PRP Records

Probable Primes Top 10000

(225451 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 ?
52512^274351+12382588Lelio R Paula06/2012
5252(1017*2^274339-1)/351582584Lelio R Paula04/2015
52536^106086+11382551Lelio R Paula12/2015
5254(17*10^82540-377)/982541Robert Price11/2017
52552^274093-5869582511Lelio R Paula07/2013
52567*10^82509-4782510Robert Price02/2017
52572^274081-655582507Lelio R Paula07/2013
52592^274074-274074+182505Robert Price10/2014
526014^71985+4782505Lelio R Paula11/2015
52585*10^82504+2182505Robert Price01/2017
52616^106014-13982495Lelio R Paula12/2015
5262(2^274046+47)/75382494Lelio R Paula12/2012
52632^274008-183809982485Enzo Doria05/2015
52642^273981-11002982477Enzo Doria04/2014
526519^64490-3082467Lelio R Paula12/2015
52662^273785+1171582418Lelio R Paula07/2013
52678*10^82417+5182418Robert Price05/2017
526811^79133-1082409Theodore Burton11/2005
526991^42063+9082404Norbert Schneider01/2016
52712^273662-6382381Lelio R Paula06/2012
52702^273661+25582381Lelio R Paula07/2013
5272(62*10^82377-17)/982378Robert Price09/2015
52732^273608+52428782365Paul Underwood08/2018
52748*10^82360-5182361Robert Price10/2017
5275(79*10^82347-1)/382349Robert Price11/2017
5276(11*10^82323+91)/382323Robert Price02/2017
5277(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
5278(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
527915^69984+3282308Lelio R Paula11/2015
52809*6^105746+782288Lelio R Paula10/2014
528189^42211-8882286Norbert Schneider01/2016
5282gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
5283(19*10^82270-43)/382271Robert Price10/2017
52842^273282-11024182267Enzo Doria05/2014
5285(13^73849+4^73849)/1782263Robert Price05/2013
528710^82254+9^(82254+1)82255Robert Price08/2016
528610^82254+45777382255Patrick De Geest12/2016
528810^82254-9960982254Patrick De Geest12/2016
5289(754*10^82250-7)/982252Robert Price11/2017
529018^65524+1382251Lelio R Paula11/2015
52912^273206-10782244Lelio R Paula06/2012
52922^273193-45914582240Enzo Doria05/2015
52942^273126+3693782220Yves Minet06/2010
529339505!2+12882220Robert Price03/2015
52952^273053-11211182198Enzo Doria06/2014
52962^273016+118582187Lelio R Paula07/2013
5297(2^273008+3)/782183Lelio R Paula12/2012
52985^117554-1538682167Enzo Doria02/2013
5299(38*10^82161+403)/982162Robert Price11/2017
53002^272907-11143982154Enzo Doria05/2014
5301(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
53022^272875-6982144Lelio R Paula06/2012
53037^97197+482141Robert Price01/2014
5304(4*6^105554+1)/582137Serge Batalov10/2014
53056^105531-10982120Lelio R Paula12/2015
53062^272766-6582111Lelio R Paula06/2012
530719^64205-7882103Lelio R Paula12/2015
53082^272702+186997982092Enzo Doria05/2016
5309(29*2^272687-1)/982088Lelio R Paula02/2014
5310(5*10^82085-119)/382086Robert Price04/2016
53112^272660-11004982079Enzo Doria04/2014
53126^105474+6782075Lelio R Paula12/2015
53132^272637+8287582072Lelio R Paula07/2013
53142^272587-3182057Lelio R Paula06/2012
5315(41*10^82044-59)/982045Robert Price10/2017
53168*5^117368+982038Lelio R Paula10/2014
5317(101525^16384+1)/13107482023Lelio R Paula11/2011
53184*5^117343-782020Lelio R Paula10/2014
5319(265*10^81990+17)/381992Robert Price05/2016
53203^171843+1081990Robert Price10/2013
5321(7*10^81985+107)/381986Robert Price02/2017
5322(3*2^272356+1)/17716381983Lelio R Paula12/2012
53232^272296-11114981970Enzo Doria05/2014
5324(9*2^272243-1)/781954Lelio R Paula02/2014
53252^272177-11122381934Enzo Doria05/2014
5326(151009^15817+1)/15101081912Faysal YAtim06/2017
5327(16*10^81896-19)/381897Robert Price03/2016
5328(2^271922+78557)/6381855Lelio R Paula12/2012
5329(10^81848+77)/381848Robert Price01/2017
5330(24737*2^271883+1)/375781846Lelio R Paula06/2014
533110^81778+3981779Robert Price03/2011
533210^81778-17199981778Patrick De Geest07/2013
5333(14*10^81767-11)/381768Erik Branger09/2014
53342^271541+186841781742Enzo Doria04/2016
5335(2^271549-1)/23874968248781734Jens K. Andersen02/2009
53362^271484-16781725Lelio R Paula06/2012
5337(8*10^81709-611)/981709Robert Price11/2017
53382^271382+1290981695Lelio R Paula07/2013
533949^48334+4881694Norbert Schneider07/2014
53407^96668+4881694Lelio R Paula10/2015
534111^78435-141081682Enzo Doria12/2012
53425*10^81653+981654Dmitry Domanov11/2010
5343(2^271211-1)/61396149515981631Jens K. Andersen02/2009
53443^171068+5281621Lelio R Paula12/2015
53452^271115-11040781614Enzo Doria05/2014
53462^271111-11063581613Enzo Doria05/2014
53472^271098-11181609Lelio R Paula06/2012
5348(77*10^81606+13)/981607Robert Price10/2015
53492^271064-279020981599Enzo Doria03/2016
5350(13*2^271053-1)/309581593Lelio R Paula02/2014
53512^271040-5781592Lelio R Paula06/2012
5352(14*10^81585+73)/381586Robert Price04/2016
5353127^38779+12681584Norbert Schneider02/2015
535418^64966-4381551Lelio R Paula11/2015
5355(2^270840+47)/59181529Lelio R Paula12/2012
535620^62654+8781515Lelio R Paula01/2016
5357(19*10^81488+191)/381489Robert Price01/2017
53588*10^81487+2181488Robert Price02/2017
5359(73*10^81485+107)/981486Robert Price08/2016
5360536^29847+29847^53681458Norbert Schneider03/2017
53618*7^96378+981450Lelio R Paula10/2014
53622^270546-11034581443Enzo Doria05/2014
536313^73105-6081435Lelio R Paula11/2015
536444^49524+4381391Norbert Schneider06/2014
5365(3*2^270368-1)/1381389Lelio R Paula02/2014
5366(10^81363+719)/981363Serge Batalov12/2014
5367(10^81353+449)/981353Serge Batalov12/2014
536814^70978-8981350Lelio R Paula11/2015
536911^78108-204081342Enzo Doria12/2012
53703^170400-5881302Lelio R Paula12/2015
5371(17*10^81300-131)/381301Robert Price12/2017
537210^81297+3699181298Patrick De Geest06/2013
537310^81297-5781297Robert Price05/2011
53742^270055-11304781295Enzo Doria07/2014
537518^64759-5581291Lelio R Paula11/2015
5376(2^269987+1)/381274H.&R. Lifchitz10/2000
5377(31^54493-1)/3081268Alexander Zhirkov10/2010
5378(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
5379(2^269816+7)/42490181218Lelio R Paula12/2012
5380(23*10^81214+1)/381215Serge Batalov06/2009
5381(17*2^269720+1)/30381193Lelio R Paula07/2012
538256^46441-55^4644181188Robert Price10/2013
53832^269664+17781177Lelio R Paula06/2012
5384(13*2^269665-1)/18581177Lelio R Paula02/2014
53852^269539-11224981140Enzo Doria06/2014
5386((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
5387(2^269495-5)/981126Lelio R Paula12/2012
53882^269490-362381125Yves Minet10/2009
5389(55459*2^269444+1)/3581114Lelio R Paula06/2014
5390(2^269417+78557)/525781099Lelio R Paula12/2012
53914*5^116011-781089Lelio R Paula10/2014
53927*10^81058+7981059Robert Price02/2017
53932^269236-10990781049Enzo Doria04/2014
5394(8*10^81029-11)/381030Erik Branger03/2014
53953*10^81021+781022Erik Branger11/2013
53966^104115+10381018Lelio R Paula12/2015
53972^269120+186915181014Enzo Doria05/2016
53985^115901+1281012Lelio R Paula10/2015
5399(2^269083-9)/32036980997Lelio R Paula12/2012
540017^65810-2080976Lelio R Paula11/2015
540120^62236-2380971Lelio R Paula01/2016
54022^268974-11218180970Enzo Doria06/2014
5404L(387433)80969Renaud Lifchitz11/2003
5403V(387433)80969Serge Batalov03/2015
5405(2^268955-509203)/580963Lelio R Paula12/2012
5406(87398^16384+1)/6553780957Lelio R Paula11/2011
5407329^32160+32160^32980954Norbert Schneider11/2014
54082^268859-15980935Lelio R Paula05/2012
5409(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
54102^268827+577580925Lelio R Paula07/2013
54112^268824-11025580925Enzo Doria05/2014
54122^268798-186832180917Enzo Doria04/2016
54132^268753-11462180903Enzo Doria05/2015
54142^268743+160580900Lelio R Paula07/2013
54156^103954-13980892Lelio R Paula12/2015
541610^80883+4980884Robert Price03/2011
541710^80883-8032780883Patrick De Geest07/2013
54186^103937+12180879Lelio R Paula12/2015
5419(26*10^80875-119)/380876Robert Price07/2016
5420(22699*2^268657+1)/635180875Lelio R Paula06/2014
54212^268581-86968810580851Lelio R Paula05/2016
5422(11*2^268521-1)/380834Lelio R Paula02/2014
54232^268516-24980832Yves Minet02/2012
54242^268500+1609580827Lelio R Paula07/2013
54253^169402+10080826Lelio R Paula12/2015
54269^84698+8^(84698-1)80823Robert Price03/2016
54272^268472-10973980819Enzo Doria04/2014
5428(9*2^268454+1)/3780813Lelio R Paula12/2012
5429(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
5430134^37987-133^3798780803Jean-Louis Charton12/2005
543115^68702-7680800Lelio R Paula11/2015
54322^268408+780799Lelio R Paula05/2012
54332^268375+14180789Lelio R Paula05/2012
543412^74856-4780784Lelio R Paula11/2015
54352^268346+52428780781Paul Underwood08/2018
54366^103770-10780749Lelio R Paula12/2015
54373^169224-6280741Lelio R Paula12/2015
5438p(16866)#/2+6480741Robert Price03/2017
54395^115502-7280733Lelio R Paula10/2015
54402^268079-192780700Yves Minet10/2009
54412^268028+11780685Lelio R Paula05/2012
5442121^38738+12080683Norbert Schneider01/2015
5443(3^169097-8)/83580677Lelio R Paula12/2012
54442^267918+6780652Lelio R Paula05/2012
5445(89*10^80650-179)/980651Robert Price11/2017
5446(302*10^80638+13)/980640Robert Price01/2017
54473^169004+266080636Lelio R Paula12/2015
54482^267860-11285980634Enzo Doria06/2014
54492^267828-11070580625Enzo Doria05/2014
54502^267743+1270580599Lelio R Paula07/2013
5451(22*10^80595+23)/980596Robert Price03/2015
54522^267674-5180578Lelio R Paula05/2012
5453(86*10^80571-41)/980572Robert Price11/2015
54542^267612-196580560Lelio R Paula07/2013
54552^267553+409780542Lelio R Paula07/2013
54567^95276-880518Robert Price01/2014
5457(15185*2^267457-1)/4782980513Lelio R Paula04/2015
54586^103467+16380513Lelio R Paula12/2015
5459(7*10^80490+143)/380491Robert Price04/2016
546086^41597-85^4159780470Robert Price04/2015
546113^72237+3080468Lelio R Paula11/2015
546217^65389+1480458Lelio R Paula11/2015
5463423^30634+30634^42380456Norbert Schneider05/2017
54642^267232+10580445Lelio R Paula05/2012
546511^77237-307200080435Enzo Doria01/2013
54662^267116-45995980410Enzo Doria06/2015
546738715!2+880406Robert Price01/2015
5468(2^267017+1)/380380H.&R. Lifchitz09/2000
54692^266968-4580366Lelio R Paula05/2012
547020^61768-6380363Lelio R Paula01/2016
54712^266920-11296780351Enzo Doria06/2014
54728*10^80342+8780343Robert Price10/2017
547312^74428-1380322Lelio R Paula11/2015
54742^266680+2780279Lelio R Paula05/2012
54752^266630-13180264Lelio R Paula05/2012
54762^266598+7681980254Enzo Doria05/2016
54772^266587+188063380251Enzo Doria10/2016
54782^266541-11004980237Enzo Doria04/2014
547938635!2-880222Robert Price06/2015
54803^168111+168111^3-180210Robert Price04/2014
54812^266443+51380208Lelio R Paula07/2013
5482(26*10^80200+61)/380201Robert Price06/2017
54832^266412-10991380199Enzo Doria04/2014
5484(10223*2^266417+1)/4509180199Lelio R Paula06/2014
548513^71988+6680191Lelio R Paula11/2015
548611^77002-432080190Enzo Doria01/2013
548718^63879-1380186Lelio R Paula11/2015
54882^266368-11229580185Enzo Doria06/2014
5489(3^168050+5)/102145480175Lelio R Paula10/2012
5490(22*10^80167+41)/980168Robert Price02/2015
5491(34*10^80162-43)/980163Ray Chandler12/2010
5493(38*10^80150-11)/980151Robert Price05/2015
5492(598*10^80149-31)/980151Robert Price02/2017
549419^62678-8080150Lelio R Paula12/2015
549510^80139+3234380140Patrick De Geest02/2011
549610^80139-980139Alexander Gramolin01/2011
54973^167955-10680135Lelio R Paula12/2015
5498(197*10^80089-11)/380091Robert Price10/2017
54992^265998+7555980074Enzo Doria04/2016
55002^265969-10980180065Enzo Doria04/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 20 2018 23:15 (Time in France)

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