PRP Records

Probable Primes Top 10000

(252932 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 ?
5751(9*2^272243-1)/781954Lelio R Paula02/2014
57522^272177-11122381934Enzo Doria05/2014
5753(151009^15817+1)/15101081912Faysal YAtim06/2017
5754(16*10^81896-19)/381897Robert Price03/2016
5755(2^271922+78557)/6381855Lelio R Paula12/2012
5756(10^81848+77)/381848Robert Price01/2017
5757(24737*2^271883+1)/375781846Lelio R Paula06/2014
575810^81778+3981779Robert Price03/2011
575910^81778-17199981778Patrick De Geest07/2013
5760(14*10^81767-11)/381768Erik Branger09/2014
57612^271541+186841781742Enzo Doria04/2016
5762(2^271549-1)/23874968248781734Jens K. Andersen02/2009
57632^271484-16781725Lelio R Paula06/2012
5764(8*10^81709-611)/981709Robert Price11/2017
57652^271382+1290981695Lelio R Paula07/2013
576649^48334+4881694Norbert Schneider07/2014
57677^96668+4881694Lelio R Paula10/2015
576811^78435-141081682Enzo Doria12/2012
57695*10^81653+981654Dmitry Domanov11/2010
5770(2^271211-1)/61396149515981631Jens K. Andersen02/2009
57713^171068+5281621Lelio R Paula12/2015
57722^271115-11040781614Enzo Doria05/2014
57732^271111-11063581613Enzo Doria05/2014
57742^271098-11181609Lelio R Paula06/2012
5775(77*10^81606+13)/981607Robert Price10/2015
57762^271064-279020981599Enzo Doria03/2016
5777(13*2^271053-1)/309581593Lelio R Paula02/2014
57782^271040-5781592Lelio R Paula06/2012
5779(14*10^81585+73)/381586Robert Price04/2016
5780127^38779+12681584Norbert Schneider02/2015
578118^64966-4381551Lelio R Paula11/2015
5782(2^270840+47)/59181529Lelio R Paula12/2012
578320^62654+8781515Lelio R Paula01/2016
5784(19*10^81488+191)/381489Robert Price01/2017
57858*10^81487+2181488Robert Price02/2017
5786(73*10^81485+107)/981486Robert Price08/2016
5787536^29847+29847^53681458Norbert Schneider03/2017
57888*7^96378+981450Lelio R Paula10/2014
57892^270546-11034581443Enzo Doria05/2014
579013^73105-6081435Lelio R Paula11/2015
579144^49524+4381391Norbert Schneider06/2014
5792(3*2^270368-1)/1381389Lelio R Paula02/2014
5793(10^81363+719)/981363Serge Batalov12/2014
5794(10^81353+449)/981353Serge Batalov12/2014
579514^70978-8981350Lelio R Paula11/2015
579611^78108-204081342Enzo Doria12/2012
57973^170400-5881302Lelio R Paula12/2015
5798(17*10^81300-131)/381301Robert Price12/2017
579910^81297+3699181298Patrick De Geest06/2013
580010^81297-5781297Robert Price05/2011
58012^270055-11304781295Enzo Doria07/2014
580218^64759-5581291Lelio R Paula11/2015
5803(2^269987+1)/381274H.&R. Lifchitz10/2000
5804(31^54493-1)/3081268Alexander Zhirkov10/2010
5805(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
58062^269819-459781224Yves Minet03/2019
5807(2^269816+7)/42490181218Lelio R Paula12/2012
5808(23*10^81214+1)/381215Serge Batalov06/2009
5809(17*2^269720+1)/30381193Lelio R Paula07/2012
581056^46441-55^4644181188Robert Price10/2013
58122^269664+17781177Lelio R Paula06/2012
5811(13*2^269665-1)/18581177Lelio R Paula02/2014
58132^269539-11224981140Enzo Doria06/2014
5814((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
5815(2^269495-5)/981126Lelio R Paula12/2012
58162^269490-362381125Yves Minet10/2009
5817(55459*2^269444+1)/3581114Lelio R Paula06/2014
5818(2^269417+78557)/525781099Lelio R Paula12/2012
58194*5^116011-781089Lelio R Paula10/2014
58207*10^81058+7981059Robert Price02/2017
58212^269236-10990781049Enzo Doria04/2014
5822(8*10^81029-11)/381030Erik Branger03/2014
58233*10^81021+781022Erik Branger11/2013
58246^104115+10381018Lelio R Paula12/2015
58252^269120+186915181014Enzo Doria05/2016
58265^115901+1281012Lelio R Paula10/2015
5827(2^269083-9)/32036980997Lelio R Paula12/2012
582817^65810-2080976Lelio R Paula11/2015
582920^62236-2380971Lelio R Paula01/2016
58302^268974-11218180970Enzo Doria06/2014
5832L(387433)80969Renaud Lifchitz11/2003
5831V(387433)80969Serge Batalov03/2015
5833(2^268955-509203)/580963Lelio R Paula12/2012
5834(87398^16384+1)/6553780957Lelio R Paula11/2011
5835329^32160+32160^32980954Norbert Schneider11/2014
58362^268859-15980935Lelio R Paula05/2012
5837(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
58382^268827+577580925Lelio R Paula07/2013
58392^268824-11025580925Enzo Doria05/2014
58402^268798-186832180917Enzo Doria04/2016
58412^268753-11462180903Enzo Doria05/2015
58422^268743+160580900Lelio R Paula07/2013
58436^103954-13980892Lelio R Paula12/2015
584410^80883+4980884Robert Price03/2011
584510^80883-8032780883Patrick De Geest07/2013
58466^103937+12180879Lelio R Paula12/2015
5847148^37266+14780877Norbert Schneider12/2018
5848(26*10^80875-119)/380876Robert Price07/2016
5849(22699*2^268657+1)/635180875Lelio R Paula06/2014
58502^268581-86968810580851Lelio R Paula05/2016
5851(11*2^268521-1)/380834Lelio R Paula02/2014
58522^268516-24980832Yves Minet02/2012
58532^268500+1609580827Lelio R Paula07/2013
58543^169402+10080826Lelio R Paula12/2015
58559^84698+8^(84698-1)80823Robert Price03/2016
58562^268472-10973980819Enzo Doria04/2014
5857(9*2^268454+1)/3780813Lelio R Paula12/2012
5858(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
5859134^37987-133^3798780803Jean-Louis Charton12/2005
586015^68702-7680800Lelio R Paula11/2015
58612^268408+780799Lelio R Paula05/2012
58622^268375+14180789Lelio R Paula05/2012
586312^74856-4780784Lelio R Paula11/2015
58642^268346+52428780781Paul Underwood08/2018
58656^103770-10780749Lelio R Paula12/2015
58673^169224-6280741Lelio R Paula12/2015
5866p(16866)#/2+6480741Robert Price03/2017
58685^115502-7280733Lelio R Paula10/2015
58692^268079-192780700Yves Minet10/2009
58702^268028+11780685Lelio R Paula05/2012
5871121^38738+12080683Norbert Schneider01/2015
5872(3^169097-8)/83580677Lelio R Paula12/2012
58732^267918+6780652Lelio R Paula05/2012
5874(89*10^80650-179)/980651Robert Price11/2017
5875(302*10^80638+13)/980640Robert Price01/2017
58763^169004+266080636Lelio R Paula12/2015
58772^267860-11285980634Enzo Doria06/2014
58782^267828-11070580625Enzo Doria05/2014
58792^267743+1270580599Lelio R Paula07/2013
5880(22*10^80595+23)/980596Robert Price03/2015
58812^267674-5180578Lelio R Paula05/2012
5882(86*10^80571-41)/980572Robert Price11/2015
58832^267612-196580560Lelio R Paula07/2013
58842^267553+409780542Lelio R Paula07/2013
58857^95276-880518Robert Price01/2014
5886(15185*2^267457-1)/4782980513Lelio R Paula04/2015
58876^103467+16380513Lelio R Paula12/2015
5888(7*10^80490+143)/380491Robert Price04/2016
588986^41597-85^4159780470Robert Price04/2015
589013^72237+3080468Lelio R Paula11/2015
589117^65389+1480458Lelio R Paula11/2015
5892423^30634+30634^42380456Norbert Schneider05/2017
58932^267232+10580445Lelio R Paula05/2012
589411^77237-307200080435Enzo Doria01/2013
58952^267116-45995980410Enzo Doria06/2015
589638715!2+880406Robert Price01/2015
5897(2^267017+1)/380380H.&R. Lifchitz09/2000
58982^266968-4580366Lelio R Paula05/2012
589920^61768-6380363Lelio R Paula01/2016
59002^266920-11296780351Enzo Doria06/2014
59018*10^80342+8780343Robert Price10/2017
590212^74428-1380322Lelio R Paula11/2015
59032^266680+2780279Lelio R Paula05/2012
59042^266630-13180264Lelio R Paula05/2012
59052^266598+7681980254Enzo Doria05/2016
59062^266587+188063380251Enzo Doria10/2016
59072^266541-11004980237Enzo Doria04/2014
590838635!2-880222Robert Price06/2015
59093^168111+168111^3-180210Robert Price04/2014
59102^266443+51380208Lelio R Paula07/2013
5911(26*10^80200+61)/380201Robert Price06/2017
59122^266412-10991380199Enzo Doria04/2014
5913(10223*2^266417+1)/4509180199Lelio R Paula06/2014
59142^266413-469380199Yves Minet05/2019
591513^71988+6680191Lelio R Paula11/2015
591611^77002-432080190Enzo Doria01/2013
591718^63879-1380186Lelio R Paula11/2015
59182^266368-11229580185Enzo Doria06/2014
5919(3^168050+5)/102145480175Lelio R Paula10/2012
5920(22*10^80167+41)/980168Robert Price02/2015
5921(34*10^80162-43)/980163Ray Chandler12/2010
5922(38*10^80150-11)/980151Robert Price05/2015
5923(598*10^80149-31)/980151Robert Price02/2017
592419^62678-8080150Lelio R Paula12/2015
592510^80139+3234380140Patrick De Geest02/2011
592610^80139-980139Alexander Gramolin01/2011
59273^167955-10680135Lelio R Paula12/2015
5928(197*10^80089-11)/380091Robert Price10/2017
59292^265998+7555980074Enzo Doria04/2016
59302^265969-10980180065Enzo Doria04/2014
59312^265888-11275780041Enzo Doria06/2014
59322^265809+170180017Lelio R Paula07/2013
5933gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
59343^167687-10480008Lelio R Paula02/2015
593511^76826-579080007Enzo Doria01/2013
593610^80000+8573180001Patrick De Geest10/2009
593710^80000-716980000Patrick De Geest09/2009
593810^79999+2239980000Patrick De Geest09/2009
593910^79999-7487379999Patrick De Geest09/2009
59403^167668+5879998Lelio R Paula02/2015
5941155^36506-279961Lelio R Paula10/2017
59422^265612+425779958Lelio R Paula07/2013
59435*3^167577+479956Lelio R Paula06/2014
5944(9179*2^265593-1)/979955Lelio R Paula04/2015
59456^102723-4379935Lelio R Paula04/2015
594611^76748-336079925Enzo Doria12/2012
5947(13*2^265498-1)/18711979919Lelio R Paula02/2014
59482^265399-10985579894Enzo Doria04/2014
5949(20^61403-1)/1979886Paul Bourdelais03/2010
595018^63635+5979880Lelio R Paula02/2015
5951(11*10^79867-107)/379868Robert Price11/2016
59523^167375+8079859Lelio R Paula02/2015
59535^114240-1448679851Enzo Doria02/2013
595449^47238+4879842Norbert Schneider07/2014
59552^265212-377979837Yves Minet04/2017
595691^40746+40746^9179824Norbert Schneider12/2014
5957(68*10^79813-257)/979814Robert Price06/2017
5958(5*2^265118-1)/6179808Lelio R Paula02/2014
59592^265074+2842579796Lelio R Paula07/2013
59602^265072+118579795Lelio R Paula07/2013
5961p(16682)#/2-12879771Robert Price05/2017
59623^167167-3479759Robert Price11/2013
596312^73906+2979758Lelio R Paula02/2015
59642^264934+25579754Lelio R Paula07/2013
59654*10^79729-8779730Robert Price03/2017
59662^264846-11170179727Enzo Doria05/2014
59672^264831-11204179723Enzo Doria06/2014
59682^264816-45579718Yves Minet03/2012
5969(55*10^79711+89)/979712Robert Price09/2017
597047^47667-4679704Theodore Burton02/2007
597113^71547+9679700Lelio R Paula03/2015
59722^264752-11288379699Enzo Doria06/2014
59732^264732+13379693Lelio R Paula05/2012
59748*3^167010+779685Lelio R Paula06/2014
597542^49087-4179681Norbert Schneider06/2014
5976(26*10^79678-119)/379679Robert Price07/2016
59772^264683-2179678Lelio R Paula05/2012
59787^94279+1879675Lelio R Paula02/2015
59792^264655-12779670Lelio R Paula02/2012
59802^264597-45904379652Enzo Doria05/2015
5981(21*2^264566+1)/579643Lelio R Paula10/2012
59822^264536+187002179634Enzo Doria05/2016
5983(17*2^264512-1)/35979625Lelio R Paula02/2014
59842^264477-10978379616Enzo Doria04/2014
598518^63419-133379609Enzo Doria03/2013
598613^71451-3679593Lelio R Paula03/2015
5987(2^264410-5)/12800260912179585Lelio R Paula10/2012
598819^62234+9079582Lelio R Paula03/2015
598912^73714+4979551Lelio R Paula02/2015
5990(3*2^264184-1)/143333979522Lelio R Paula02/2014
59912^264103-11253179503Enzo Doria06/2014
599219^62170+7879501Lelio R Paula03/2015
599311^76340-258079500Enzo Doria12/2012
5994(23*10^79492-11)/379493Robert Price10/2015
5995((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
59962^264060-11213379490Enzo Doria06/2014
5997((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
59989^83298+6^83298-2^8329879487Mike Oakes08/2010
599918^63319+3579483Lelio R Paula02/2015
600038303!2+25679461Robert Price01/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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