PRP Records

Probable Primes Top 10000

(191107 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 ?
47512^276316-10965583180Enzo Doria04/2014
47522^276305-11206383177Enzo Doria06/2014
4753(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
475474913!4-283161Robert Price07/2017
47552^276227-183720783153Enzo Doria05/2015
4756(2^276227+3)/783152Lelio R Paula12/2012
47572^276184-6338983140Paul Bourdelais02/2012
47582^276066-11160383105Enzo Doria05/2014
4759(2^276028-3)*6-783094Gilbert Mozzo09/2016
4760(2^275897+9)/115383051Lelio R Paula12/2012
47612^275879-10980783048Enzo Doria04/2014
4763F(397379)83047Henri Lifchitz08/2003
4762U(397379)83047Serge Batalov03/2015
47653^174040-1483039Robert Price08/2013
4764(86*10^83038-221)/983039Robert Price06/2017
47662^275841-688383037Lelio R Paula07/2011
47673^174002-14083021Lelio R Paula12/2015
47686^106681+7783014Lelio R Paula12/2015
4769187^36539-283011Lelio R Paula10/2017
477011^79701-315083001Enzo Doria12/2012
4771(55459*2^275657+1)/2182985Lelio R Paula06/2014
4772(7*10^82960-457)/982960Robert Price09/2017
47732^275535-685582945Lelio R Paula08/2013
47743^173828-1482938Robert Price08/2013
47752^275512-10967782938Enzo Doria04/2014
47762^275446-11004582918Enzo Doria04/2014
4777(2^275473+47)/2952609744782916Lelio R Paula12/2012
47783^173755-1482903Robert Price08/2013
4779(182*10^82898+43)/982900Robert Price11/2017
47802^275363-11230982893Enzo Doria06/2014
478161^46427-6082888Norbert Schneider10/2014
47823*10^82880-7^8288082881Mike Oakes02/2010
47842^275290+9019582871Lelio R Paula07/2013
4783(35*10^82870-71)/982871Robert Price05/2015
47852^275270-185962182865Enzo Doria03/2016
47862^275259+8182862Henri Lifchitz01/2007
47877^98003+98003^7+182823Robert Price05/2014
478810^82790+12604382791Patrick De Geest07/2013
478910^82790-4782790Robert Price05/2011
47902^274985-11266382779Enzo Doria06/2014
47912^274935+1501582764Lelio R Paula07/2013
4792(17*2^274922+1)/382761Lelio R Paula12/2012
4793(43*10^82752-61)/982753Robert Price06/2015
4794(3*2^274862+1)/102782740Lelio R Paula12/2012
4795(31*2^274848-1)/406582736Lelio R Paula02/2014
4796(4^137405+23)/382726Robert Price02/2017
47972^274791-11049182721Enzo Doria05/2014
4798(11*2^274776-1)/9582715Lelio R Paula02/2014
4799(47*10^82706-119)/982707Robert Price09/2017
48002^274704-11139582695Enzo Doria05/2014
48012^274686-391182689Yves Minet04/2017
4802(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
4803(3^173263-5)/1449882664Lelio R Paula12/2012
48042^274511-6487582637Lelio R Paula08/2013
480512^76572-8382636Lelio R Paula11/2015
48063^173191-2^17319182634Mike Oakes02/2004
480714^72072-1582604Lelio R Paula11/2015
4808(55459*2^274339+1)/382589Lelio R Paula06/2014
48092^274351+12382588Lelio R Paula06/2012
4810(1017*2^274339-1)/351582584Lelio R Paula04/2015
48116^106086+11382551Lelio R Paula12/2015
4812(17*10^82540-377)/982541Robert Price11/2017
48132^274093-5869582511Lelio R Paula07/2013
48147*10^82509-4782510Robert Price02/2017
48152^274081-655582507Lelio R Paula07/2013
48172^274074-274074+182505Robert Price10/2014
481814^71985+4782505Lelio R Paula11/2015
48165*10^82504+2182505Robert Price01/2017
48196^106014-13982495Lelio R Paula12/2015
4820(2^274046+47)/75382494Lelio R Paula12/2012
48212^274008-183809982485Enzo Doria05/2015
48222^273981-11002982477Enzo Doria04/2014
482319^64490-3082467Lelio R Paula12/2015
48242^273785+1171582418Lelio R Paula07/2013
48258*10^82417+5182418Robert Price05/2017
482611^79133-1082409Theodore Burton11/2005
482791^42063+9082404Norbert Schneider01/2016
48282^273662-6382381Lelio R Paula06/2012
48292^273661+25582381Lelio R Paula07/2013
4830(62*10^82377-17)/982378Robert Price09/2015
48318*10^82360-5182361Robert Price10/2017
4832(79*10^82347-1)/382349Robert Price11/2017
4833(11*10^82323+91)/382323Robert Price02/2017
4834(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
4835(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
483615^69984+3282308Lelio R Paula11/2015
48379*6^105746+782288Lelio R Paula10/2014
483889^42211-8882286Norbert Schneider01/2016
4839gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
4840(19*10^82270-43)/382271Robert Price10/2017
48412^273282-11024182267Enzo Doria05/2014
4842(13^73849+4^73849)/1782263Robert Price05/2013
484310^82254+9^(82254+1)82255Robert Price08/2016
484410^82254+45777382255Patrick De Geest12/2016
484510^82254-9960982254Patrick De Geest12/2016
4846(754*10^82250-7)/982252Robert Price11/2017
484718^65524+1382251Lelio R Paula11/2015
48482^273206-10782244Lelio R Paula06/2012
48492^273193-45914582240Enzo Doria05/2015
48512^273126+3693782220Yves Minet06/2010
485039505!2+12882220Robert Price03/2015
48522^273053-11211182198Enzo Doria06/2014
48532^273016+118582187Lelio R Paula07/2013
4854(2^273008+3)/782183Lelio R Paula12/2012
48555^117554-1538682167Enzo Doria02/2013
48562^272907-11143982154Enzo Doria05/2014
4857(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
48582^272875-6982144Lelio R Paula06/2012
48597^97197+482141Robert Price01/2014
4860(4*6^105554+1)/582137Serge Batalov10/2014
48616^105531-10982120Lelio R Paula12/2015
48622^272766-6582111Lelio R Paula06/2012
486319^64205-7882103Lelio R Paula12/2015
48642^272702+186997982092Enzo Doria05/2016
4865(29*2^272687-1)/982088Lelio R Paula02/2014
4866(5*10^82085-119)/382086Robert Price04/2016
48672^272660-11004982079Enzo Doria04/2014
48686^105474+6782075Lelio R Paula12/2015
48692^272637+8287582072Lelio R Paula07/2013
48702^272587-3182057Lelio R Paula06/2012
4871(41*10^82044-59)/982045Robert Price10/2017
48728*5^117368+982038Lelio R Paula10/2014
4873(101525^16384+1)/13107482023Lelio R Paula11/2011
48744*5^117343-782020Lelio R Paula10/2014
4875(265*10^81990+17)/381992Robert Price05/2016
48763^171843+1081990Robert Price10/2013
4877(7*10^81985+107)/381986Robert Price02/2017
4878(3*2^272356+1)/17716381983Lelio R Paula12/2012
48792^272296-11114981970Enzo Doria05/2014
4880(9*2^272243-1)/781954Lelio R Paula02/2014
48812^272177-11122381934Enzo Doria05/2014
4882(151009^15817+1)/15101081912Faysal YAtim06/2017
4883(16*10^81896-19)/381897Robert Price03/2016
4884(2^271922+78557)/6381855Lelio R Paula12/2012
4885(10^81848+77)/381848Robert Price01/2017
4886(24737*2^271883+1)/375781846Lelio R Paula06/2014
488710^81778+3981779Robert Price03/2011
488810^81778-17199981778Patrick De Geest07/2013
4889(14*10^81767-11)/381768Erik Branger09/2014
48902^271541+186841781742Enzo Doria04/2016
4891(2^271549-1)/23874968248781734Jens K. Andersen02/2009
48922^271484-16781725Lelio R Paula06/2012
48932^271382+1290981695Lelio R Paula07/2013
489449^48334+4881694Norbert Schneider07/2014
48957^96668+4881694Lelio R Paula10/2015
489611^78435-141081682Enzo Doria12/2012
48975*10^81653+981654Dmitry Domanov11/2010
4898(2^271211-1)/61396149515981631Jens K. Andersen02/2009
48993^171068+5281621Lelio R Paula12/2015
49002^271115-11040781614Enzo Doria05/2014
49012^271111-11063581613Enzo Doria05/2014
49022^271098-11181609Lelio R Paula06/2012
4903(77*10^81606+13)/981607Robert Price10/2015
49042^271064-279020981599Enzo Doria03/2016
4905(13*2^271053-1)/309581593Lelio R Paula02/2014
49062^271040-5781592Lelio R Paula06/2012
4907(14*10^81585+73)/381586Robert Price04/2016
4908127^38779+12681584Norbert Schneider02/2015
490918^64966-4381551Lelio R Paula11/2015
4910(2^270840+47)/59181529Lelio R Paula12/2012
491120^62654+8781515Lelio R Paula01/2016
4912(19*10^81488+191)/381489Robert Price01/2017
49138*10^81487+2181488Robert Price02/2017
4914(73*10^81485+107)/981486Robert Price08/2016
4915536^29847+29847^53681458Norbert Schneider03/2017
49168*7^96378+981450Lelio R Paula10/2014
49172^270546-11034581443Enzo Doria05/2014
491813^73105-6081435Lelio R Paula11/2015
491944^49524+4381391Norbert Schneider06/2014
4920(3*2^270368-1)/1381389Lelio R Paula02/2014
4921(10^81363+719)/981363Serge Batalov12/2014
4922(10^81353+449)/981353Serge Batalov12/2014
492314^70978-8981350Lelio R Paula11/2015
492411^78108-204081342Enzo Doria12/2012
49253^170400-5881302Lelio R Paula12/2015
492610^81297+3699181298Patrick De Geest06/2013
492710^81297-5781297Robert Price05/2011
49282^270055-11304781295Enzo Doria07/2014
492918^64759-5581291Lelio R Paula11/2015
4930(2^269987+1)/381274H.&R. Lifchitz10/2000
4931(31^54493-1)/3081268Alexander Zhirkov10/2010
4932(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
4933(2^269816+7)/42490181218Lelio R Paula12/2012
4934(23*10^81214+1)/381215Serge Batalov06/2009
4935(17*2^269720+1)/30381193Lelio R Paula07/2012
493656^46441-55^4644181188Robert Price10/2013
49372^269664+17781177Lelio R Paula06/2012
4938(13*2^269665-1)/18581177Lelio R Paula02/2014
49392^269539-11224981140Enzo Doria06/2014
4940((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
4941(2^269495-5)/981126Lelio R Paula12/2012
49422^269490-362381125Yves Minet10/2009
4943(55459*2^269444+1)/3581114Lelio R Paula06/2014
4944(2^269417+78557)/525781099Lelio R Paula12/2012
49454*5^116011-781089Lelio R Paula10/2014
49467*10^81058+7981059Robert Price02/2017
49472^269236-10990781049Enzo Doria04/2014
4948(8*10^81029-11)/381030Erik Branger03/2014
49493*10^81021+781022Erik Branger11/2013
49506^104115+10381018Lelio R Paula12/2015
49512^269120+186915181014Enzo Doria05/2016
49525^115901+1281012Lelio R Paula10/2015
4953(2^269083-9)/32036980997Lelio R Paula12/2012
495417^65810-2080976Lelio R Paula11/2015
495520^62236-2380971Lelio R Paula01/2016
49562^268974-11218180970Enzo Doria06/2014
4958L(387433)80969Renaud Lifchitz11/2003
4957V(387433)80969Serge Batalov03/2015
4959(2^268955-509203)/580963Lelio R Paula12/2012
4960(87398^16384+1)/6553780957Lelio R Paula11/2011
4961329^32160+32160^32980954Norbert Schneider11/2014
49622^268859-15980935Lelio R Paula05/2012
4963(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
49642^268827+577580925Lelio R Paula07/2013
49652^268824-11025580925Enzo Doria05/2014
49662^268798-186832180917Enzo Doria04/2016
49672^268753-11462180903Enzo Doria05/2015
49682^268743+160580900Lelio R Paula07/2013
49696^103954-13980892Lelio R Paula12/2015
497010^80883+4980884Robert Price03/2011
497110^80883-8032780883Patrick De Geest07/2013
49726^103937+12180879Lelio R Paula12/2015
4973(26*10^80875-119)/380876Robert Price07/2016
4974(22699*2^268657+1)/635180875Lelio R Paula06/2014
49752^268581-86968810580851Lelio R Paula05/2016
4976(11*2^268521-1)/380834Lelio R Paula02/2014
49772^268516-24980832Yves Minet02/2012
49782^268500+1609580827Lelio R Paula07/2013
49793^169402+10080826Lelio R Paula12/2015
49809^84698+8^(84698-1)80823Robert Price03/2016
49812^268472-10973980819Enzo Doria04/2014
4982(9*2^268454+1)/3780813Lelio R Paula12/2012
4983(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
4984134^37987-133^3798780803Jean-Louis Charton12/2005
498515^68702-7680800Lelio R Paula11/2015
49862^268408+780799Lelio R Paula05/2012
49872^268375+14180789Lelio R Paula05/2012
498812^74856-4780784Lelio R Paula11/2015
49896^103770-10780749Lelio R Paula12/2015
49913^169224-6280741Lelio R Paula12/2015
4990p(16866)#/2+6480741Robert Price03/2017
49925^115502-7280733Lelio R Paula10/2015
49932^268079-192780700Yves Minet10/2009
49942^268028+11780685Lelio R Paula05/2012
4995121^38738+12080683Norbert Schneider01/2015
4996(3^169097-8)/83580677Lelio R Paula12/2012
49972^267918+6780652Lelio R Paula05/2012
4998(89*10^80650-179)/980651Robert Price11/2017
4999(302*10^80638+13)/980640Robert Price01/2017
50003^169004+266080636Lelio R Paula12/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 22 2017 23:29 (Time in France)

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