PRP Records

Probable Primes Top 10000

(173006 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 ?
475112^74428-1380322Lelio R Paula11/2015
47522^266680+2780279Lelio R Paula05/2012
47532^266630-13180264Lelio R Paula05/2012
47542^266598+7681980254Enzo Doria05/2016
47552^266587+188063380251Enzo Doria10/2016
47562^266541-11004980237Enzo Doria04/2014
475738635!2-880222Robert Price06/2015
47583^168111+168111^3-180210Robert Price04/2014
47592^266443+51380208Lelio R Paula07/2013
47602^266412-10991380199Enzo Doria04/2014
4761(10223*2^266417+1)/4509180199Lelio R Paula06/2014
476213^71988+6680191Lelio R Paula11/2015
476311^77002-432080190Enzo Doria01/2013
476418^63879-1380186Lelio R Paula11/2015
47652^266368-11229580185Enzo Doria06/2014
4766(3^168050+5)/102145480175Lelio R Paula10/2012
4767(22*10^80167+41)/980168Robert Price02/2015
4768(34*10^80162-43)/980163Ray Chandler12/2010
4769(38*10^80150-11)/980151Robert Price05/2015
4770(598*10^80149-31)/980151Robert Price02/2017
477119^62678-8080150Lelio R Paula12/2015
477210^80139+3234380140Patrick De Geest02/2011
477310^80139-980139Alexander Gramolin01/2011
47743^167955-10680135Lelio R Paula12/2015
47752^265998+7555980074Enzo Doria04/2016
47762^265969-10980180065Enzo Doria04/2014
47772^265888-11275780041Enzo Doria06/2014
47782^265809+170180017Lelio R Paula07/2013
4779gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
47803^167687-10480008Lelio R Paula02/2015
478111^76826-579080007Enzo Doria01/2013
478210^80000+8573180001Patrick De Geest10/2009
478310^80000-716980000Patrick De Geest09/2009
478410^79999+2239980000Patrick De Geest09/2009
478510^79999-7487379999Patrick De Geest09/2009
47863^167668+5879998Lelio R Paula02/2015
47872^265612+425779958Lelio R Paula07/2013
47885*3^167577+479956Lelio R Paula06/2014
4789(9179*2^265593-1)/979955Lelio R Paula04/2015
47906^102723-4379935Lelio R Paula04/2015
479111^76748-336079925Enzo Doria12/2012
4792(13*2^265498-1)/18711979919Lelio R Paula02/2014
47932^265399-10985579894Enzo Doria04/2014
4794(20^61403-1)/1979886Paul Bourdelais03/2010
479518^63635+5979880Lelio R Paula02/2015
4796(11*10^79867-107)/379868Robert Price11/2016
47973^167375+8079859Lelio R Paula02/2015
47985^114240-1448679851Enzo Doria02/2013
479949^47238+4879842Norbert Schneider07/2014
48002^265212-377979837Yves Minet04/2017
480191^40746+40746^9179824Norbert Schneider12/2014
4802(5*2^265118-1)/6179808Lelio R Paula02/2014
48032^265074+2842579796Lelio R Paula07/2013
48042^265072+118579795Lelio R Paula07/2013
4805p(16682)#/2-12879771Robert Price05/2017
48063^167167-3479759Robert Price11/2013
480712^73906+2979758Lelio R Paula02/2015
48082^264934+25579754Lelio R Paula07/2013
48094*10^79729-8779730Robert Price03/2017
48102^264846-11170179727Enzo Doria05/2014
48112^264831-11204179723Enzo Doria06/2014
48122^264816-45579718Yves Minet03/2012
481347^47667-4679704Theodore Burton02/2007
481413^71547+9679700Lelio R Paula03/2015
48152^264752-11288379699Enzo Doria06/2014
48162^264732+13379693Lelio R Paula05/2012
48178*3^167010+779685Lelio R Paula06/2014
481842^49087-4179681Norbert Schneider06/2014
4819(26*10^79678-119)/379679Robert Price07/2016
48202^264683-2179678Lelio R Paula05/2012
48217^94279+1879675Lelio R Paula02/2015
48222^264655-12779670Lelio R Paula02/2012
48232^264597-45904379652Enzo Doria05/2015
4824(21*2^264566+1)/579643Lelio R Paula10/2012
48252^264536+187002179634Enzo Doria05/2016
4826(17*2^264512-1)/35979625Lelio R Paula02/2014
48272^264477-10978379616Enzo Doria04/2014
482818^63419-133379609Enzo Doria03/2013
482913^71451-3679593Lelio R Paula03/2015
4830(2^264410-5)/12800260912179585Lelio R Paula10/2012
483119^62234+9079582Lelio R Paula03/2015
483212^73714+4979551Lelio R Paula02/2015
4833(3*2^264184-1)/143333979522Lelio R Paula02/2014
48342^264103-11253179503Enzo Doria06/2014
483519^62170+7879501Lelio R Paula03/2015
483611^76340-258079500Enzo Doria12/2012
4837(23*10^79492-11)/379493Robert Price10/2015
4838((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
48392^264060-11213379490Enzo Doria06/2014
4840((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
48419^83298+6^83298-2^8329879487Mike Oakes08/2010
484218^63319+3579483Lelio R Paula02/2015
484338303!2+25679461Robert Price01/2015
4844(29*10^79445+61)/979446Robert Price04/2015
48452^263902-19579443Lelio R Paula05/2012
48463^166499-11269679441Enzo Doria06/2014
484711^76279-276079437Enzo Doria12/2012
48486^102077-2579432Lelio R Paula03/2015
48492^263852-101779428Lelio R Paula07/2013
48502^263842-3379425Lelio R Paula05/2012
485112^73584-5579411Lelio R Paula02/2015
48522^263772-18579404Lelio R Paula05/2012
4853(15^67489+1)/1679373Paul Bourdelais03/2010
48542^263664+1501579371Lelio R Paula07/2013
485510^79362+3^7936379363Mike Oakes06/2010
4856Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
48573^166262+4479328Lelio R Paula02/2015
48584*10^79327-6379328Robert Price12/2016
48592^263486+51379318Lelio R Paula07/2013
48602^263448-51950979306Paul Bourdelais03/2013
486121^59971-20^5997179295Robert Price05/2012
48622^263372+12379283Lelio R Paula05/2012
486317^64429+8479277Lelio R Paula03/2015
486411^76124-1143079275Enzo Doria12/2012
4865(206*10^79268-17)/979270Robert Price03/2017
486613^71157+1879265Lelio R Paula03/2015
48672^263297+6583579261Lelio R Paula07/2013
486819^61980-1879258Theodore Burton12/2005
48692*10^79242+9379243Robert Price07/2016
4870(103*29^54179-39)/479233Curtis Bright05/2015
487117^64382-2679219Lelio R Paula03/2015
48727^93733-7479214Lelio R Paula02/2015
487315^67352+3879213Lelio R Paula02/2015
48742^263135-11023579212Enzo Doria05/2014
48752^263044+425779185Lelio R Paula07/2013
48762^263032+8751779181Yves Minet11/2010
48776^101755+9579181Lelio R Paula03/2015
48784^131497-3^13149779170Jean-Louis Charton05/2004
48795*7^93674+879165Lelio R Paula10/2014
4880lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
488111^75978-4279123Lelio R Paula02/2015
48828*5^113180+979111Lelio R Paula10/2014
4883(6883*2^262741-1)/483579094Lelio R Paula04/2015
4884(9*2^262745+1)/13779093Lelio R Paula10/2012
488512^73285+8579088Lelio R Paula02/2015
488619^61840+5279079Lelio R Paula03/2015
4887(10^79067+77)/379067Robert Price01/2017
4888(1017*2^262640-1)/1155779062Lelio R Paula04/2015
488910^79040+13794979041Patrick De Geest02/2016
489110^79040-100729779040Robert Price02/2015
489010^79040-7742779040Patrick De Geest02/2016
48922^262551-1729579036Lelio R Paula07/2013
48933^165597+34079010Lelio R Paula02/2015
4894(23*2^262435+1)/5579001Lelio R Paula10/2012
489511^75860-210079001Enzo Doria12/2012
48968*7^93463+978987Lelio R Paula10/2014
489767^43240-278960Lelio R Paula09/2013
48981000001^13159-1000000^1315978953Jean-Louis Charton10/2003
48992^262199-11028778930Enzo Doria05/2014
4900(19*2^262180-1)/17778924Lelio R Paula02/2014
4901(3^165403+4)/778917Lelio R Paula10/2012
49022^21068*(2^241076+1)-178914Makoto Morimoto03/2014
49032^29258*(2^232886+1)-178914Makoto Morimoto03/2014
49042^262144+1853178914Makoto Morimoto12/2015
490514^68837+7578897Lelio R Paula02/2015
4906106^38949+10578884Norbert Schneider12/2016
4907(25*2^261917-1)/2092778842Lelio R Paula02/2014
49082^261881-185971378835Enzo Doria03/2016
49092^261874+191578832Lelio R Paula07/2013
49102^261856+9876533178827Jason Earls01/2009
4911(5*2^261857-1)/2050127778821Lelio R Paula02/2014
49122^261724+9269178787Tony Prest / Never Odd Or Even03/2014
49132^261724+28511178787Tony Prest / Never Odd Or Even04/2014
49142^261724+29371378787Tony Prest / Never Odd Or Even04/2014
4915(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
49162^261724+57297178787Tony Prest / Never Odd Or Even05/2014
4917(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
4918(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
4919(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
4920(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
4921(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
4922(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
4923(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
4924(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
4925(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
4926(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
4927(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
4928(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
4929(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
4930(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
4931(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
4932(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
4933(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
4934(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
4935(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
4936(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
4937(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
4938(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
4939(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
4940(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
4941(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
4942(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
4943(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
4944(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
4945(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
4946(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
4947(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
4948(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
4949(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
4950(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
4951(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
4952(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
4953(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
4954(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
4955(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
4956(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
4957(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
4958(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
4959(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
4960(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
4961(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
4962(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
4963(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
4964(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
4965(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
4966(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
4967(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
4968(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
4969(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
4971(23*2^261642+1)/9378762Lelio R Paula10/2012
4970(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
4972(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
4973(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
4974(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
49752^261507-228778722Yves Minet04/2009
49768*10^78717+3978718Robert Price01/2017
4977(78557*2^261440+1)/378706Lelio R Paula06/2014
49786^101128-1643378693Enzo Doria02/2013
497920^60482+9978689Lelio R Paula03/2015
49802^261348-11063378674Enzo Doria05/2014
4981191^34487+278666Lelio R Paula05/2013
49822^261305-11013978661Enzo Doria04/2014
4983(82*10^78635-1)/978636Robert Price12/2014
498410^78632+8178633Robert Price03/2011
498510^78632-40269378632Patrick De Geest07/2013
49863*10^78631+1778632Robert Price03/2017
49872^261174-391178622Yves Minet04/2017
49882^261167+7484378620Enzo Doria04/2016
4989L(376121)+F(376122)78605Henri Lifchitz01/2007
499014^68580-2978602Lelio R Paula02/2015
4991(73*10^78576-1)/978577Robert Price01/2015
4992(17*2^261026-1)/4045178574Lelio R Paula02/2014
49932^261001-19578570Lelio R Paula05/2012
49945*2^260950+978555Lelio R Paula06/2014
49952^260931-760578549Lelio R Paula07/2013
499615^66778-3278538Lelio R Paula02/2015
4997(11*2^260896-1)/24578537Lelio R Paula02/2014
499830^53166+2978533Norbert Schneider03/2017
4999lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
50007*3^164574-278523Lelio R Paula06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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