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 ?
4751(22699*2^268657+1)/635180875Lelio R Paula06/2014
47522^268581-86968810580851Lelio R Paula05/2016
4753(11*2^268521-1)/380834Lelio R Paula02/2014
47542^268516-24980832Yves Minet02/2012
47552^268500+1609580827Lelio R Paula07/2013
47563^169402+10080826Lelio R Paula12/2015
47579^84698+8^(84698-1)80823Robert Price03/2016
47582^268472-10973980819Enzo Doria04/2014
4759(9*2^268454+1)/3780813Lelio R Paula12/2012
4760(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
4761134^37987-133^3798780803Jean-Louis Charton12/2005
476215^68702-7680800Lelio R Paula11/2015
47632^268408+780799Lelio R Paula05/2012
47642^268375+14180789Lelio R Paula05/2012
476512^74856-4780784Lelio R Paula11/2015
47666^103770-10780749Lelio R Paula12/2015
47673^169224-6280741Lelio R Paula12/2015
4768p(16866)#/2+6480741Robert Price03/2017
47695^115502-7280733Lelio R Paula10/2015
47702^268079-192780700Yves Minet10/2009
47712^268028+11780685Lelio R Paula05/2012
4772121^38738+12080683Norbert Schneider01/2015
4773(3^169097-8)/83580677Lelio R Paula12/2012
47742^267918+6780652Lelio R Paula05/2012
4775(302*10^80638+13)/980640Robert Price01/2017
47763^169004+266080636Lelio R Paula12/2015
47772^267860-11285980634Enzo Doria06/2014
47782^267828-11070580625Enzo Doria05/2014
47792^267743+1270580599Lelio R Paula07/2013
4780(22*10^80595+23)/980596Robert Price03/2015
47812^267674-5180578Lelio R Paula05/2012
4782(86*10^80571-41)/980572Robert Price11/2015
47832^267612-196580560Lelio R Paula07/2013
47842^267553+409780542Lelio R Paula07/2013
47857^95276-880518Robert Price01/2014
4786(15185*2^267457-1)/4782980513Lelio R Paula04/2015
47876^103467+16380513Lelio R Paula12/2015
4788(7*10^80490+143)/380491Robert Price04/2016
478986^41597-85^4159780470Robert Price04/2015
479013^72237+3080468Lelio R Paula11/2015
479117^65389+1480458Lelio R Paula11/2015
4792423^30634+30634^42380456Norbert Schneider05/2017
47932^267232+10580445Lelio R Paula05/2012
479411^77237-307200080435Enzo Doria01/2013
47952^267116-45995980410Enzo Doria06/2015
479638715!2+880406Robert Price01/2015
4797(2^267017+1)/380380H.&R. Lifchitz09/2000
47982^266968-4580366Lelio R Paula05/2012
479920^61768-6380363Lelio R Paula01/2016
48002^266920-11296780351Enzo Doria06/2014
480112^74428-1380322Lelio R Paula11/2015
48022^266680+2780279Lelio R Paula05/2012
48032^266630-13180264Lelio R Paula05/2012
48042^266598+7681980254Enzo Doria05/2016
48052^266587+188063380251Enzo Doria10/2016
48062^266541-11004980237Enzo Doria04/2014
480738635!2-880222Robert Price06/2015
48083^168111+168111^3-180210Robert Price04/2014
48092^266443+51380208Lelio R Paula07/2013
4810(26*10^80200+61)/380201Robert Price06/2017
48112^266412-10991380199Enzo Doria04/2014
4812(10223*2^266417+1)/4509180199Lelio R Paula06/2014
481313^71988+6680191Lelio R Paula11/2015
481411^77002-432080190Enzo Doria01/2013
481518^63879-1380186Lelio R Paula11/2015
48162^266368-11229580185Enzo Doria06/2014
4817(3^168050+5)/102145480175Lelio R Paula10/2012
4818(22*10^80167+41)/980168Robert Price02/2015
4819(34*10^80162-43)/980163Ray Chandler12/2010
4820(38*10^80150-11)/980151Robert Price05/2015
4821(598*10^80149-31)/980151Robert Price02/2017
482219^62678-8080150Lelio R Paula12/2015
482310^80139+3234380140Patrick De Geest02/2011
482410^80139-980139Alexander Gramolin01/2011
48253^167955-10680135Lelio R Paula12/2015
48262^265998+7555980074Enzo Doria04/2016
48272^265969-10980180065Enzo Doria04/2014
48282^265888-11275780041Enzo Doria06/2014
48292^265809+170180017Lelio R Paula07/2013
4830gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
48313^167687-10480008Lelio R Paula02/2015
483211^76826-579080007Enzo Doria01/2013
483310^80000+8573180001Patrick De Geest10/2009
483410^80000-716980000Patrick De Geest09/2009
483510^79999+2239980000Patrick De Geest09/2009
483610^79999-7487379999Patrick De Geest09/2009
48373^167668+5879998Lelio R Paula02/2015
48382^265612+425779958Lelio R Paula07/2013
48395*3^167577+479956Lelio R Paula06/2014
4840(9179*2^265593-1)/979955Lelio R Paula04/2015
48416^102723-4379935Lelio R Paula04/2015
484211^76748-336079925Enzo Doria12/2012
4843(13*2^265498-1)/18711979919Lelio R Paula02/2014
48442^265399-10985579894Enzo Doria04/2014
4845(20^61403-1)/1979886Paul Bourdelais03/2010
484618^63635+5979880Lelio R Paula02/2015
4847(11*10^79867-107)/379868Robert Price11/2016
48483^167375+8079859Lelio R Paula02/2015
48495^114240-1448679851Enzo Doria02/2013
485049^47238+4879842Norbert Schneider07/2014
48512^265212-377979837Yves Minet04/2017
485291^40746+40746^9179824Norbert Schneider12/2014
4853(68*10^79813-257)/979814Robert Price06/2017
4854(5*2^265118-1)/6179808Lelio R Paula02/2014
48552^265074+2842579796Lelio R Paula07/2013
48562^265072+118579795Lelio R Paula07/2013
4857p(16682)#/2-12879771Robert Price05/2017
48583^167167-3479759Robert Price11/2013
485912^73906+2979758Lelio R Paula02/2015
48602^264934+25579754Lelio R Paula07/2013
48614*10^79729-8779730Robert Price03/2017
48622^264846-11170179727Enzo Doria05/2014
48632^264831-11204179723Enzo Doria06/2014
48642^264816-45579718Yves Minet03/2012
486547^47667-4679704Theodore Burton02/2007
486613^71547+9679700Lelio R Paula03/2015
48672^264752-11288379699Enzo Doria06/2014
48682^264732+13379693Lelio R Paula05/2012
48698*3^167010+779685Lelio R Paula06/2014
487042^49087-4179681Norbert Schneider06/2014
4871(26*10^79678-119)/379679Robert Price07/2016
48722^264683-2179678Lelio R Paula05/2012
48737^94279+1879675Lelio R Paula02/2015
48742^264655-12779670Lelio R Paula02/2012
48752^264597-45904379652Enzo Doria05/2015
4876(21*2^264566+1)/579643Lelio R Paula10/2012
48772^264536+187002179634Enzo Doria05/2016
4878(17*2^264512-1)/35979625Lelio R Paula02/2014
48792^264477-10978379616Enzo Doria04/2014
488018^63419-133379609Enzo Doria03/2013
488113^71451-3679593Lelio R Paula03/2015
4882(2^264410-5)/12800260912179585Lelio R Paula10/2012
488319^62234+9079582Lelio R Paula03/2015
488412^73714+4979551Lelio R Paula02/2015
4885(3*2^264184-1)/143333979522Lelio R Paula02/2014
48862^264103-11253179503Enzo Doria06/2014
488719^62170+7879501Lelio R Paula03/2015
488811^76340-258079500Enzo Doria12/2012
4889(23*10^79492-11)/379493Robert Price10/2015
4890((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
48912^264060-11213379490Enzo Doria06/2014
4892((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
48939^83298+6^83298-2^8329879487Mike Oakes08/2010
489418^63319+3579483Lelio R Paula02/2015
489538303!2+25679461Robert Price01/2015
4896(29*10^79445+61)/979446Robert Price04/2015
48972^263902-19579443Lelio R Paula05/2012
48983^166499-11269679441Enzo Doria06/2014
489911^76279-276079437Enzo Doria12/2012
49006^102077-2579432Lelio R Paula03/2015
49012^263852-101779428Lelio R Paula07/2013
49022^263842-3379425Lelio R Paula05/2012
490312^73584-5579411Lelio R Paula02/2015
49042^263772-18579404Lelio R Paula05/2012
4905(15^67489+1)/1679373Paul Bourdelais03/2010
49062^263664+1501579371Lelio R Paula07/2013
490710^79362+3^7936379363Mike Oakes06/2010
4908Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
49093^166262+4479328Lelio R Paula02/2015
49104*10^79327-6379328Robert Price12/2016
49112^263486+51379318Lelio R Paula07/2013
49122^263448-51950979306Paul Bourdelais03/2013
491321^59971-20^5997179295Robert Price05/2012
49142^263372+12379283Lelio R Paula05/2012
491517^64429+8479277Lelio R Paula03/2015
491611^76124-1143079275Enzo Doria12/2012
4917(206*10^79268-17)/979270Robert Price03/2017
491813^71157+1879265Lelio R Paula03/2015
49192^263297+6583579261Lelio R Paula07/2013
492019^61980-1879258Theodore Burton12/2005
49212*10^79242+9379243Robert Price07/2016
4922(103*29^54179-39)/479233Curtis Bright05/2015
492317^64382-2679219Lelio R Paula03/2015
49247^93733-7479214Lelio R Paula02/2015
492515^67352+3879213Lelio R Paula02/2015
49262^263135-11023579212Enzo Doria05/2014
49272^263044+425779185Lelio R Paula07/2013
49292^263032+8751779181Yves Minet11/2010
49286^101755+9579181Lelio R Paula03/2015
49304^131497-3^13149779170Jean-Louis Charton05/2004
49315*7^93674+879165Lelio R Paula10/2014
4932lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
493311^75978-4279123Lelio R Paula02/2015
49348*5^113180+979111Lelio R Paula10/2014
4935(6883*2^262741-1)/483579094Lelio R Paula04/2015
4936(9*2^262745+1)/13779093Lelio R Paula10/2012
493712^73285+8579088Lelio R Paula02/2015
493819^61840+5279079Lelio R Paula03/2015
4939(10^79067+77)/379067Robert Price01/2017
4940(1017*2^262640-1)/1155779062Lelio R Paula04/2015
494110^79040+13794979041Patrick De Geest02/2016
494310^79040-100729779040Robert Price02/2015
494210^79040-7742779040Patrick De Geest02/2016
49442^262551-1729579036Lelio R Paula07/2013
49453^165597+34079010Lelio R Paula02/2015
4946(23*2^262435+1)/5579001Lelio R Paula10/2012
494711^75860-210079001Enzo Doria12/2012
49488*7^93463+978987Lelio R Paula10/2014
494967^43240-278960Lelio R Paula09/2013
49501000001^13159-1000000^1315978953Jean-Louis Charton10/2003
49512^262199-11028778930Enzo Doria05/2014
4952(19*2^262180-1)/17778924Lelio R Paula02/2014
4953(3^165403+4)/778917Lelio R Paula10/2012
49552^21068*(2^241076+1)-178914Makoto Morimoto03/2014
49562^29258*(2^232886+1)-178914Makoto Morimoto03/2014
49542^262144+1853178914Makoto Morimoto12/2015
495714^68837+7578897Lelio R Paula02/2015
4958106^38949+10578884Norbert Schneider12/2016
4959(25*2^261917-1)/2092778842Lelio R Paula02/2014
49602^261881-185971378835Enzo Doria03/2016
49612^261874+191578832Lelio R Paula07/2013
49622^261856+9876533178827Jason Earls01/2009
4963(5*2^261857-1)/2050127778821Lelio R Paula02/2014
49642^261724+9269178787Tony Prest / Never Odd Or Even03/2014
49652^261724+28511178787Tony Prest / Never Odd Or Even04/2014
49662^261724+29371378787Tony Prest / Never Odd Or Even04/2014
4967(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
49682^261724+57297178787Tony Prest / Never Odd Or Even05/2014
4969(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
4970(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
4971(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
4972(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
4973(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
4974(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
4975(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
4976(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
4977(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
4978(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
4979(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
4980(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
4981(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
4982(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
4983(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
4984(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
4985(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
4986(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
4987(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
4988(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
4989(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
4990(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
4991(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
4992(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
4993(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
4994(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
4995(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
4996(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
4997(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
4998(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
4999(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
5000(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014


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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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