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 ?
575110^80883-8032780883Patrick De Geest07/2013
57526^103937+12180879Lelio R Paula12/2015
5753148^37266+14780877Norbert Schneider12/2018
5754(26*10^80875-119)/380876Robert Price07/2016
5755(22699*2^268657+1)/635180875Lelio R Paula06/2014
57562^268581-86968810580851Lelio R Paula05/2016
5757(11*2^268521-1)/380834Lelio R Paula02/2014
57582^268516-24980832Yves Minet02/2012
57592^268500+1609580827Lelio R Paula07/2013
57603^169402+10080826Lelio R Paula12/2015
57619^84698+8^(84698-1)80823Robert Price03/2016
57622^268472-10973980819Enzo Doria04/2014
5763(9*2^268454+1)/3780813Lelio R Paula12/2012
5764(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
5765134^37987-133^3798780803Jean-Louis Charton12/2005
576615^68702-7680800Lelio R Paula11/2015
57672^268408+780799Lelio R Paula05/2012
57682^268375+14180789Lelio R Paula05/2012
576912^74856-4780784Lelio R Paula11/2015
57702^268346+52428780781Paul Underwood08/2018
57716^103770-10780749Lelio R Paula12/2015
57733^169224-6280741Lelio R Paula12/2015
5772p(16866)#/2+6480741Robert Price03/2017
57745^115502-7280733Lelio R Paula10/2015
57752^268079-192780700Yves Minet10/2009
57762^268028+11780685Lelio R Paula05/2012
5777121^38738+12080683Norbert Schneider01/2015
5778(3^169097-8)/83580677Lelio R Paula12/2012
57792^267918+6780652Lelio R Paula05/2012
5780(89*10^80650-179)/980651Robert Price11/2017
5781(302*10^80638+13)/980640Robert Price01/2017
57823^169004+266080636Lelio R Paula12/2015
57832^267860-11285980634Enzo Doria06/2014
57842^267828-11070580625Enzo Doria05/2014
57852^267743+1270580599Lelio R Paula07/2013
5786(22*10^80595+23)/980596Robert Price03/2015
57872^267674-5180578Lelio R Paula05/2012
5788(86*10^80571-41)/980572Robert Price11/2015
57892^267612-196580560Lelio R Paula07/2013
57902^267553+409780542Lelio R Paula07/2013
57917^95276-880518Robert Price01/2014
5792(15185*2^267457-1)/4782980513Lelio R Paula04/2015
57936^103467+16380513Lelio R Paula12/2015
5794(7*10^80490+143)/380491Robert Price04/2016
579586^41597-85^4159780470Robert Price04/2015
579613^72237+3080468Lelio R Paula11/2015
579717^65389+1480458Lelio R Paula11/2015
5798423^30634+30634^42380456Norbert Schneider05/2017
57992^267232+10580445Lelio R Paula05/2012
580011^77237-307200080435Enzo Doria01/2013
58012^267116-45995980410Enzo Doria06/2015
580238715!2+880406Robert Price01/2015
5803(2^267017+1)/380380H.&R. Lifchitz09/2000
58042^266968-4580366Lelio R Paula05/2012
580520^61768-6380363Lelio R Paula01/2016
58062^266920-11296780351Enzo Doria06/2014
58078*10^80342+8780343Robert Price10/2017
580812^74428-1380322Lelio R Paula11/2015
58092^266680+2780279Lelio R Paula05/2012
58102^266630-13180264Lelio R Paula05/2012
58112^266598+7681980254Enzo Doria05/2016
58122^266587+188063380251Enzo Doria10/2016
58132^266541-11004980237Enzo Doria04/2014
581438635!2-880222Robert Price06/2015
58153^168111+168111^3-180210Robert Price04/2014
58162^266443+51380208Lelio R Paula07/2013
5817(26*10^80200+61)/380201Robert Price06/2017
58182^266412-10991380199Enzo Doria04/2014
5819(10223*2^266417+1)/4509180199Lelio R Paula06/2014
582013^71988+6680191Lelio R Paula11/2015
582111^77002-432080190Enzo Doria01/2013
582218^63879-1380186Lelio R Paula11/2015
58232^266368-11229580185Enzo Doria06/2014
5824(3^168050+5)/102145480175Lelio R Paula10/2012
5825(22*10^80167+41)/980168Robert Price02/2015
5826(34*10^80162-43)/980163Ray Chandler12/2010
5827(38*10^80150-11)/980151Robert Price05/2015
5828(598*10^80149-31)/980151Robert Price02/2017
582919^62678-8080150Lelio R Paula12/2015
583010^80139+3234380140Patrick De Geest02/2011
583110^80139-980139Alexander Gramolin01/2011
58323^167955-10680135Lelio R Paula12/2015
5833(197*10^80089-11)/380091Robert Price10/2017
58342^265998+7555980074Enzo Doria04/2016
58352^265969-10980180065Enzo Doria04/2014
58362^265888-11275780041Enzo Doria06/2014
58372^265809+170180017Lelio R Paula07/2013
5838gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
58393^167687-10480008Lelio R Paula02/2015
584011^76826-579080007Enzo Doria01/2013
584110^80000+8573180001Patrick De Geest10/2009
584210^80000-716980000Patrick De Geest09/2009
584310^79999+2239980000Patrick De Geest09/2009
584410^79999-7487379999Patrick De Geest09/2009
58453^167668+5879998Lelio R Paula02/2015
5846155^36506-279961Lelio R Paula10/2017
58472^265612+425779958Lelio R Paula07/2013
58485*3^167577+479956Lelio R Paula06/2014
5849(9179*2^265593-1)/979955Lelio R Paula04/2015
58506^102723-4379935Lelio R Paula04/2015
585111^76748-336079925Enzo Doria12/2012
5852(13*2^265498-1)/18711979919Lelio R Paula02/2014
58532^265399-10985579894Enzo Doria04/2014
5854(20^61403-1)/1979886Paul Bourdelais03/2010
585518^63635+5979880Lelio R Paula02/2015
5856(11*10^79867-107)/379868Robert Price11/2016
58573^167375+8079859Lelio R Paula02/2015
58585^114240-1448679851Enzo Doria02/2013
585949^47238+4879842Norbert Schneider07/2014
58602^265212-377979837Yves Minet04/2017
586191^40746+40746^9179824Norbert Schneider12/2014
5862(68*10^79813-257)/979814Robert Price06/2017
5863(5*2^265118-1)/6179808Lelio R Paula02/2014
58642^265074+2842579796Lelio R Paula07/2013
58652^265072+118579795Lelio R Paula07/2013
5866p(16682)#/2-12879771Robert Price05/2017
58673^167167-3479759Robert Price11/2013
586812^73906+2979758Lelio R Paula02/2015
58692^264934+25579754Lelio R Paula07/2013
58704*10^79729-8779730Robert Price03/2017
58712^264846-11170179727Enzo Doria05/2014
58722^264831-11204179723Enzo Doria06/2014
58732^264816-45579718Yves Minet03/2012
5874(55*10^79711+89)/979712Robert Price09/2017
587547^47667-4679704Theodore Burton02/2007
587613^71547+9679700Lelio R Paula03/2015
58772^264752-11288379699Enzo Doria06/2014
58782^264732+13379693Lelio R Paula05/2012
58798*3^167010+779685Lelio R Paula06/2014
588042^49087-4179681Norbert Schneider06/2014
5881(26*10^79678-119)/379679Robert Price07/2016
58822^264683-2179678Lelio R Paula05/2012
58837^94279+1879675Lelio R Paula02/2015
58842^264655-12779670Lelio R Paula02/2012
58852^264597-45904379652Enzo Doria05/2015
5886(21*2^264566+1)/579643Lelio R Paula10/2012
58872^264536+187002179634Enzo Doria05/2016
5888(17*2^264512-1)/35979625Lelio R Paula02/2014
58892^264477-10978379616Enzo Doria04/2014
589018^63419-133379609Enzo Doria03/2013
589113^71451-3679593Lelio R Paula03/2015
5892(2^264410-5)/12800260912179585Lelio R Paula10/2012
589319^62234+9079582Lelio R Paula03/2015
589412^73714+4979551Lelio R Paula02/2015
5895(3*2^264184-1)/143333979522Lelio R Paula02/2014
58962^264103-11253179503Enzo Doria06/2014
589719^62170+7879501Lelio R Paula03/2015
589811^76340-258079500Enzo Doria12/2012
5899(23*10^79492-11)/379493Robert Price10/2015
5900((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
59012^264060-11213379490Enzo Doria06/2014
5902((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
59039^83298+6^83298-2^8329879487Mike Oakes08/2010
590418^63319+3579483Lelio R Paula02/2015
590538303!2+25679461Robert Price01/2015
5906(29*10^79445+61)/979446Robert Price04/2015
59072^263902-19579443Lelio R Paula05/2012
59083^166499-11269679441Enzo Doria06/2014
590911^76279-276079437Enzo Doria12/2012
59106^102077-2579432Lelio R Paula03/2015
59112^263852-101779428Lelio R Paula07/2013
59122^263842-3379425Lelio R Paula05/2012
591312^73584-5579411Lelio R Paula02/2015
59142^263772-18579404Lelio R Paula05/2012
5915(15^67489+1)/1679373Paul Bourdelais03/2010
59162^263664+1501579371Lelio R Paula07/2013
591710^79362+3^7936379363Mike Oakes06/2010
5918Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
59193^166262+4479328Lelio R Paula02/2015
59204*10^79327-6379328Robert Price12/2016
59212^263486+51379318Lelio R Paula07/2013
59222^263448-51950979306Paul Bourdelais03/2013
592369153^16384+279296Matt Stath01/2019
592421^59971-20^5997179295Robert Price05/2012
59252^263372+12379283Lelio R Paula05/2012
592617^64429+8479277Lelio R Paula03/2015
592711^76124-1143079275Enzo Doria12/2012
5928(206*10^79268-17)/979270Robert Price03/2017
592913^71157+1879265Lelio R Paula03/2015
59302^263297+6583579261Lelio R Paula07/2013
593119^61980-1879258Theodore Burton12/2005
59322*10^79242+9379243Robert Price07/2016
5933(88^40751-1)/8779238Paul Bourdelais08/2017
5934(103*29^54179-39)/479233Curtis Bright05/2015
59359^83024-83024^979226Norbert Schneider08/2017
593617^64382-2679219Lelio R Paula03/2015
59377^93733-7479214Lelio R Paula02/2015
593815^67352+3879213Lelio R Paula02/2015
59392^263135-11023579212Enzo Doria05/2014
59402^263044+425779185Lelio R Paula07/2013
59412^263032+8751779181Yves Minet11/2010
59426^101755+9579181Lelio R Paula03/2015
59434^131497-3^13149779170Jean-Louis Charton05/2004
59445*7^93674+879165Lelio R Paula10/2014
5945lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
5946260^32768+179^3276879134Serge Batalov03/2018
594711^75978-4279123Lelio R Paula02/2015
59488*5^113180+979111Lelio R Paula10/2014
5949(6883*2^262741-1)/483579094Lelio R Paula04/2015
5950(9*2^262745+1)/13779093Lelio R Paula10/2012
595112^73285+8579088Lelio R Paula02/2015
595219^61840+5279079Lelio R Paula03/2015
5953(10^79067+77)/379067Robert Price01/2017
5954(1017*2^262640-1)/1155779062Lelio R Paula04/2015
595510^79040+13794979041Patrick De Geest02/2016
595710^79040-100729779040Robert Price02/2015
595610^79040-7742779040Patrick De Geest02/2016
59582^262551-1729579036Lelio R Paula07/2013
59593^165597+34079010Lelio R Paula02/2015
5960(23*2^262435+1)/5579001Lelio R Paula10/2012
596111^75860-210079001Enzo Doria12/2012
59628*7^93463+978987Lelio R Paula10/2014
596367^43240-278960Lelio R Paula09/2013
59641000001^13159-1000000^1315978953Jean-Louis Charton10/2003
59652^262199-11028778930Enzo Doria05/2014
5966(19*2^262180-1)/17778924Lelio R Paula02/2014
5967(3^165403+4)/778917Lelio R Paula10/2012
59682^21068*(2^241076+1)-178914Makoto Morimoto03/2014
59692^29258*(2^232886+1)-178914Makoto Morimoto03/2014
59702^262144+1853178914Makoto Morimoto12/2015
5971(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
5972(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
597314^68837+7578897Lelio R Paula02/2015
5974106^38949+10578884Norbert Schneider12/2016
5975(70^42737+1)/7178853Paul Bourdelais08/2017
5976(25*2^261917-1)/2092778842Lelio R Paula02/2014
59772^261881-185971378835Enzo Doria03/2016
59782^261874+191578832Lelio R Paula07/2013
59792^261856+9876533178827Jason Earls01/2009
5980(5*2^261857-1)/2050127778821Lelio R Paula02/2014
59812^261724+9269178787Tony Prest / Never Odd Or Even03/2014
59822^261724+28511178787Tony Prest / Never Odd Or Even04/2014
59832^261724+29371378787Tony Prest / Never Odd Or Even04/2014
5984(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
59852^261724+57297178787Tony Prest / Never Odd Or Even05/2014
5986(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
5987(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
5988(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
5989(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
5990(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
5991(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
5992(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
5993(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
5994(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
5995(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
5996(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
5997(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
5998(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
5999(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
6000(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014


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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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