PRP Records

Probable Primes Top 10000

(177649 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 ?
45015^119439-6683485Lelio R Paula10/2015
4502(14*10^83471-101)/383472Robert Price04/2017
45035*6^107263+783468Lelio R Paula10/2014
4504(64*10^83461-1)/983462Serge Batalov11/2010
450517^67796-9283420Lelio R Paula11/2015
45062^277106-11005783418Enzo Doria04/2014
45076^107200-1983418Lelio R Paula12/2015
450811^80096-183083412Enzo Doria12/2012
45093^174801+5683402Lelio R Paula12/2015
45102^277033-11197383396Enzo Doria05/2014
451120519^11572+11572^2051983378Hans Havermann03/2017
451220850^9971+9971^2085083374Hans Havermann03/2017
45136^107122-1886383358Enzo Doria03/2013
45143^174697-3483352Robert Price11/2013
4515(9787*2^276855-1)/234583343Lelio R Paula04/2015
45162^276825+7522783333Enzo Doria04/2016
45175^119214+8483328Lelio R Paula10/2015
45182^276803-15983327Lelio R Paula06/2012
4519(3*2^276753-1)/2583311Lelio R Paula02/2014
4520114^40495+40495^11483295Norbert Schneider12/2014
452139967!2+102483282Robert Price02/2015
45232^276641+5783278Lelio R Paula06/2012
452235^53934-341483278Enzo Doria03/2013
4524(2^276655+78557)/36542583276Lelio R Paula12/2012
45252^276615-403583270Lelio R Paula08/2013
45262^276588+115583262Lelio R Paula08/2013
45282^276587-93783261Yves Minet10/2009
45272^276584-11318383261Enzo Doria07/2014
4529(2^276592-1017)/1384373983256Lelio R Paula12/2012
45302^276547-10959183249Enzo Doria04/2014
453113^74733-3283249Lelio R Paula11/2015
45322^276523-258783242Yves Minet07/2014
453318^66311-4383239Lelio R Paula11/2015
453411^79919-153083228Enzo Doria12/2012
45352^276468-10974583226Enzo Doria04/2014
45362^276462+538583224Lelio R Paula08/2013
4537(9787*2^276422-1)/383215Lelio R Paula04/2015
45392^276391-1583202Lelio R Paula06/2012
4538(4*10^83201+173)/383202Robert Price01/2017
45402^276316-10965583180Enzo Doria04/2014
45412^276305-11206383177Enzo Doria06/2014
4542(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
454374913!4-283161Robert Price07/2017
45442^276227-183720783153Enzo Doria05/2015
4545(2^276227+3)/783152Lelio R Paula12/2012
45462^276184-6338983140Paul Bourdelais02/2012
45472^276066-11160383105Enzo Doria05/2014
4548(2^276028-3)*6-783094Gilbert Mozzo09/2016
4549(2^275897+9)/115383051Lelio R Paula12/2012
45502^275879-10980783048Enzo Doria04/2014
4552F(397379)83047Henri Lifchitz08/2003
4551U(397379)83047Serge Batalov03/2015
45533^174040-1483039Robert Price08/2013
4554(86*10^83038-221)/983039Robert Price06/2017
45552^275841-688383037Lelio R Paula07/2011
45563^174002-14083021Lelio R Paula12/2015
45576^106681+7783014Lelio R Paula12/2015
455811^79701-315083001Enzo Doria12/2012
4559(55459*2^275657+1)/2182985Lelio R Paula06/2014
45602^275535-685582945Lelio R Paula08/2013
45623^173828-1482938Robert Price08/2013
45612^275512-10967782938Enzo Doria04/2014
45632^275446-11004582918Enzo Doria04/2014
4564(2^275473+47)/2952609744782916Lelio R Paula12/2012
45653^173755-1482903Robert Price08/2013
45662^275363-11230982893Enzo Doria06/2014
456761^46427-6082888Norbert Schneider10/2014
45683*10^82880-7^8288082881Mike Oakes02/2010
45702^275290+9019582871Lelio R Paula07/2013
4569(35*10^82870-71)/982871Robert Price05/2015
45712^275270-185962182865Enzo Doria03/2016
45722^275259+8182862Henri Lifchitz01/2007
45737^98003+98003^7+182823Robert Price05/2014
457410^82790+12604382791Patrick De Geest07/2013
457510^82790-4782790Robert Price05/2011
45762^274985-11266382779Enzo Doria06/2014
45772^274935+1501582764Lelio R Paula07/2013
4578(17*2^274922+1)/382761Lelio R Paula12/2012
4579(43*10^82752-61)/982753Robert Price06/2015
4580(3*2^274862+1)/102782740Lelio R Paula12/2012
4581(31*2^274848-1)/406582736Lelio R Paula02/2014
4582(4^137405+23)/382726Robert Price02/2017
45832^274791-11049182721Enzo Doria05/2014
4584(11*2^274776-1)/9582715Lelio R Paula02/2014
45852^274704-11139582695Enzo Doria05/2014
45862^274686-391182689Yves Minet04/2017
4587(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
4588(3^173263-5)/1449882664Lelio R Paula12/2012
45892^274511-6487582637Lelio R Paula08/2013
459012^76572-8382636Lelio R Paula11/2015
45913^173191-2^17319182634Mike Oakes02/2004
459214^72072-1582604Lelio R Paula11/2015
4593(55459*2^274339+1)/382589Lelio R Paula06/2014
45942^274351+12382588Lelio R Paula06/2012
4595(1017*2^274339-1)/351582584Lelio R Paula04/2015
45966^106086+11382551Lelio R Paula12/2015
45972^274093-5869582511Lelio R Paula07/2013
45987*10^82509-4782510Robert Price02/2017
45992^274081-655582507Lelio R Paula07/2013
46012^274074-274074+182505Robert Price10/2014
460214^71985+4782505Lelio R Paula11/2015
46005*10^82504+2182505Robert Price01/2017
46036^106014-13982495Lelio R Paula12/2015
4604(2^274046+47)/75382494Lelio R Paula12/2012
46052^274008-183809982485Enzo Doria05/2015
46062^273981-11002982477Enzo Doria04/2014
460719^64490-3082467Lelio R Paula12/2015
46092^273785+1171582418Lelio R Paula07/2013
46088*10^82417+5182418Robert Price05/2017
461011^79133-1082409Theodore Burton11/2005
461191^42063+9082404Norbert Schneider01/2016
46132^273662-6382381Lelio R Paula06/2012
46122^273661+25582381Lelio R Paula07/2013
4614(62*10^82377-17)/982378Robert Price09/2015
4615(11*10^82323+91)/382323Robert Price02/2017
461615^69984+3282308Lelio R Paula11/2015
46179*6^105746+782288Lelio R Paula10/2014
461889^42211-8882286Norbert Schneider01/2016
4619gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
46202^273282-11024182267Enzo Doria05/2014
4621(13^73849+4^73849)/1782263Robert Price05/2013
462310^82254+9^(82254+1)82255Robert Price08/2016
462210^82254+45777382255Patrick De Geest12/2016
462410^82254-9960982254Patrick De Geest12/2016
462518^65524+1382251Lelio R Paula11/2015
46262^273206-10782244Lelio R Paula06/2012
46272^273193-45914582240Enzo Doria05/2015
46292^273126+3693782220Yves Minet06/2010
462839505!2+12882220Robert Price03/2015
46302^273053-11211182198Enzo Doria06/2014
46312^273016+118582187Lelio R Paula07/2013
4632(2^273008+3)/782183Lelio R Paula12/2012
46335^117554-1538682167Enzo Doria02/2013
46342^272907-11143982154Enzo Doria05/2014
4635(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
46362^272875-6982144Lelio R Paula06/2012
46377^97197+482141Robert Price01/2014
4638(4*6^105554+1)/582137Serge Batalov10/2014
46396^105531-10982120Lelio R Paula12/2015
46402^272766-6582111Lelio R Paula06/2012
464119^64205-7882103Lelio R Paula12/2015
46422^272702+186997982092Enzo Doria05/2016
4643(29*2^272687-1)/982088Lelio R Paula02/2014
4644(5*10^82085-119)/382086Robert Price04/2016
46452^272660-11004982079Enzo Doria04/2014
46466^105474+6782075Lelio R Paula12/2015
46472^272637+8287582072Lelio R Paula07/2013
46482^272587-3182057Lelio R Paula06/2012
46498*5^117368+982038Lelio R Paula10/2014
4650(101525^16384+1)/13107482023Lelio R Paula11/2011
46514*5^117343-782020Lelio R Paula10/2014
4652(265*10^81990+17)/381992Robert Price05/2016
46533^171843+1081990Robert Price10/2013
4654(7*10^81985+107)/381986Robert Price02/2017
4655(3*2^272356+1)/17716381983Lelio R Paula12/2012
46562^272296-11114981970Enzo Doria05/2014
4657(9*2^272243-1)/781954Lelio R Paula02/2014
46582^272177-11122381934Enzo Doria05/2014
4659(151009^15817+1)/15101081912Faysal YAtim06/2017
4660(16*10^81896-19)/381897Robert Price03/2016
4661(2^271922+78557)/6381855Lelio R Paula12/2012
4662(10^81848+77)/381848Robert Price01/2017
4663(24737*2^271883+1)/375781846Lelio R Paula06/2014
466410^81778+3981779Robert Price03/2011
466510^81778-17199981778Patrick De Geest07/2013
4666(14*10^81767-11)/381768Erik Branger09/2014
46672^271541+186841781742Enzo Doria04/2016
4668(2^271549-1)/23874968248781734Jens K. Andersen02/2009
46692^271484-16781725Lelio R Paula06/2012
46702^271382+1290981695Lelio R Paula07/2013
467149^48334+4881694Norbert Schneider07/2014
46727^96668+4881694Lelio R Paula10/2015
467311^78435-141081682Enzo Doria12/2012
46745*10^81653+981654Dmitry Domanov11/2010
4675(2^271211-1)/61396149515981631Jens K. Andersen02/2009
46763^171068+5281621Lelio R Paula12/2015
46772^271115-11040781614Enzo Doria05/2014
46782^271111-11063581613Enzo Doria05/2014
46792^271098-11181609Lelio R Paula06/2012
4680(77*10^81606+13)/981607Robert Price10/2015
46812^271064-279020981599Enzo Doria03/2016
4682(13*2^271053-1)/309581593Lelio R Paula02/2014
46832^271040-5781592Lelio R Paula06/2012
4684(14*10^81585+73)/381586Robert Price04/2016
4685127^38779+12681584Norbert Schneider02/2015
468618^64966-4381551Lelio R Paula11/2015
4687(2^270840+47)/59181529Lelio R Paula12/2012
468820^62654+8781515Lelio R Paula01/2016
4689(19*10^81488+191)/381489Robert Price01/2017
46908*10^81487+2181488Robert Price02/2017
4691(73*10^81485+107)/981486Robert Price08/2016
4692536^29847+29847^53681458Norbert Schneider03/2017
46938*7^96378+981450Lelio R Paula10/2014
46942^270546-11034581443Enzo Doria05/2014
469513^73105-6081435Lelio R Paula11/2015
469644^49524+4381391Norbert Schneider06/2014
4697(3*2^270368-1)/1381389Lelio R Paula02/2014
4698(10^81363+719)/981363Serge Batalov12/2014
4699(10^81353+449)/981353Serge Batalov12/2014
470014^70978-8981350Lelio R Paula11/2015
470111^78108-204081342Enzo Doria12/2012
47023^170400-5881302Lelio R Paula12/2015
470310^81297+3699181298Patrick De Geest06/2013
470410^81297-5781297Robert Price05/2011
47052^270055-11304781295Enzo Doria07/2014
470618^64759-5581291Lelio R Paula11/2015
4707(2^269987+1)/381274H.&R. Lifchitz10/2000
4708(31^54493-1)/3081268Alexander Zhirkov10/2010
4709(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
4710(2^269816+7)/42490181218Lelio R Paula12/2012
4711(23*10^81214+1)/381215Serge Batalov06/2009
4712(17*2^269720+1)/30381193Lelio R Paula07/2012
471356^46441-55^4644181188Robert Price10/2013
47152^269664+17781177Lelio R Paula06/2012
4714(13*2^269665-1)/18581177Lelio R Paula02/2014
47162^269539-11224981140Enzo Doria06/2014
4717((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
4718(2^269495-5)/981126Lelio R Paula12/2012
47192^269490-362381125Yves Minet10/2009
4720(55459*2^269444+1)/3581114Lelio R Paula06/2014
4721(2^269417+78557)/525781099Lelio R Paula12/2012
47224*5^116011-781089Lelio R Paula10/2014
47237*10^81058+7981059Robert Price02/2017
47242^269236-10990781049Enzo Doria04/2014
4725(8*10^81029-11)/381030Erik Branger03/2014
47263*10^81021+781022Erik Branger11/2013
47276^104115+10381018Lelio R Paula12/2015
47282^269120+186915181014Enzo Doria05/2016
47295^115901+1281012Lelio R Paula10/2015
4730(2^269083-9)/32036980997Lelio R Paula12/2012
473117^65810-2080976Lelio R Paula11/2015
473220^62236-2380971Lelio R Paula01/2016
47332^268974-11218180970Enzo Doria06/2014
4735L(387433)80969Renaud Lifchitz11/2003
4734V(387433)80969Serge Batalov03/2015
4736(2^268955-509203)/580963Lelio R Paula12/2012
4737(87398^16384+1)/6553780957Lelio R Paula11/2011
4738329^32160+32160^32980954Norbert Schneider11/2014
47392^268859-15980935Lelio R Paula05/2012
4740(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
47412^268827+577580925Lelio R Paula07/2013
47422^268824-11025580925Enzo Doria05/2014
47432^268798-186832180917Enzo Doria04/2016
47442^268753-11462180903Enzo Doria05/2015
47452^268743+160580900Lelio R Paula07/2013
47466^103954-13980892Lelio R Paula12/2015
474710^80883+4980884Robert Price03/2011
474810^80883-8032780883Patrick De Geest07/2013
47496^103937+12180879Lelio R Paula12/2015
4750(26*10^80875-119)/380876Robert Price07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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