103937+12180879Lelio R Paula12/2015
5412(26*10^80875-119)/380876Robert Price07/2016
5413(22699*2^268657+1)/635180875Lelio R Paula06/2014
54142^268581-86968810580851Lelio R Paula05/2016
5415(11*2^268521-1)/380834Lelio R Paula02/2014
54162^268516-24980832Yves Minet02/2012
54172^268500+1609580827Lelio R Paula07/2013
54183^169402+10080826Lelio R Paula12/2015
54199^84698+8^(84698-1)80823Robert Price03/2016
54202^268472-10973980819Enzo Doria04/2014
5421(9*2^268454+1)/3780813Lelio R Paula12/2012
5422(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
5423134^37987-133^3798780803Jean-Louis Charton12/2005
542415^68702-7680800Lelio R Paula11/2015
54252^268408+780799Lelio R Paula05/2012
54262^268375+14180789Lelio R Paula05/2012
542712^74856-4780784Lelio R Paula11/2015
54282^268346+52428780781Paul Underwood08/2018
54296^103770-10780749Lelio R Paula12/2015
54313^169224-6280741Lelio R Paula12/2015
5430p(16866)#/2+6480741Robert Price03/2017
54325^115502-7280733Lelio R Paula10/2015
54332^268079-192780700Yves Minet10/2009
54342^268028+11780685Lelio R Paula05/2012
5435121^38738+12080683Norbert Schneider01/2015
5436(3^169097-8)/83580677Lelio R Paula12/2012
54372^267918+6780652Lelio R Paula05/2012
5438(89*10^80650-179)/980651Robert Price11/2017
5439(302*10^80638+13)/980640Robert Price01/2017
54403^169004+266080636Lelio R Paula12/2015
54412^267860-11285980634Enzo Doria06/2014
54422^267828-11070580625Enzo Doria05/2014
54432^267743+1270580599Lelio R Paula07/2013
5444(22*10^80595+23)/980596Robert Price03/2015
54452^267674-5180578Lelio R Paula05/2012
5446(86*10^80571-41)/980572Robert Price11/2015
54472^267612-196580560Lelio R Paula07/2013
54482^267553+409780542Lelio R Paula07/2013
54497^95276-880518Robert Price01/2014
5450(15185*2^267457-1)/4782980513Lelio R Paula04/2015
54516^103467+16380513Lelio R Paula12/2015
5452(7*10^80490+143)/380491Robert Price04/2016
545386^41597-85^4159780470Robert Price04/2015
545413^72237+3080468Lelio R Paula11/2015
545517^65389+1480458Lelio R Paula11/2015
5456423^30634+30634^42380456Norbert Schneider05/2017
54572^267232+10580445Lelio R Paula05/2012
545811^77237-307200080435Enzo Doria01/2013
54592^267116-45995980410Enzo Doria06/2015
546038715!2+880406Robert Price01/2015
5461(2^267017+1)/380380H.&R. Lifchitz09/2000
54622^266968-4580366Lelio R Paula05/2012
546320^61768-6380363Lelio R Paula01/2016
54642^266920-11296780351Enzo Doria06/2014
54658*10^80342+8780343Robert Price10/2017
546612^74428-1380322Lelio R Paula11/2015
54672^266680+2780279Lelio R Paula05/2012
54682^266630-13180264Lelio R Paula05/2012
54692^266598+7681980254Enzo Doria05/2016
54702^266587+188063380251Enzo Doria10/2016
54712^266541-11004980237Enzo Doria04/2014
547238635!2-880222Robert Price06/2015
54733^168111+168111^3-180210Robert Price04/2014
54742^266443+51380208Lelio R Paula07/2013
5475(26*10^80200+61)/380201Robert Price06/2017
54762^266412-10991380199Enzo Doria04/2014
5477(10223*2^266417+1)/4509180199Lelio R Paula06/2014
547813^71988+6680191Lelio R Paula11/2015
547911^77002-432080190Enzo Doria01/2013
548018^63879-1380186Lelio R Paula11/2015
54812^266368-11229580185Enzo Doria06/2014
5482(3^168050+5)/102145480175Lelio R Paula10/2012
5483(22*10^80167+41)/980168Robert Price02/2015
5484(34*10^80162-43)/980163Ray Chandler12/2010
5486(38*10^80150-11)/980151Robert Price05/2015
5485(598*10^80149-31)/980151Robert Price02/2017
548719^62678-8080150Lelio R Paula12/2015
548810^80139+3234380140Patrick De Geest02/2011
548910^80139-980139Alexander Gramolin01/2011
54903^167955-10680135Lelio R Paula12/2015
5491(197*10^80089-11)/380091Robert Price10/2017
54922^265998+7555980074Enzo Doria04/2016
54932^265969-10980180065Enzo Doria04/2014
54942^265888-11275780041Enzo Doria06/2014
54952^265809+170180017Lelio R Paula07/2013
5496gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
54973^167687-10480008Lelio R Paula02/2015
549811^76826-579080007Enzo Doria01/2013
549910^80000+8573180001Patrick De Geest10/2009
550010^80000-716980000Patrick De Geest09/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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