PRP Records

Probable Primes Top 10000

(211563 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 ?
50012^275879-10980783048Enzo Doria04/2014
5003F(397379)83047Henri Lifchitz08/2003
5002U(397379)83047Serge Batalov03/2015
50053^174040-1483039Robert Price08/2013
5004(86*10^83038-221)/983039Robert Price06/2017
50062^275841-688383037Lelio R Paula07/2011
50073^174002-14083021Lelio R Paula12/2015
50086^106681+7783014Lelio R Paula12/2015
5009187^36539-283011Lelio R Paula10/2017
501011^79701-315083001Enzo Doria12/2012
5011(55459*2^275657+1)/2182985Lelio R Paula06/2014
5012(7*10^82960-457)/982960Robert Price09/2017
50132^275535-685582945Lelio R Paula08/2013
50143^173828-1482938Robert Price08/2013
50152^275512-10967782938Enzo Doria04/2014
50162^275446-11004582918Enzo Doria04/2014
5017(2^275473+47)/2952609744782916Lelio R Paula12/2012
50183^173755-1482903Robert Price08/2013
5019(182*10^82898+43)/982900Robert Price11/2017
50202^275363-11230982893Enzo Doria06/2014
502161^46427-6082888Norbert Schneider10/2014
50223*10^82880-7^8288082881Mike Oakes02/2010
50242^275290+9019582871Lelio R Paula07/2013
5023(35*10^82870-71)/982871Robert Price05/2015
50252^275270-185962182865Enzo Doria03/2016
50262^275259+8182862Henri Lifchitz01/2007
5027(113703^16384+1)/282834Richard Fischer04/2018
50287^98003+98003^7+182823Robert Price05/2014
502910^82790+12604382791Patrick De Geest07/2013
503010^82790-4782790Robert Price05/2011
50312^274985-11266382779Enzo Doria06/2014
50322^274935+1501582764Lelio R Paula07/2013
5033(17*2^274922+1)/382761Lelio R Paula12/2012
5034(43*10^82752-61)/982753Robert Price06/2015
5035(3*2^274862+1)/102782740Lelio R Paula12/2012
5036(31*2^274848-1)/406582736Lelio R Paula02/2014
5037(4^137405+23)/382726Robert Price02/2017
50382^274791-11049182721Enzo Doria05/2014
5039(11*2^274776-1)/9582715Lelio R Paula02/2014
5040(47*10^82706-119)/982707Robert Price09/2017
50412^274704-11139582695Enzo Doria05/2014
50422^274686-391182689Yves Minet04/2017
5043(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
5044(3^173263-5)/1449882664Lelio R Paula12/2012
50452^274511-6487582637Lelio R Paula08/2013
504612^76572-8382636Lelio R Paula11/2015
50473^173191-2^17319182634Mike Oakes02/2004
504814^72072-1582604Lelio R Paula11/2015
5049(55459*2^274339+1)/382589Lelio R Paula06/2014
50502^274351+12382588Lelio R Paula06/2012
5051(1017*2^274339-1)/351582584Lelio R Paula04/2015
50526^106086+11382551Lelio R Paula12/2015
5053(17*10^82540-377)/982541Robert Price11/2017
50542^274093-5869582511Lelio R Paula07/2013
50557*10^82509-4782510Robert Price02/2017
50562^274081-655582507Lelio R Paula07/2013
50582^274074-274074+182505Robert Price10/2014
505914^71985+4782505Lelio R Paula11/2015
50575*10^82504+2182505Robert Price01/2017
50606^106014-13982495Lelio R Paula12/2015
5061(2^274046+47)/75382494Lelio R Paula12/2012
50622^274008-183809982485Enzo Doria05/2015
50632^273981-11002982477Enzo Doria04/2014
506419^64490-3082467Lelio R Paula12/2015
50652^273785+1171582418Lelio R Paula07/2013
50668*10^82417+5182418Robert Price05/2017
506711^79133-1082409Theodore Burton11/2005
506891^42063+9082404Norbert Schneider01/2016
50702^273662-6382381Lelio R Paula06/2012
50692^273661+25582381Lelio R Paula07/2013
5071(62*10^82377-17)/982378Robert Price09/2015
50728*10^82360-5182361Robert Price10/2017
5073(79*10^82347-1)/382349Robert Price11/2017
5074(11*10^82323+91)/382323Robert Price02/2017
5075(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
5076(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
507715^69984+3282308Lelio R Paula11/2015
50789*6^105746+782288Lelio R Paula10/2014
507989^42211-8882286Norbert Schneider01/2016
5080gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
5081(19*10^82270-43)/382271Robert Price10/2017
50822^273282-11024182267Enzo Doria05/2014
5083(13^73849+4^73849)/1782263Robert Price05/2013
508410^82254+9^(82254+1)82255Robert Price08/2016
508510^82254+45777382255Patrick De Geest12/2016
508610^82254-9960982254Patrick De Geest12/2016
5087(754*10^82250-7)/982252Robert Price11/2017
508818^65524+1382251Lelio R Paula11/2015
50892^273206-10782244Lelio R Paula06/2012
50902^273193-45914582240Enzo Doria05/2015
50922^273126+3693782220Yves Minet06/2010
509139505!2+12882220Robert Price03/2015
50932^273053-11211182198Enzo Doria06/2014
50942^273016+118582187Lelio R Paula07/2013
5095(2^273008+3)/782183Lelio R Paula12/2012
50965^117554-1538682167Enzo Doria02/2013
5097(38*10^82161+403)/982162Robert Price11/2017
50982^272907-11143982154Enzo Doria05/2014
5099(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
51002^272875-6982144Lelio R Paula06/2012
51017^97197+482141Robert Price01/2014
5102(4*6^105554+1)/582137Serge Batalov10/2014
51036^105531-10982120Lelio R Paula12/2015
51042^272766-6582111Lelio R Paula06/2012
510519^64205-7882103Lelio R Paula12/2015
51062^272702+186997982092Enzo Doria05/2016
5107(29*2^272687-1)/982088Lelio R Paula02/2014
5108(5*10^82085-119)/382086Robert Price04/2016
51092^272660-11004982079Enzo Doria04/2014
51106^105474+6782075Lelio R Paula12/2015
51112^272637+8287582072Lelio R Paula07/2013
51122^272587-3182057Lelio R Paula06/2012
5113(41*10^82044-59)/982045Robert Price10/2017
51148*5^117368+982038Lelio R Paula10/2014
5115(101525^16384+1)/13107482023Lelio R Paula11/2011
51164*5^117343-782020Lelio R Paula10/2014
5117(265*10^81990+17)/381992Robert Price05/2016
51183^171843+1081990Robert Price10/2013
5119(7*10^81985+107)/381986Robert Price02/2017
5120(3*2^272356+1)/17716381983Lelio R Paula12/2012
51212^272296-11114981970Enzo Doria05/2014
5122(9*2^272243-1)/781954Lelio R Paula02/2014
51232^272177-11122381934Enzo Doria05/2014
5124(151009^15817+1)/15101081912Faysal YAtim06/2017
5125(16*10^81896-19)/381897Robert Price03/2016
5126(2^271922+78557)/6381855Lelio R Paula12/2012
5127(10^81848+77)/381848Robert Price01/2017
5128(24737*2^271883+1)/375781846Lelio R Paula06/2014
512910^81778+3981779Robert Price03/2011
513010^81778-17199981778Patrick De Geest07/2013
5131(14*10^81767-11)/381768Erik Branger09/2014
51322^271541+186841781742Enzo Doria04/2016
5133(2^271549-1)/23874968248781734Jens K. Andersen02/2009
51342^271484-16781725Lelio R Paula06/2012
5135(8*10^81709-611)/981709Robert Price11/2017
51362^271382+1290981695Lelio R Paula07/2013
513749^48334+4881694Norbert Schneider07/2014
51387^96668+4881694Lelio R Paula10/2015
513911^78435-141081682Enzo Doria12/2012
51405*10^81653+981654Dmitry Domanov11/2010
5141(2^271211-1)/61396149515981631Jens K. Andersen02/2009
51423^171068+5281621Lelio R Paula12/2015
51432^271115-11040781614Enzo Doria05/2014
51442^271111-11063581613Enzo Doria05/2014
51452^271098-11181609Lelio R Paula06/2012
5146(77*10^81606+13)/981607Robert Price10/2015
51472^271064-279020981599Enzo Doria03/2016
5148(13*2^271053-1)/309581593Lelio R Paula02/2014
51492^271040-5781592Lelio R Paula06/2012
5150(14*10^81585+73)/381586Robert Price04/2016
5151127^38779+12681584Norbert Schneider02/2015
515218^64966-4381551Lelio R Paula11/2015
5153(2^270840+47)/59181529Lelio R Paula12/2012
515420^62654+8781515Lelio R Paula01/2016
5155(19*10^81488+191)/381489Robert Price01/2017
51568*10^81487+2181488Robert Price02/2017
5157(73*10^81485+107)/981486Robert Price08/2016
5158536^29847+29847^53681458Norbert Schneider03/2017
51598*7^96378+981450Lelio R Paula10/2014
51602^270546-11034581443Enzo Doria05/2014
516113^73105-6081435Lelio R Paula11/2015
516244^49524+4381391Norbert Schneider06/2014
5163(3*2^270368-1)/1381389Lelio R Paula02/2014
5164(10^81363+719)/981363Serge Batalov12/2014
5165(10^81353+449)/981353Serge Batalov12/2014
516614^70978-8981350Lelio R Paula11/2015
516711^78108-204081342Enzo Doria12/2012
51683^170400-5881302Lelio R Paula12/2015
5169(17*10^81300-131)/381301Robert Price12/2017
517010^81297+3699181298Patrick De Geest06/2013
517110^81297-5781297Robert Price05/2011
51722^270055-11304781295Enzo Doria07/2014
517318^64759-5581291Lelio R Paula11/2015
5174(2^269987+1)/381274H.&R. Lifchitz10/2000
5175(31^54493-1)/3081268Alexander Zhirkov10/2010
5176(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
5177(2^269816+7)/42490181218Lelio R Paula12/2012
5178(23*10^81214+1)/381215Serge Batalov06/2009
5179(17*2^269720+1)/30381193Lelio R Paula07/2012
518056^46441-55^4644181188Robert Price10/2013
51822^269664+17781177Lelio R Paula06/2012
5181(13*2^269665-1)/18581177Lelio R Paula02/2014
51832^269539-11224981140Enzo Doria06/2014
5184((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
5185(2^269495-5)/981126Lelio R Paula12/2012
51862^269490-362381125Yves Minet10/2009
5187(55459*2^269444+1)/3581114Lelio R Paula06/2014
5188(2^269417+78557)/525781099Lelio R Paula12/2012
51894*5^116011-781089Lelio R Paula10/2014
51907*10^81058+7981059Robert Price02/2017
51912^269236-10990781049Enzo Doria04/2014
5192(8*10^81029-11)/381030Erik Branger03/2014
51933*10^81021+781022Erik Branger11/2013
51946^104115+10381018Lelio R Paula12/2015
51952^269120+186915181014Enzo Doria05/2016
51965^115901+1281012Lelio R Paula10/2015
5197(2^269083-9)/32036980997Lelio R Paula12/2012
519817^65810-2080976Lelio R Paula11/2015
519920^62236-2380971Lelio R Paula01/2016
52002^268974-11218180970Enzo Doria06/2014
5202L(387433)80969Renaud Lifchitz11/2003
5201V(387433)80969Serge Batalov03/2015
5203(2^268955-509203)/580963Lelio R Paula12/2012
5204(87398^16384+1)/6553780957Lelio R Paula11/2011
5205329^32160+32160^32980954Norbert Schneider11/2014
52062^268859-15980935Lelio R Paula05/2012
5207(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
52082^268827+577580925Lelio R Paula07/2013
52092^268824-11025580925Enzo Doria05/2014
52102^268798-186832180917Enzo Doria04/2016
52112^268753-11462180903Enzo Doria05/2015
52122^268743+160580900Lelio R Paula07/2013
52136^103954-13980892Lelio R Paula12/2015
521410^80883+4980884Robert Price03/2011
521510^80883-8032780883Patrick De Geest07/2013
52166^103937+12180879Lelio R Paula12/2015
5217(26*10^80875-119)/380876Robert Price07/2016
5218(22699*2^268657+1)/635180875Lelio R Paula06/2014
52192^268581-86968810580851Lelio R Paula05/2016
5220(11*2^268521-1)/380834Lelio R Paula02/2014
52212^268516-24980832Yves Minet02/2012
52222^268500+1609580827Lelio R Paula07/2013
52233^169402+10080826Lelio R Paula12/2015
52249^84698+8^(84698-1)80823Robert Price03/2016
52252^268472-10973980819Enzo Doria04/2014
5226(9*2^268454+1)/3780813Lelio R Paula12/2012
5227(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
5228134^37987-133^3798780803Jean-Louis Charton12/2005
522915^68702-7680800Lelio R Paula11/2015
52302^268408+780799Lelio R Paula05/2012
52312^268375+14180789Lelio R Paula05/2012
523212^74856-4780784Lelio R Paula11/2015
52336^103770-10780749Lelio R Paula12/2015
52343^169224-6280741Lelio R Paula12/2015
5235p(16866)#/2+6480741Robert Price03/2017
52365^115502-7280733Lelio R Paula10/2015
52372^268079-192780700Yves Minet10/2009
52382^268028+11780685Lelio R Paula05/2012
5239121^38738+12080683Norbert Schneider01/2015
5240(3^169097-8)/83580677Lelio R Paula12/2012
52412^267918+6780652Lelio R Paula05/2012
5242(89*10^80650-179)/980651Robert Price11/2017
5243(302*10^80638+13)/980640Robert Price01/2017
52443^169004+266080636Lelio R Paula12/2015
52452^267860-11285980634Enzo Doria06/2014
52462^267828-11070580625Enzo Doria05/2014
52472^267743+1270580599Lelio R Paula07/2013
5248(22*10^80595+23)/980596Robert Price03/2015
52492^267674-5180578Lelio R Paula05/2012
5250(86*10^80571-41)/980572Robert Price11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

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