PRP Records

Probable Primes Top 10000

(202632 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 ?
500114^70978-8981350Lelio R Paula11/2015
500211^78108-204081342Enzo Doria12/2012
50033^170400-5881302Lelio R Paula12/2015
5004(17*10^81300-131)/381301Robert Price12/2017
500510^81297+3699181298Patrick De Geest06/2013
500610^81297-5781297Robert Price05/2011
50072^270055-11304781295Enzo Doria07/2014
500818^64759-5581291Lelio R Paula11/2015
5009(2^269987+1)/381274H.&R. Lifchitz10/2000
5010(31^54493-1)/3081268Alexander Zhirkov10/2010
5011(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
5012(2^269816+7)/42490181218Lelio R Paula12/2012
5013(23*10^81214+1)/381215Serge Batalov06/2009
5014(17*2^269720+1)/30381193Lelio R Paula07/2012
501556^46441-55^4644181188Robert Price10/2013
50162^269664+17781177Lelio R Paula06/2012
5017(13*2^269665-1)/18581177Lelio R Paula02/2014
50182^269539-11224981140Enzo Doria06/2014
5019((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
5020(2^269495-5)/981126Lelio R Paula12/2012
50212^269490-362381125Yves Minet10/2009
5022(55459*2^269444+1)/3581114Lelio R Paula06/2014
5023(2^269417+78557)/525781099Lelio R Paula12/2012
50244*5^116011-781089Lelio R Paula10/2014
50257*10^81058+7981059Robert Price02/2017
50262^269236-10990781049Enzo Doria04/2014
5027(8*10^81029-11)/381030Erik Branger03/2014
50283*10^81021+781022Erik Branger11/2013
50296^104115+10381018Lelio R Paula12/2015
50302^269120+186915181014Enzo Doria05/2016
50315^115901+1281012Lelio R Paula10/2015
5032(2^269083-9)/32036980997Lelio R Paula12/2012
503317^65810-2080976Lelio R Paula11/2015
503420^62236-2380971Lelio R Paula01/2016
50352^268974-11218180970Enzo Doria06/2014
5037L(387433)80969Renaud Lifchitz11/2003
5036V(387433)80969Serge Batalov03/2015
5038(2^268955-509203)/580963Lelio R Paula12/2012
5039(87398^16384+1)/6553780957Lelio R Paula11/2011
5040329^32160+32160^32980954Norbert Schneider11/2014
50412^268859-15980935Lelio R Paula05/2012
5042(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
50442^268827+577580925Lelio R Paula07/2013
50432^268824-11025580925Enzo Doria05/2014
50452^268798-186832180917Enzo Doria04/2016
50462^268753-11462180903Enzo Doria05/2015
50472^268743+160580900Lelio R Paula07/2013
50486^103954-13980892Lelio R Paula12/2015
504910^80883+4980884Robert Price03/2011
505010^80883-8032780883Patrick De Geest07/2013
50516^103937+12180879Lelio R Paula12/2015
5052(26*10^80875-119)/380876Robert Price07/2016
5053(22699*2^268657+1)/635180875Lelio R Paula06/2014
50542^268581-86968810580851Lelio R Paula05/2016
5055(11*2^268521-1)/380834Lelio R Paula02/2014
50562^268516-24980832Yves Minet02/2012
50572^268500+1609580827Lelio R Paula07/2013
50583^169402+10080826Lelio R Paula12/2015
50599^84698+8^(84698-1)80823Robert Price03/2016
50602^268472-10973980819Enzo Doria04/2014
5061(9*2^268454+1)/3780813Lelio R Paula12/2012
5062(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
5063134^37987-133^3798780803Jean-Louis Charton12/2005
506415^68702-7680800Lelio R Paula11/2015
50652^268408+780799Lelio R Paula05/2012
50662^268375+14180789Lelio R Paula05/2012
506712^74856-4780784Lelio R Paula11/2015
50686^103770-10780749Lelio R Paula12/2015
50693^169224-6280741Lelio R Paula12/2015
5070p(16866)#/2+6480741Robert Price03/2017
50715^115502-7280733Lelio R Paula10/2015
50722^268079-192780700Yves Minet10/2009
50732^268028+11780685Lelio R Paula05/2012
5074121^38738+12080683Norbert Schneider01/2015
5075(3^169097-8)/83580677Lelio R Paula12/2012
50762^267918+6780652Lelio R Paula05/2012
5077(89*10^80650-179)/980651Robert Price11/2017
5078(302*10^80638+13)/980640Robert Price01/2017
50793^169004+266080636Lelio R Paula12/2015
50802^267860-11285980634Enzo Doria06/2014
50812^267828-11070580625Enzo Doria05/2014
50822^267743+1270580599Lelio R Paula07/2013
5083(22*10^80595+23)/980596Robert Price03/2015
50842^267674-5180578Lelio R Paula05/2012
5085(86*10^80571-41)/980572Robert Price11/2015
50862^267612-196580560Lelio R Paula07/2013
50872^267553+409780542Lelio R Paula07/2013
50887^95276-880518Robert Price01/2014
5089(15185*2^267457-1)/4782980513Lelio R Paula04/2015
50906^103467+16380513Lelio R Paula12/2015
5091(7*10^80490+143)/380491Robert Price04/2016
509286^41597-85^4159780470Robert Price04/2015
509313^72237+3080468Lelio R Paula11/2015
509417^65389+1480458Lelio R Paula11/2015
5095423^30634+30634^42380456Norbert Schneider05/2017
50962^267232+10580445Lelio R Paula05/2012
509711^77237-307200080435Enzo Doria01/2013
50982^267116-45995980410Enzo Doria06/2015
509938715!2+880406Robert Price01/2015
5100(2^267017+1)/380380H.&R. Lifchitz09/2000
51012^266968-4580366Lelio R Paula05/2012
510220^61768-6380363Lelio R Paula01/2016
51032^266920-11296780351Enzo Doria06/2014
51048*10^80342+8780343Robert Price10/2017
510512^74428-1380322Lelio R Paula11/2015
51062^266680+2780279Lelio R Paula05/2012
51072^266630-13180264Lelio R Paula05/2012
51082^266598+7681980254Enzo Doria05/2016
51092^266587+188063380251Enzo Doria10/2016
51102^266541-11004980237Enzo Doria04/2014
511138635!2-880222Robert Price06/2015
51123^168111+168111^3-180210Robert Price04/2014
51132^266443+51380208Lelio R Paula07/2013
5114(26*10^80200+61)/380201Robert Price06/2017
51152^266412-10991380199Enzo Doria04/2014
5116(10223*2^266417+1)/4509180199Lelio R Paula06/2014
511713^71988+6680191Lelio R Paula11/2015
511811^77002-432080190Enzo Doria01/2013
511918^63879-1380186Lelio R Paula11/2015
51202^266368-11229580185Enzo Doria06/2014
5121(3^168050+5)/102145480175Lelio R Paula10/2012
5122(22*10^80167+41)/980168Robert Price02/2015
5123(34*10^80162-43)/980163Ray Chandler12/2010
5124(38*10^80150-11)/980151Robert Price05/2015
5125(598*10^80149-31)/980151Robert Price02/2017
512619^62678-8080150Lelio R Paula12/2015
512710^80139+3234380140Patrick De Geest02/2011
512810^80139-980139Alexander Gramolin01/2011
51293^167955-10680135Lelio R Paula12/2015
5130(197*10^80089-11)/380091Robert Price10/2017
51312^265998+7555980074Enzo Doria04/2016
51322^265969-10980180065Enzo Doria04/2014
51332^265888-11275780041Enzo Doria06/2014
51342^265809+170180017Lelio R Paula07/2013
5135gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
51363^167687-10480008Lelio R Paula02/2015
513711^76826-579080007Enzo Doria01/2013
513810^80000+8573180001Patrick De Geest10/2009
513910^80000-716980000Patrick De Geest09/2009
514010^79999+2239980000Patrick De Geest09/2009
514110^79999-7487379999Patrick De Geest09/2009
51423^167668+5879998Lelio R Paula02/2015
5143155^36506-279961Lelio R Paula10/2017
51442^265612+425779958Lelio R Paula07/2013
51455*3^167577+479956Lelio R Paula06/2014
5146(9179*2^265593-1)/979955Lelio R Paula04/2015
51476^102723-4379935Lelio R Paula04/2015
514811^76748-336079925Enzo Doria12/2012
5149(13*2^265498-1)/18711979919Lelio R Paula02/2014
51502^265399-10985579894Enzo Doria04/2014
5151(20^61403-1)/1979886Paul Bourdelais03/2010
515218^63635+5979880Lelio R Paula02/2015
5153(11*10^79867-107)/379868Robert Price11/2016
51543^167375+8079859Lelio R Paula02/2015
51555^114240-1448679851Enzo Doria02/2013
515649^47238+4879842Norbert Schneider07/2014
51572^265212-377979837Yves Minet04/2017
515891^40746+40746^9179824Norbert Schneider12/2014
5159(68*10^79813-257)/979814Robert Price06/2017
5160(5*2^265118-1)/6179808Lelio R Paula02/2014
51612^265074+2842579796Lelio R Paula07/2013
51622^265072+118579795Lelio R Paula07/2013
5163p(16682)#/2-12879771Robert Price05/2017
51643^167167-3479759Robert Price11/2013
516512^73906+2979758Lelio R Paula02/2015
51662^264934+25579754Lelio R Paula07/2013
51674*10^79729-8779730Robert Price03/2017
51682^264846-11170179727Enzo Doria05/2014
51692^264831-11204179723Enzo Doria06/2014
51702^264816-45579718Yves Minet03/2012
5171(55*10^79711+89)/979712Robert Price09/2017
517247^47667-4679704Theodore Burton02/2007
517313^71547+9679700Lelio R Paula03/2015
51742^264752-11288379699Enzo Doria06/2014
51752^264732+13379693Lelio R Paula05/2012
51768*3^167010+779685Lelio R Paula06/2014
517742^49087-4179681Norbert Schneider06/2014
5178(26*10^79678-119)/379679Robert Price07/2016
51792^264683-2179678Lelio R Paula05/2012
51807^94279+1879675Lelio R Paula02/2015
51812^264655-12779670Lelio R Paula02/2012
51822^264597-45904379652Enzo Doria05/2015
5183(21*2^264566+1)/579643Lelio R Paula10/2012
51842^264536+187002179634Enzo Doria05/2016
5185(17*2^264512-1)/35979625Lelio R Paula02/2014
51862^264477-10978379616Enzo Doria04/2014
518718^63419-133379609Enzo Doria03/2013
518813^71451-3679593Lelio R Paula03/2015
5189(2^264410-5)/12800260912179585Lelio R Paula10/2012
519019^62234+9079582Lelio R Paula03/2015
519112^73714+4979551Lelio R Paula02/2015
5192(3*2^264184-1)/143333979522Lelio R Paula02/2014
51932^264103-11253179503Enzo Doria06/2014
519419^62170+7879501Lelio R Paula03/2015
519511^76340-258079500Enzo Doria12/2012
5196(23*10^79492-11)/379493Robert Price10/2015
5197((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
51982^264060-11213379490Enzo Doria06/2014
5199((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
52009^83298+6^83298-2^8329879487Mike Oakes08/2010
520118^63319+3579483Lelio R Paula02/2015
520238303!2+25679461Robert Price01/2015
5203(29*10^79445+61)/979446Robert Price04/2015
52042^263902-19579443Lelio R Paula05/2012
52053^166499-11269679441Enzo Doria06/2014
520611^76279-276079437Enzo Doria12/2012
52076^102077-2579432Lelio R Paula03/2015
52082^263852-101779428Lelio R Paula07/2013
52092^263842-3379425Lelio R Paula05/2012
521012^73584-5579411Lelio R Paula02/2015
52112^263772-18579404Lelio R Paula05/2012
5212(15^67489+1)/1679373Paul Bourdelais03/2010
52132^263664+1501579371Lelio R Paula07/2013
521410^79362+3^7936379363Mike Oakes06/2010
5215Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
52163^166262+4479328Lelio R Paula02/2015
52174*10^79327-6379328Robert Price12/2016
52182^263486+51379318Lelio R Paula07/2013
52192^263448-51950979306Paul Bourdelais03/2013
522021^59971-20^5997179295Robert Price05/2012
52212^263372+12379283Lelio R Paula05/2012
522217^64429+8479277Lelio R Paula03/2015
522311^76124-1143079275Enzo Doria12/2012
5224(206*10^79268-17)/979270Robert Price03/2017
522513^71157+1879265Lelio R Paula03/2015
52262^263297+6583579261Lelio R Paula07/2013
522719^61980-1879258Theodore Burton12/2005
52282*10^79242+9379243Robert Price07/2016
5229(88^40751-1)/8779238Paul Bourdelais08/2017
5230(103*29^54179-39)/479233Curtis Bright05/2015
52319^83024-83024^979226Norbert Schneider08/2017
523217^64382-2679219Lelio R Paula03/2015
52337^93733-7479214Lelio R Paula02/2015
523415^67352+3879213Lelio R Paula02/2015
52352^263135-11023579212Enzo Doria05/2014
52362^263044+425779185Lelio R Paula07/2013
52382^263032+8751779181Yves Minet11/2010
52376^101755+9579181Lelio R Paula03/2015
52394^131497-3^13149779170Jean-Louis Charton05/2004
52405*7^93674+879165Lelio R Paula10/2014
5241lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
524211^75978-4279123Lelio R Paula02/2015
52438*5^113180+979111Lelio R Paula10/2014
5244(6883*2^262741-1)/483579094Lelio R Paula04/2015
5245(9*2^262745+1)/13779093Lelio R Paula10/2012
524612^73285+8579088Lelio R Paula02/2015
524719^61840+5279079Lelio R Paula03/2015
5248(10^79067+77)/379067Robert Price01/2017
5249(1017*2^262640-1)/1155779062Lelio R Paula04/2015
525010^79040+13794979041Patrick De Geest02/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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