PRP Records

Probable Primes Top 10000

(183432 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 ?
500113^71547+9679700Lelio R Paula03/2015
50022^264752-11288379699Enzo Doria06/2014
50032^264732+13379693Lelio R Paula05/2012
50048*3^167010+779685Lelio R Paula06/2014
500542^49087-4179681Norbert Schneider06/2014
5006(26*10^79678-119)/379679Robert Price07/2016
50072^264683-2179678Lelio R Paula05/2012
50087^94279+1879675Lelio R Paula02/2015
50092^264655-12779670Lelio R Paula02/2012
50102^264597-45904379652Enzo Doria05/2015
5011(21*2^264566+1)/579643Lelio R Paula10/2012
50122^264536+187002179634Enzo Doria05/2016
5013(17*2^264512-1)/35979625Lelio R Paula02/2014
50142^264477-10978379616Enzo Doria04/2014
501518^63419-133379609Enzo Doria03/2013
501613^71451-3679593Lelio R Paula03/2015
5017(2^264410-5)/12800260912179585Lelio R Paula10/2012
501819^62234+9079582Lelio R Paula03/2015
501912^73714+4979551Lelio R Paula02/2015
5020(3*2^264184-1)/143333979522Lelio R Paula02/2014
50212^264103-11253179503Enzo Doria06/2014
502219^62170+7879501Lelio R Paula03/2015
502311^76340-258079500Enzo Doria12/2012
5024(23*10^79492-11)/379493Robert Price10/2015
5025((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
50262^264060-11213379490Enzo Doria06/2014
5027((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
50289^83298+6^83298-2^8329879487Mike Oakes08/2010
502918^63319+3579483Lelio R Paula02/2015
503038303!2+25679461Robert Price01/2015
5031(29*10^79445+61)/979446Robert Price04/2015
50322^263902-19579443Lelio R Paula05/2012
50333^166499-11269679441Enzo Doria06/2014
503411^76279-276079437Enzo Doria12/2012
50356^102077-2579432Lelio R Paula03/2015
50362^263852-101779428Lelio R Paula07/2013
50372^263842-3379425Lelio R Paula05/2012
503812^73584-5579411Lelio R Paula02/2015
50392^263772-18579404Lelio R Paula05/2012
5040(15^67489+1)/1679373Paul Bourdelais03/2010
50412^263664+1501579371Lelio R Paula07/2013
504210^79362+3^7936379363Mike Oakes06/2010
5043Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
50443^166262+4479328Lelio R Paula02/2015
50454*10^79327-6379328Robert Price12/2016
50462^263486+51379318Lelio R Paula07/2013
50472^263448-51950979306Paul Bourdelais03/2013
504821^59971-20^5997179295Robert Price05/2012
50492^263372+12379283Lelio R Paula05/2012
505017^64429+8479277Lelio R Paula03/2015
505111^76124-1143079275Enzo Doria12/2012
5052(206*10^79268-17)/979270Robert Price03/2017
505313^71157+1879265Lelio R Paula03/2015
50542^263297+6583579261Lelio R Paula07/2013
505519^61980-1879258Theodore Burton12/2005
50562*10^79242+9379243Robert Price07/2016
5057(88^40751-1)/8779238Paul Bourdelais08/2017
5058(103*29^54179-39)/479233Curtis Bright05/2015
50599^83024-83024^979226Norbert Schneider08/2017
506017^64382-2679219Lelio R Paula03/2015
50617^93733-7479214Lelio R Paula02/2015
506215^67352+3879213Lelio R Paula02/2015
50632^263135-11023579212Enzo Doria05/2014
50642^263044+425779185Lelio R Paula07/2013
50662^263032+8751779181Yves Minet11/2010
50656^101755+9579181Lelio R Paula03/2015
50674^131497-3^13149779170Jean-Louis Charton05/2004
50685*7^93674+879165Lelio R Paula10/2014
5069lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
507011^75978-4279123Lelio R Paula02/2015
50718*5^113180+979111Lelio R Paula10/2014
5072(6883*2^262741-1)/483579094Lelio R Paula04/2015
5073(9*2^262745+1)/13779093Lelio R Paula10/2012
507412^73285+8579088Lelio R Paula02/2015
507519^61840+5279079Lelio R Paula03/2015
5076(10^79067+77)/379067Robert Price01/2017
5077(1017*2^262640-1)/1155779062Lelio R Paula04/2015
507810^79040+13794979041Patrick De Geest02/2016
508010^79040-100729779040Robert Price02/2015
507910^79040-7742779040Patrick De Geest02/2016
50812^262551-1729579036Lelio R Paula07/2013
50823^165597+34079010Lelio R Paula02/2015
5083(23*2^262435+1)/5579001Lelio R Paula10/2012
508411^75860-210079001Enzo Doria12/2012
50858*7^93463+978987Lelio R Paula10/2014
508667^43240-278960Lelio R Paula09/2013
50871000001^13159-1000000^1315978953Jean-Louis Charton10/2003
50882^262199-11028778930Enzo Doria05/2014
5089(19*2^262180-1)/17778924Lelio R Paula02/2014
5090(3^165403+4)/778917Lelio R Paula10/2012
50912^21068*(2^241076+1)-178914Makoto Morimoto03/2014
50922^29258*(2^232886+1)-178914Makoto Morimoto03/2014
50932^262144+1853178914Makoto Morimoto12/2015
5094(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
5095(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
509614^68837+7578897Lelio R Paula02/2015
5097106^38949+10578884Norbert Schneider12/2016
5098(70^42737+1)/7178853Paul Bourdelais08/2017
5099(25*2^261917-1)/2092778842Lelio R Paula02/2014
51002^261881-185971378835Enzo Doria03/2016
51012^261874+191578832Lelio R Paula07/2013
51022^261856+9876533178827Jason Earls01/2009
5103(5*2^261857-1)/2050127778821Lelio R Paula02/2014
51042^261724+9269178787Tony Prest / Never Odd Or Even03/2014
51052^261724+28511178787Tony Prest / Never Odd Or Even04/2014
51062^261724+29371378787Tony Prest / Never Odd Or Even04/2014
5107(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
51082^261724+57297178787Tony Prest / Never Odd Or Even05/2014
5109(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
5110(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
5111(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
5112(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
5113(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
5114(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
5115(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
5116(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
5117(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
5118(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
5119(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
5120(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
5121(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
5122(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
5123(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
5124(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
5125(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
5126(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
5127(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
5128(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
5129(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
5130(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
5131(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
5132(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
5133(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
5134(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
5135(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
5136(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
5137(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
5138(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
5139(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
5140(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
5141(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
5142(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
5143(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
5144(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
5145(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
5146(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
5147(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
5148(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
5149(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
5150(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
5151(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
5152(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
5153(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
5154(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
5155(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
5156(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
5157(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
5158(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
5159(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
5160(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
5161(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
5163(23*2^261642+1)/9378762Lelio R Paula10/2012
5162(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
5164(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
5165(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
5166(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
51672^261507-228778722Yves Minet04/2009
51688*10^78717+3978718Robert Price01/2017
5169(78557*2^261440+1)/378706Lelio R Paula06/2014
51706^101128-1643378693Enzo Doria02/2013
517120^60482+9978689Lelio R Paula03/2015
51722^261348-11063378674Enzo Doria05/2014
5173191^34487+278666Lelio R Paula05/2013
51742^261305-11013978661Enzo Doria04/2014
5175(82*10^78635-1)/978636Robert Price12/2014
517610^78632+8178633Robert Price03/2011
517710^78632-40269378632Patrick De Geest07/2013
51783*10^78631+1778632Robert Price03/2017
51792^261174-391178622Yves Minet04/2017
51802^261167+7484378620Enzo Doria04/2016
5181L(376121)+F(376122)78605Henri Lifchitz01/2007
518214^68580-2978602Lelio R Paula02/2015
5183(73*10^78576-1)/978577Robert Price01/2015
5184(17*2^261026-1)/4045178574Lelio R Paula02/2014
51852^261001-19578570Lelio R Paula05/2012
51865*2^260950+978555Lelio R Paula06/2014
51872^260931-760578549Lelio R Paula07/2013
518815^66778-3278538Lelio R Paula02/2015
5189(11*2^260896-1)/24578537Lelio R Paula02/2014
519030^53166+2978533Norbert Schneider03/2017
5191lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
51927*3^164574-278523Lelio R Paula06/2014
51932^260830-11213378518Enzo Doria06/2014
519413^70486+4278518Lelio R Paula03/2015
519511^75386-708078507Enzo Doria01/2013
5196(86^40583-1)/8578506Paul Bourdelais08/2017
51972^260711-5869578482Lelio R Paula07/2013
51982^260678-11106578472Enzo Doria05/2014
519918^62501-9778456Lelio R Paula02/2015
520053^45498-278452Lelio R Paula08/2013
52012^260513-11112178423Enzo Doria05/2014
520237845!2-6478412Robert Price06/2015
52032^260469-11069578409Enzo Doria05/2014
5204(11*10^78408-113)/378409Robert Price01/2017
52052^260447+841578403Lelio R Paula07/2013
520637837!2-6478394Robert Price06/2015
5207(19*2^260379-1)/5378382Lelio R Paula02/2014
52082^260377-11323378382Enzo Doria07/2014
52099^82138+6^82138-2^8213878380Mike Oakes08/2010
521069^42624+278380Lelio R Paula05/2013
52112^260369-185971378379Enzo Doria03/2016
521214*10^78362+108978364Jens K. Andersen11/2007
52135^112070-5478334Lelio R Paula02/2015
5214(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
52152^260182-11345378323Enzo Doria07/2014
5216f(16405)78319Robert Price09/2017
5217(78557*2^260084+1)/51978296Lelio R Paula06/2014
521810^78288+9^(78288+1)78289Robert Price08/2016
521910^78288+3910978289Patrick De Geest12/2016
522010^78288-21629978288Patrick De Geest12/2016
52215^111997+3678283Lelio R Paula02/2015
5222(21^59183+1)/2278252Paul Bourdelais03/2010
5223(88*10^78242-7)/978243Robert Price11/2014
52242*6^100547+778242Lelio R Paula10/2014
52252^259860-11108978226Enzo Doria05/2014
522637^49875-278215Lelio R Paula09/2013
5227(13*10^78213+401)/978214Robert Price10/2017
52287*5^111893-478211Lelio R Paula10/2014
5229(11*2^259809-1)/143778209Lelio R Paula02/2014
52307^92511-678181Theodore Burton11/2005
5231(3^163859-4)/25378179Lelio R Paula10/2012
5232(27*2^259666-1)/62569178163Lelio R Paula02/2014
52333*10^78146+1778147Robert Price03/2017
52342^259503+7433378119Enzo Doria04/2016
5235(31*2^259504-1)/1336578116Lelio R Paula02/2014
5237(58547^16384+1)/278111Lelio R Paula11/2011
52366^100379+1378111Lelio R Paula03/2015
52382^259469-10990978108Enzo Doria04/2014
523915^66413-2678108Lelio R Paula02/2015
52407^92410-926678096Mike Oakes02/2010
52412^259398+7579978087Enzo Doria04/2016
52422^259394+187618978086Enzo Doria07/2016
5243PIPrime(78073)78073Eric W. Weisstein07/2006
52445*2^259344-778072Lelio R Paula06/2014
524514^68097-8778048Lelio R Paula02/2015
52462^259233-47557378037Paul Bourdelais03/2013
5247181^34554-278012Lelio R Paula10/2017
52483^163500-2878010Robert Price12/2013
5249(65*10^77992+691)/977993Robert Price08/2016
52502^259013-11259177971Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

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