PRP Records

Probable Primes Top 10000

(205869 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 ?
5251(68*10^79813-257)/979814Robert Price06/2017
5252(5*2^265118-1)/6179808Lelio R Paula02/2014
52532^265074+2842579796Lelio R Paula07/2013
52542^265072+118579795Lelio R Paula07/2013
5255p(16682)#/2-12879771Robert Price05/2017
52563^167167-3479759Robert Price11/2013
525712^73906+2979758Lelio R Paula02/2015
52582^264934+25579754Lelio R Paula07/2013
52594*10^79729-8779730Robert Price03/2017
52602^264846-11170179727Enzo Doria05/2014
52612^264831-11204179723Enzo Doria06/2014
52622^264816-45579718Yves Minet03/2012
5263(55*10^79711+89)/979712Robert Price09/2017
526447^47667-4679704Theodore Burton02/2007
526513^71547+9679700Lelio R Paula03/2015
52662^264752-11288379699Enzo Doria06/2014
52672^264732+13379693Lelio R Paula05/2012
52688*3^167010+779685Lelio R Paula06/2014
526942^49087-4179681Norbert Schneider06/2014
5270(26*10^79678-119)/379679Robert Price07/2016
52712^264683-2179678Lelio R Paula05/2012
52727^94279+1879675Lelio R Paula02/2015
52732^264655-12779670Lelio R Paula02/2012
52742^264597-45904379652Enzo Doria05/2015
5275(21*2^264566+1)/579643Lelio R Paula10/2012
52762^264536+187002179634Enzo Doria05/2016
5277(17*2^264512-1)/35979625Lelio R Paula02/2014
52782^264477-10978379616Enzo Doria04/2014
527918^63419-133379609Enzo Doria03/2013
528013^71451-3679593Lelio R Paula03/2015
5281(2^264410-5)/12800260912179585Lelio R Paula10/2012
528219^62234+9079582Lelio R Paula03/2015
528312^73714+4979551Lelio R Paula02/2015
5284(3*2^264184-1)/143333979522Lelio R Paula02/2014
52852^264103-11253179503Enzo Doria06/2014
528619^62170+7879501Lelio R Paula03/2015
528711^76340-258079500Enzo Doria12/2012
5288(23*10^79492-11)/379493Robert Price10/2015
5289((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
52902^264060-11213379490Enzo Doria06/2014
5291((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
52929^83298+6^83298-2^8329879487Mike Oakes08/2010
529318^63319+3579483Lelio R Paula02/2015
529438303!2+25679461Robert Price01/2015
5295(29*10^79445+61)/979446Robert Price04/2015
52962^263902-19579443Lelio R Paula05/2012
52973^166499-11269679441Enzo Doria06/2014
529811^76279-276079437Enzo Doria12/2012
52996^102077-2579432Lelio R Paula03/2015
53002^263852-101779428Lelio R Paula07/2013
53012^263842-3379425Lelio R Paula05/2012
530212^73584-5579411Lelio R Paula02/2015
53032^263772-18579404Lelio R Paula05/2012
5304(15^67489+1)/1679373Paul Bourdelais03/2010
53052^263664+1501579371Lelio R Paula07/2013
530610^79362+3^7936379363Mike Oakes06/2010
5307Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
53083^166262+4479328Lelio R Paula02/2015
53094*10^79327-6379328Robert Price12/2016
53102^263486+51379318Lelio R Paula07/2013
53112^263448-51950979306Paul Bourdelais03/2013
531221^59971-20^5997179295Robert Price05/2012
53132^263372+12379283Lelio R Paula05/2012
531417^64429+8479277Lelio R Paula03/2015
531511^76124-1143079275Enzo Doria12/2012
5316(206*10^79268-17)/979270Robert Price03/2017
531713^71157+1879265Lelio R Paula03/2015
53182^263297+6583579261Lelio R Paula07/2013
531919^61980-1879258Theodore Burton12/2005
53202*10^79242+9379243Robert Price07/2016
5321(88^40751-1)/8779238Paul Bourdelais08/2017
5322(103*29^54179-39)/479233Curtis Bright05/2015
53239^83024-83024^979226Norbert Schneider08/2017
532417^64382-2679219Lelio R Paula03/2015
53257^93733-7479214Lelio R Paula02/2015
532615^67352+3879213Lelio R Paula02/2015
53272^263135-11023579212Enzo Doria05/2014
53282^263044+425779185Lelio R Paula07/2013
53302^263032+8751779181Yves Minet11/2010
53296^101755+9579181Lelio R Paula03/2015
53314^131497-3^13149779170Jean-Louis Charton05/2004
53325*7^93674+879165Lelio R Paula10/2014
5333lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
5334260^32768+179^3276879134Serge Batalov03/2018
533511^75978-4279123Lelio R Paula02/2015
53368*5^113180+979111Lelio R Paula10/2014
5337(6883*2^262741-1)/483579094Lelio R Paula04/2015
5338(9*2^262745+1)/13779093Lelio R Paula10/2012
533912^73285+8579088Lelio R Paula02/2015
534019^61840+5279079Lelio R Paula03/2015
5341(10^79067+77)/379067Robert Price01/2017
5342(1017*2^262640-1)/1155779062Lelio R Paula04/2015
534310^79040+13794979041Patrick De Geest02/2016
534510^79040-100729779040Robert Price02/2015
534410^79040-7742779040Patrick De Geest02/2016
53462^262551-1729579036Lelio R Paula07/2013
53473^165597+34079010Lelio R Paula02/2015
5348(23*2^262435+1)/5579001Lelio R Paula10/2012
534911^75860-210079001Enzo Doria12/2012
53508*7^93463+978987Lelio R Paula10/2014
535167^43240-278960Lelio R Paula09/2013
53521000001^13159-1000000^1315978953Jean-Louis Charton10/2003
53532^262199-11028778930Enzo Doria05/2014
5354(19*2^262180-1)/17778924Lelio R Paula02/2014
5355(3^165403+4)/778917Lelio R Paula10/2012
53572^21068*(2^241076+1)-178914Makoto Morimoto03/2014
53582^29258*(2^232886+1)-178914Makoto Morimoto03/2014
53562^262144+1853178914Makoto Morimoto12/2015
5359(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
5360(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
536114^68837+7578897Lelio R Paula02/2015
5362106^38949+10578884Norbert Schneider12/2016
5363(70^42737+1)/7178853Paul Bourdelais08/2017
5364(25*2^261917-1)/2092778842Lelio R Paula02/2014
53652^261881-185971378835Enzo Doria03/2016
53662^261874+191578832Lelio R Paula07/2013
53672^261856+9876533178827Jason Earls01/2009
5368(5*2^261857-1)/2050127778821Lelio R Paula02/2014
53692^261724+9269178787Tony Prest / Never Odd Or Even03/2014
53702^261724+28511178787Tony Prest / Never Odd Or Even04/2014
53712^261724+29371378787Tony Prest / Never Odd Or Even04/2014
5372(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
53732^261724+57297178787Tony Prest / Never Odd Or Even05/2014
5374(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
5375(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
5376(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
5377(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
5378(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
5379(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
5380(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
5381(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
5382(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
5383(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
5384(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
5385(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
5386(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
5387(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
5388(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
5389(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
5390(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
5391(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
5392(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
5393(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
5394(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
5395(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
5396(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
5397(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
5398(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
5399(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
5400(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
5401(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
5402(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
5403(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
5404(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
5405(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
5406(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
5407(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
5408(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
5409(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
5410(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
5411(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
5412(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
5413(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
5414(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
5415(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
5416(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
5417(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
5418(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
5419(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
5420(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
5421(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
5422(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
5423(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
5424(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
5425(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
5426(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
5428(23*2^261642+1)/9378762Lelio R Paula10/2012
5427(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
5429(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
5430(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
5431(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
54322^261507-228778722Yves Minet04/2009
54338*10^78717+3978718Robert Price01/2017
5434(78557*2^261440+1)/378706Lelio R Paula06/2014
54356^101128-1643378693Enzo Doria02/2013
543620^60482+9978689Lelio R Paula03/2015
54372^261348-11063378674Enzo Doria05/2014
5438191^34487+278666Lelio R Paula05/2013
54392^261305-11013978661Enzo Doria04/2014
5440(82*10^78635-1)/978636Robert Price12/2014
544110^78632+8178633Robert Price03/2011
544210^78632-40269378632Patrick De Geest07/2013
54433*10^78631+1778632Robert Price03/2017
54442^261174-391178622Yves Minet04/2017
54452^261167+7484378620Enzo Doria04/2016
5446L(376121)+F(376122)78605Henri Lifchitz01/2007
544714^68580-2978602Lelio R Paula02/2015
5448(73*10^78576-1)/978577Robert Price01/2015
5449(17*2^261026-1)/4045178574Lelio R Paula02/2014
54502^261001-19578570Lelio R Paula05/2012
54515*2^260950+978555Lelio R Paula06/2014
54522^260931-760578549Lelio R Paula07/2013
545315^66778-3278538Lelio R Paula02/2015
5454(11*2^260896-1)/24578537Lelio R Paula02/2014
545530^53166+2978533Norbert Schneider03/2017
5456lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
54577*3^164574-278523Lelio R Paula06/2014
54582^260830-11213378518Enzo Doria06/2014
545913^70486+4278518Lelio R Paula03/2015
546011^75386-708078507Enzo Doria01/2013
5461(86^40583-1)/8578506Paul Bourdelais08/2017
54622^260711-5869578482Lelio R Paula07/2013
54632^260678-11106578472Enzo Doria05/2014
546418^62501-9778456Lelio R Paula02/2015
546553^45498-278452Lelio R Paula08/2013
54662^260513-11112178423Enzo Doria05/2014
546737845!2-6478412Robert Price06/2015
54682^260469-11069578409Enzo Doria05/2014
5469(11*10^78408-113)/378409Robert Price01/2017
54702^260447+841578403Lelio R Paula07/2013
547137837!2-6478394Robert Price06/2015
5472(19*2^260379-1)/5378382Lelio R Paula02/2014
54732^260377-11323378382Enzo Doria07/2014
54749^82138+6^82138-2^8213878380Mike Oakes08/2010
547569^42624+278380Lelio R Paula05/2013
54762^260369-185971378379Enzo Doria03/2016
547714*10^78362+108978364Jens K. Andersen11/2007
54785^112070-5478334Lelio R Paula02/2015
5479(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
54802^260182-11345378323Enzo Doria07/2014
5481f(16405)78319Robert Price09/2017
5482(78557*2^260084+1)/51978296Lelio R Paula06/2014
548310^78288+9^(78288+1)78289Robert Price08/2016
548410^78288+3910978289Patrick De Geest12/2016
548510^78288-21629978288Patrick De Geest12/2016
54865^111997+3678283Lelio R Paula02/2015
5487(21^59183+1)/2278252Paul Bourdelais03/2010
5488(88*10^78242-7)/978243Robert Price11/2014
54892*6^100547+778242Lelio R Paula10/2014
54902^259860-11108978226Enzo Doria05/2014
549137^49875-278215Lelio R Paula09/2013
5492(13*10^78213+401)/978214Robert Price10/2017
54937*5^111893-478211Lelio R Paula10/2014
5494(11*2^259809-1)/143778209Lelio R Paula02/2014
54957^92511-678181Theodore Burton11/2005
5496(3^163859-4)/25378179Lelio R Paula10/2012
5497(27*2^259666-1)/62569178163Lelio R Paula02/2014
54983*10^78146+1778147Robert Price03/2017
5499(576^28307+1)/57778137Richard Fischer01/2018
55002^259503+7433378119Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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