PRP Records

Probable Primes Top 10000

(224926 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 ?
550110^79999+2239980000Patrick De Geest09/2009
550210^79999-7487379999Patrick De Geest09/2009
55033^167668+5879998Lelio R Paula02/2015
5504155^36506-279961Lelio R Paula10/2017
55052^265612+425779958Lelio R Paula07/2013
55065*3^167577+479956Lelio R Paula06/2014
5507(9179*2^265593-1)/979955Lelio R Paula04/2015
55086^102723-4379935Lelio R Paula04/2015
550911^76748-336079925Enzo Doria12/2012
5510(13*2^265498-1)/18711979919Lelio R Paula02/2014
55112^265399-10985579894Enzo Doria04/2014
5512(20^61403-1)/1979886Paul Bourdelais03/2010
551318^63635+5979880Lelio R Paula02/2015
5514(11*10^79867-107)/379868Robert Price11/2016
55153^167375+8079859Lelio R Paula02/2015
55165^114240-1448679851Enzo Doria02/2013
551749^47238+4879842Norbert Schneider07/2014
55182^265212-377979837Yves Minet04/2017
551991^40746+40746^9179824Norbert Schneider12/2014
5520(68*10^79813-257)/979814Robert Price06/2017
5521(5*2^265118-1)/6179808Lelio R Paula02/2014
55222^265074+2842579796Lelio R Paula07/2013
55232^265072+118579795Lelio R Paula07/2013
5524p(16682)#/2-12879771Robert Price05/2017
55253^167167-3479759Robert Price11/2013
552612^73906+2979758Lelio R Paula02/2015
55272^264934+25579754Lelio R Paula07/2013
55284*10^79729-8779730Robert Price03/2017
55292^264846-11170179727Enzo Doria05/2014
55302^264831-11204179723Enzo Doria06/2014
55312^264816-45579718Yves Minet03/2012
5532(55*10^79711+89)/979712Robert Price09/2017
553347^47667-4679704Theodore Burton02/2007
553413^71547+9679700Lelio R Paula03/2015
55352^264752-11288379699Enzo Doria06/2014
55362^264732+13379693Lelio R Paula05/2012
55378*3^167010+779685Lelio R Paula06/2014
553842^49087-4179681Norbert Schneider06/2014
5539(26*10^79678-119)/379679Robert Price07/2016
55402^264683-2179678Lelio R Paula05/2012
55417^94279+1879675Lelio R Paula02/2015
55422^264655-12779670Lelio R Paula02/2012
55432^264597-45904379652Enzo Doria05/2015
5544(21*2^264566+1)/579643Lelio R Paula10/2012
55452^264536+187002179634Enzo Doria05/2016
5546(17*2^264512-1)/35979625Lelio R Paula02/2014
55472^264477-10978379616Enzo Doria04/2014
554818^63419-133379609Enzo Doria03/2013
554913^71451-3679593Lelio R Paula03/2015
5550(2^264410-5)/12800260912179585Lelio R Paula10/2012
555119^62234+9079582Lelio R Paula03/2015
555212^73714+4979551Lelio R Paula02/2015
5553(3*2^264184-1)/143333979522Lelio R Paula02/2014
55542^264103-11253179503Enzo Doria06/2014
555519^62170+7879501Lelio R Paula03/2015
555611^76340-258079500Enzo Doria12/2012
5557(23*10^79492-11)/379493Robert Price10/2015
5558((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
55592^264060-11213379490Enzo Doria06/2014
5560((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
55619^83298+6^83298-2^8329879487Mike Oakes08/2010
556218^63319+3579483Lelio R Paula02/2015
556338303!2+25679461Robert Price01/2015
5564(29*10^79445+61)/979446Robert Price04/2015
55652^263902-19579443Lelio R Paula05/2012
55663^166499-11269679441Enzo Doria06/2014
556711^76279-276079437Enzo Doria12/2012
55686^102077-2579432Lelio R Paula03/2015
55692^263852-101779428Lelio R Paula07/2013
55702^263842-3379425Lelio R Paula05/2012
557112^73584-5579411Lelio R Paula02/2015
55722^263772-18579404Lelio R Paula05/2012
5573(15^67489+1)/1679373Paul Bourdelais03/2010
55742^263664+1501579371Lelio R Paula07/2013
557510^79362+3^7936379363Mike Oakes06/2010
5576Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
55773^166262+4479328Lelio R Paula02/2015
55784*10^79327-6379328Robert Price12/2016
55792^263486+51379318Lelio R Paula07/2013
55802^263448-51950979306Paul Bourdelais03/2013
558121^59971-20^5997179295Robert Price05/2012
55822^263372+12379283Lelio R Paula05/2012
558317^64429+8479277Lelio R Paula03/2015
558411^76124-1143079275Enzo Doria12/2012
5585(206*10^79268-17)/979270Robert Price03/2017
558613^71157+1879265Lelio R Paula03/2015
55872^263297+6583579261Lelio R Paula07/2013
558819^61980-1879258Theodore Burton12/2005
55892*10^79242+9379243Robert Price07/2016
5590(88^40751-1)/8779238Paul Bourdelais08/2017
5591(103*29^54179-39)/479233Curtis Bright05/2015
55929^83024-83024^979226Norbert Schneider08/2017
559317^64382-2679219Lelio R Paula03/2015
55947^93733-7479214Lelio R Paula02/2015
559515^67352+3879213Lelio R Paula02/2015
55962^263135-11023579212Enzo Doria05/2014
55972^263044+425779185Lelio R Paula07/2013
55992^263032+8751779181Yves Minet11/2010
55986^101755+9579181Lelio R Paula03/2015
56004^131497-3^13149779170Jean-Louis Charton05/2004
56015*7^93674+879165Lelio R Paula10/2014
5602lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
5603260^32768+179^3276879134Serge Batalov03/2018
560411^75978-4279123Lelio R Paula02/2015
56058*5^113180+979111Lelio R Paula10/2014
5606(6883*2^262741-1)/483579094Lelio R Paula04/2015
5607(9*2^262745+1)/13779093Lelio R Paula10/2012
560812^73285+8579088Lelio R Paula02/2015
560919^61840+5279079Lelio R Paula03/2015
5610(10^79067+77)/379067Robert Price01/2017
5611(1017*2^262640-1)/1155779062Lelio R Paula04/2015
561210^79040+13794979041Patrick De Geest02/2016
561410^79040-100729779040Robert Price02/2015
561310^79040-7742779040Patrick De Geest02/2016
56152^262551-1729579036Lelio R Paula07/2013
56163^165597+34079010Lelio R Paula02/2015
5617(23*2^262435+1)/5579001Lelio R Paula10/2012
561811^75860-210079001Enzo Doria12/2012
56198*7^93463+978987Lelio R Paula10/2014
562067^43240-278960Lelio R Paula09/2013
56211000001^13159-1000000^1315978953Jean-Louis Charton10/2003
56222^262199-11028778930Enzo Doria05/2014
5623(19*2^262180-1)/17778924Lelio R Paula02/2014
5624(3^165403+4)/778917Lelio R Paula10/2012
56262^21068*(2^241076+1)-178914Makoto Morimoto03/2014
56272^29258*(2^232886+1)-178914Makoto Morimoto03/2014
56252^262144+1853178914Makoto Morimoto12/2015
5628(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
5629(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
563014^68837+7578897Lelio R Paula02/2015
5631106^38949+10578884Norbert Schneider12/2016
5632(70^42737+1)/7178853Paul Bourdelais08/2017
5633(25*2^261917-1)/2092778842Lelio R Paula02/2014
56342^261881-185971378835Enzo Doria03/2016
56352^261874+191578832Lelio R Paula07/2013
56362^261856+9876533178827Jason Earls01/2009
5637(5*2^261857-1)/2050127778821Lelio R Paula02/2014
56382^261724+9269178787Tony Prest / Never Odd Or Even03/2014
56392^261724+28511178787Tony Prest / Never Odd Or Even04/2014
56402^261724+29371378787Tony Prest / Never Odd Or Even04/2014
5641(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
56422^261724+57297178787Tony Prest / Never Odd Or Even05/2014
5643(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
5644(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
5645(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
5646(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
5647(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
5648(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
5649(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
5650(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
5651(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
5652(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
5653(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
5654(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
5655(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
5656(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
5657(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
5658(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
5659(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
5660(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
5661(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
5662(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
5663(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
5664(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
5665(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
5666(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
5667(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
5668(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
5669(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
5670(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
5671(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
5672(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
5673(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
5674(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
5675(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
5676(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
5677(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
5678(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
5679(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
5680(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
5681(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
5682(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
5683(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
5684(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
5685(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
5686(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
5687(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
5688(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
5689(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
5690(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
5691(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
5692(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
5693(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
5694(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
5695(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
5697(23*2^261642+1)/9378762Lelio R Paula10/2012
5696(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
5698(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
5699(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
5700(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
57012^261507-228778722Yves Minet04/2009
57028*10^78717+3978718Robert Price01/2017
5703(78557*2^261440+1)/378706Lelio R Paula06/2014
57046^101128-1643378693Enzo Doria02/2013
570520^60482+9978689Lelio R Paula03/2015
57062^261348-11063378674Enzo Doria05/2014
5707191^34487+278666Lelio R Paula05/2013
57082^261305-11013978661Enzo Doria04/2014
5709(82*10^78635-1)/978636Robert Price12/2014
571010^78632+8178633Robert Price03/2011
571110^78632-40269378632Patrick De Geest07/2013
57123*10^78631+1778632Robert Price03/2017
57132^261174-391178622Yves Minet04/2017
57142^261167+7484378620Enzo Doria04/2016
5715L(376121)+F(376122)78605Henri Lifchitz01/2007
571614^68580-2978602Lelio R Paula02/2015
5717(73*10^78576-1)/978577Robert Price01/2015
5718(17*2^261026-1)/4045178574Lelio R Paula02/2014
57192^261001-19578570Lelio R Paula05/2012
57205*2^260950+978555Lelio R Paula06/2014
57212^260931-760578549Lelio R Paula07/2013
572215^66778-3278538Lelio R Paula02/2015
5723(11*2^260896-1)/24578537Lelio R Paula02/2014
572430^53166+2978533Norbert Schneider03/2017
5725lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
57267*3^164574-278523Lelio R Paula06/2014
57272^260830-11213378518Enzo Doria06/2014
572813^70486+4278518Lelio R Paula03/2015
572911^75386-708078507Enzo Doria01/2013
5730(86^40583-1)/8578506Paul Bourdelais08/2017
57312^260711-5869578482Lelio R Paula07/2013
57322^260678-11106578472Enzo Doria05/2014
573318^62501-9778456Lelio R Paula02/2015
573453^45498-278452Lelio R Paula08/2013
57352^260513-11112178423Enzo Doria05/2014
573637845!2-6478412Robert Price06/2015
57372^260469-11069578409Enzo Doria05/2014
5738(11*10^78408-113)/378409Robert Price01/2017
57392^260447+841578403Lelio R Paula07/2013
574037837!2-6478394Robert Price06/2015
5741(19*2^260379-1)/5378382Lelio R Paula02/2014
57422^260377-11323378382Enzo Doria07/2014
57449^82138+6^82138-2^8213878380Mike Oakes08/2010
574369^42624+278380Lelio R Paula05/2013
57452^260369-185971378379Enzo Doria03/2016
574614*10^78362+108978364Jens K. Andersen11/2007
57475^112070-5478334Lelio R Paula02/2015
5748(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
57492^260182-11345378323Enzo Doria07/2014
5750f(16405)78319Robert Price09/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 18 2018 22:22 (Time in France)

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