PRP Records

Probable Primes Top 10000

(252675 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 (> 50000) Who ? When ?
55015^119214+8483328Lelio R Paula10/2015
55022^276803-15983327Lelio R Paula06/2012
5503(3*2^276753-1)/2583311Lelio R Paula02/2014
5504114^40495+40495^11483295Norbert Schneider12/2014
550539967!2+102483282Robert Price02/2015
55062^276641+5783278Lelio R Paula06/2012
550735^53934-341483278Enzo Doria03/2013
5508(2^276655+78557)/36542583276Lelio R Paula12/2012
55092^276615-403583270Lelio R Paula08/2013
55102^276588+115583262Lelio R Paula08/2013
55122^276587-93783261Yves Minet10/2009
55112^276584-11318383261Enzo Doria07/2014
5513(2^276592-1017)/1384373983256Lelio R Paula12/2012
55142^276547-10959183249Enzo Doria04/2014
551513^74733-3283249Lelio R Paula11/2015
55162^276523-258783242Yves Minet07/2014
551718^66311-4383239Lelio R Paula11/2015
551811^79919-153083228Enzo Doria12/2012
55192^276468-10974583226Enzo Doria04/2014
55202^276462+538583224Lelio R Paula08/2013
5521(9787*2^276422-1)/383215Lelio R Paula04/2015
55222^276391-1583202Lelio R Paula06/2012
5523(4*10^83201+173)/383202Robert Price01/2017
55242^276316-10965583180Enzo Doria04/2014
55252^276305-11206383177Enzo Doria06/2014
5526(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
552774913!4-283161Robert Price07/2017
55282^276227-183720783153Enzo Doria05/2015
5529(2^276227+3)/783152Lelio R Paula12/2012
55302^276184-6338983140Paul Bourdelais02/2012
55312^276066-11160383105Enzo Doria05/2014
5532(2^276028-3)*6-783094Gilbert Mozzo09/2016
5533(2^275897+9)/115383051Lelio R Paula12/2012
55342^275879-10980783048Enzo Doria04/2014
5536F(397379)83047Henri Lifchitz08/2003
5535U(397379)83047Serge Batalov03/2015
55383^174040-1483039Robert Price08/2013
5537(86*10^83038-221)/983039Robert Price06/2017
55392^275841-688383037Lelio R Paula07/2011
55403^174002-14083021Lelio R Paula12/2015
55416^106681+7783014Lelio R Paula12/2015
5542187^36539-283011Lelio R Paula10/2017
554311^79701-315083001Enzo Doria12/2012
5544(55459*2^275657+1)/2182985Lelio R Paula06/2014
5545(7*10^82960-457)/982960Robert Price09/2017
55462^275535-685582945Lelio R Paula08/2013
55483^173828-1482938Robert Price08/2013
55472^275512-10967782938Enzo Doria04/2014
55492^275446-11004582918Enzo Doria04/2014
5550(2^275473+47)/2952609744782916Lelio R Paula12/2012
55513^173755-1482903Robert Price08/2013
5552(182*10^82898+43)/982900Robert Price11/2017
55532^275363-11230982893Enzo Doria06/2014
555461^46427-6082888Norbert Schneider10/2014
55553*10^82880-7^8288082881Mike Oakes02/2010
55572^275290+9019582871Lelio R Paula07/2013
5556(35*10^82870-71)/982871Robert Price05/2015
55582^275270-185962182865Enzo Doria03/2016
55592^275259+8182862Henri Lifchitz01/2007
5560(113703^16384+1)/282834Richard Fischer04/2018
55617^98003+98003^7+182823Robert Price05/2014
556210^82790+12604382791Patrick De Geest07/2013
556310^82790-4782790Robert Price05/2011
55642^274985-11266382779Enzo Doria06/2014
55652^274935+1501582764Lelio R Paula07/2013
5566(17*2^274922+1)/382761Lelio R Paula12/2012
5567(43*10^82752-61)/982753Robert Price06/2015
5568(3*2^274862+1)/102782740Lelio R Paula12/2012
5569(31*2^274848-1)/406582736Lelio R Paula02/2014
5570(4^137405+23)/382726Robert Price02/2017
55712^274791-11049182721Enzo Doria05/2014
5572(11*2^274776-1)/9582715Lelio R Paula02/2014
5573(47*10^82706-119)/982707Robert Price09/2017
55742^274704-11139582695Enzo Doria05/2014
55752^274686-391182689Yves Minet04/2017
5576(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
5577(3^173263-5)/1449882664Lelio R Paula12/2012
55782^274511-6487582637Lelio R Paula08/2013
557912^76572-8382636Lelio R Paula11/2015
55803^173191-2^17319182634Mike Oakes02/2004
558114^72072-1582604Lelio R Paula11/2015
5582(55459*2^274339+1)/382589Lelio R Paula06/2014
55832^274351+12382588Lelio R Paula06/2012
5584(1017*2^274339-1)/351582584Lelio R Paula04/2015
55856^106086+11382551Lelio R Paula12/2015
5586(17*10^82540-377)/982541Robert Price11/2017
55872^274093-5869582511Lelio R Paula07/2013
55887*10^82509-4782510Robert Price02/2017
55892^274081-655582507Lelio R Paula07/2013
55902^274074-274074+182505Robert Price10/2014
559114^71985+4782505Lelio R Paula11/2015
55925*10^82504+2182505Robert Price01/2017
55936^106014-13982495Lelio R Paula12/2015
5594(2^274046+47)/75382494Lelio R Paula12/2012
55952^274008-183809982485Enzo Doria05/2015
55962^273981-11002982477Enzo Doria04/2014
559719^64490-3082467Lelio R Paula12/2015
55992^273785+1171582418Lelio R Paula07/2013
55988*10^82417+5182418Robert Price05/2017
560011^79133-1082409Theodore Burton11/2005
560191^42063+9082404Norbert Schneider01/2016
56032^273662-6382381Lelio R Paula06/2012
56022^273661+25582381Lelio R Paula07/2013
5604(62*10^82377-17)/982378Robert Price09/2015
56052^273608+52428782365Paul Underwood08/2018
56068*10^82360-5182361Robert Price10/2017
5607(79*10^82347-1)/382349Robert Price11/2017
5608(11*10^82323+91)/382323Robert Price02/2017
5609(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
5610(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
561115^69984+3282308Lelio R Paula11/2015
56129*6^105746+782288Lelio R Paula10/2014
561389^42211-8882286Norbert Schneider01/2016
5614gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
5615(19*10^82270-43)/382271Robert Price10/2017
56162^273282-11024182267Enzo Doria05/2014
5617(13^73849+4^73849)/1782263Robert Price05/2013
561810^82254+9^(82254+1)82255Robert Price08/2016
561910^82254+45777382255Patrick De Geest12/2016
562010^82254-9960982254Patrick De Geest12/2016
5621(754*10^82250-7)/982252Robert Price11/2017
562218^65524+1382251Lelio R Paula11/2015
56232^273206-10782244Lelio R Paula06/2012
56242^273193-45914582240Enzo Doria05/2015
56262^273126+3693782220Yves Minet06/2010
562539505!2+12882220Robert Price03/2015
56272^273053-11211182198Enzo Doria06/2014
56282^273016+118582187Lelio R Paula07/2013
5629(2^273008+3)/782183Lelio R Paula12/2012
56305^117554-1538682167Enzo Doria02/2013
5631(38*10^82161+403)/982162Robert Price11/2017
56322^272907-11143982154Enzo Doria05/2014
5633(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
56342^272875-6982144Lelio R Paula06/2012
56357^97197+482141Robert Price01/2014
5636(4*6^105554+1)/582137Serge Batalov10/2014
56372^272826-443382129Yves Minet03/2019
56386^105531-10982120Lelio R Paula12/2015
56392^272766-6582111Lelio R Paula06/2012
564019^64205-7882103Lelio R Paula12/2015
56412^272702+186997982092Enzo Doria05/2016
5642(29*2^272687-1)/982088Lelio R Paula02/2014
5643(5*10^82085-119)/382086Robert Price04/2016
56442^272660-11004982079Enzo Doria04/2014
56456^105474+6782075Lelio R Paula12/2015
56462^272637+8287582072Lelio R Paula07/2013
56472^272587-3182057Lelio R Paula06/2012
5648(41*10^82044-59)/982045Robert Price10/2017
56498*5^117368+982038Lelio R Paula10/2014
5650(101525^16384+1)/13107482023Lelio R Paula11/2011
56514*5^117343-782020Lelio R Paula10/2014
5652(265*10^81990+17)/381992Robert Price05/2016
56533^171843+1081990Robert Price10/2013
5654(7*10^81985+107)/381986Robert Price02/2017
5655(3*2^272356+1)/17716381983Lelio R Paula12/2012
56562^272296-11114981970Enzo Doria05/2014
5657(9*2^272243-1)/781954Lelio R Paula02/2014
56582^272177-11122381934Enzo Doria05/2014
5659(151009^15817+1)/15101081912Faysal YAtim06/2017
5660(16*10^81896-19)/381897Robert Price03/2016
5661(2^271922+78557)/6381855Lelio R Paula12/2012
5662(10^81848+77)/381848Robert Price01/2017
5663(24737*2^271883+1)/375781846Lelio R Paula06/2014
566410^81778+3981779Robert Price03/2011
566510^81778-17199981778Patrick De Geest07/2013
5666(14*10^81767-11)/381768Erik Branger09/2014
56672^271541+186841781742Enzo Doria04/2016
5668(2^271549-1)/23874968248781734Jens K. Andersen02/2009
56692^271484-16781725Lelio R Paula06/2012
5670(8*10^81709-611)/981709Robert Price11/2017
56712^271382+1290981695Lelio R Paula07/2013
567249^48334+4881694Norbert Schneider07/2014
56737^96668+4881694Lelio R Paula10/2015
567411^78435-141081682Enzo Doria12/2012
56755*10^81653+981654Dmitry Domanov11/2010
5676(2^271211-1)/61396149515981631Jens K. Andersen02/2009
56773^171068+5281621Lelio R Paula12/2015
56782^271115-11040781614Enzo Doria05/2014
56792^271111-11063581613Enzo Doria05/2014
56802^271098-11181609Lelio R Paula06/2012
5681(77*10^81606+13)/981607Robert Price10/2015
56822^271064-279020981599Enzo Doria03/2016
5683(13*2^271053-1)/309581593Lelio R Paula02/2014
56842^271040-5781592Lelio R Paula06/2012
5685(14*10^81585+73)/381586Robert Price04/2016
5686127^38779+12681584Norbert Schneider02/2015
568718^64966-4381551Lelio R Paula11/2015
5688(2^270840+47)/59181529Lelio R Paula12/2012
568920^62654+8781515Lelio R Paula01/2016
5690(19*10^81488+191)/381489Robert Price01/2017
56918*10^81487+2181488Robert Price02/2017
5692(73*10^81485+107)/981486Robert Price08/2016
5693536^29847+29847^53681458Norbert Schneider03/2017
56948*7^96378+981450Lelio R Paula10/2014
56952^270546-11034581443Enzo Doria05/2014
569613^73105-6081435Lelio R Paula11/2015
569744^49524+4381391Norbert Schneider06/2014
5698(3*2^270368-1)/1381389Lelio R Paula02/2014
5699(10^81363+719)/981363Serge Batalov12/2014
5700(10^81353+449)/981353Serge Batalov12/2014
570114^70978-8981350Lelio R Paula11/2015
570211^78108-204081342Enzo Doria12/2012
57033^170400-5881302Lelio R Paula12/2015
5704(17*10^81300-131)/381301Robert Price12/2017
570510^81297+3699181298Patrick De Geest06/2013
570610^81297-5781297Robert Price05/2011
57072^270055-11304781295Enzo Doria07/2014
570818^64759-5581291Lelio R Paula11/2015
5709(2^269987+1)/381274H.&R. Lifchitz10/2000
5710(31^54493-1)/3081268Alexander Zhirkov10/2010
5711(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
57122^269819-459781224Yves Minet03/2019
5713(2^269816+7)/42490181218Lelio R Paula12/2012
5714(23*10^81214+1)/381215Serge Batalov06/2009
5715(17*2^269720+1)/30381193Lelio R Paula07/2012
571656^46441-55^4644181188Robert Price10/2013
57172^269664+17781177Lelio R Paula06/2012
5718(13*2^269665-1)/18581177Lelio R Paula02/2014
57192^269539-11224981140Enzo Doria06/2014
5720((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
5721(2^269495-5)/981126Lelio R Paula12/2012
57222^269490-362381125Yves Minet10/2009
5723(55459*2^269444+1)/3581114Lelio R Paula06/2014
5724(2^269417+78557)/525781099Lelio R Paula12/2012
57254*5^116011-781089Lelio R Paula10/2014
57267*10^81058+7981059Robert Price02/2017
57272^269236-10990781049Enzo Doria04/2014
5728(8*10^81029-11)/381030Erik Branger03/2014
57293*10^81021+781022Erik Branger11/2013
57306^104115+10381018Lelio R Paula12/2015
57312^269120+186915181014Enzo Doria05/2016
57325^115901+1281012Lelio R Paula10/2015
5733(2^269083-9)/32036980997Lelio R Paula12/2012
573417^65810-2080976Lelio R Paula11/2015
573520^62236-2380971Lelio R Paula01/2016
57362^268974-11218180970Enzo Doria06/2014
5738L(387433)80969Renaud Lifchitz11/2003
5737V(387433)80969Serge Batalov03/2015
5739(2^268955-509203)/580963Lelio R Paula12/2012
5740(87398^16384+1)/6553780957Lelio R Paula11/2011
5741329^32160+32160^32980954Norbert Schneider11/2014
57422^268859-15980935Lelio R Paula05/2012
5743(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
57442^268827+577580925Lelio R Paula07/2013
57452^268824-11025580925Enzo Doria05/2014
57462^268798-186832180917Enzo Doria04/2016
57472^268753-11462180903Enzo Doria05/2015
57482^268743+160580900Lelio R Paula07/2013
57496^103954-13980892Lelio R Paula12/2015
575010^80883+4980884Robert Price03/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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