PRP Records

Probable Primes Top 10000

(280928 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 (> 50000) Who ? When ?
1751(17*10^157705+67)/3157706Robert Price01/2019
1752(46^94841+1)/47157696Robert Price01/2014
17532^523774+77839157672Enzo Doria05/2016
17542^523587+2799143157616Enzo Doria04/2016
17552^523371+1872113157551Enzo Doria05/2016
1756(8*10^157368+49)/3157369Robert Price05/2020
1757(82*10^157319+449)/9157320Robert Price11/2019
17582^522535-351457157299Enzo Doria07/2015
17592^522226+2799079157206Enzo Doria04/2016
17602^522134-1849451157178Enzo Doria08/2015
17619*10^157152+71157153Robert Price08/2020
17624*10^157150+93157151Robert Price08/2018
17632^521401-29593156958Enzo Doria08/2015
17647*10^156956+87156957Robert Price07/2019
17652^521348-23397156942Enzo Doria08/2013
176610^156902-80000001156902Robert Price04/2021
1767(98^78797+1)/99156901Paul Bourdelais12/2017
176865^86522+64156857Lelio R Paula04/2016
17698^173687-7^173687156855Jean-Louis Charton09/2004
17702^520977-1858183156830Enzo Doria10/2015
1771(8*10^156718-101)/3156719Robert Price08/2018
17722^520314-1849481156631Enzo Doria08/2015
1773(13*10^156522+89)/3156523Robert Price09/2018
1774(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
17753*10^156435-97156436Robert Price07/2018
1776(8*10^156371-77)/3156372Robert Price07/2018
177753^90679-52^90679156356Robert Price01/2013
17782^519106-59141156267Enzo Doria10/2015
17792^519053+6077156251Enzo Doria02/2016
17802^518968-1860989156225Enzo Doria11/2015
1781(25*10^156221-7)/9156222Robert Price05/2018
17822^518931-2782297156214Enzo Doria09/2015
17832^518608-2939156117Yves Minet09/2014
178410*27^109005+697156027Curtis Bright05/2015
17852^517967-113485155924Enzo Doria08/2014
1786(103*10^155904+17)/3155906Robert Price08/2020
1787(8*10^155887-719)/9155887Robert Price03/2021
17884*10^155853-39155854Robert Price09/2020
17892^517698+4429155843Lelio R Paula01/2013
17902^517543-113257155796Enzo Doria07/2014
1791(14*10^155740-143)/3155741Robert Price11/2018
179231^104309-30^104309155563Henri Lifchitz08/2013
17932^516742-39851155555Enzo Doria09/2015
1794(19*10^155504+131)/3155505Robert Price06/2020
17957*10^155496+61155497Robert Price08/2019
17962^516440+1878421155464Enzo Doria08/2016
17972^515863-1867237155291Enzo Doria03/2016
17982^515786-461861155268Enzo Doria07/2015
17992^515644-113247155225Enzo Doria07/2014
1800(7*10^155203+107)/3155204Robert Price02/2018
180110^155163-40001155163Robert Price01/2021
1802(17*10^155133-89)/9155134Robert Price07/2018
18032^515227-114997155099Enzo Doria06/2015
1805EPrime(155025)155025Eric W. Weisstein10/2010
1804(14*10^155024-221)/9155025Robert Price04/2018
1806(4*10^155022+173)/3155023Robert Price02/2018
1807(266*10^154897+1)/3154899Robert Price04/2020
1808(115*10^154869-1)/3154871Serge Batalov12/2014
1809(86*10^154853-221)/9154854Robert Price09/2019
18102^514361+78167154839Enzo Doria05/2016
18112^514281-115033154815Enzo Doria06/2015
18122^514194-3311154788Yves Minet12/2014
1813(14*10^154773+37)/3154774Robert Price12/2018
18146*10^154742-31154743Robert Price07/2020
18155*10^154618-79154619Robert Price03/2021
18162^513437+1879337154560Enzo Doria09/2016
18172^513306-113201154521Enzo Doria07/2014
1818(10^154494-13)/3154494Robert Price12/2017
18192^513042-113787154442Enzo Doria09/2014
1820(151*10^154434-7)/9154436Robert Price01/2020
18212^512628-114053154317Enzo Doria11/2014
18222^512529-49783154287Enzo Doria10/2015
1823(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
18242^512315-115297154223Enzo Doria06/2015
18252^512168+79561154178Enzo Doria06/2016
18264*10^154078-57154079Robert Price10/2018
1827(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
18287*10^154038-57154039Robert Price06/2020
18292^511658-114371154025Enzo Doria02/2015
1830(57^87719+1)/58154022Paul Bourdelais11/2017
18312^511580-1846679154001Enzo Doria07/2015
1832(259*10^153998-1)/3154000Robert Price12/2020
18332^511541-113713153990Enzo Doria09/2014
183449958^32768+49957^32768153965Kellen Shenton11/2020
183510^153935-1000001153935Robert Price08/2020
1836(16*10^153868-73)/3153869Robert Price07/2020
18379*10^153851-67153852Robert Price11/2020
18382^511077-112723153850Enzo Doria06/2014
183969^83653-68^83653153826Robert Price12/2013
18402^510963-113707153816Enzo Doria09/2014
1841(154*10^153810-1)/9153812Serge Batalov12/2014
1842(181*25^109991-75077)/8153763Curtis Bright05/2015
18432*10^153746-3153747Robert Price07/2015
18442^510626+1179379153714Enzo Doria05/2016
1845(7*10^153664+113)/3153665Robert Price02/2018
18462^510420+81121153652Enzo Doria07/2016
1847(197*7^181761-1)/2153608Karsten Bonath05/2017
18482^509894-459161153494Enzo Doria05/2015
18492^509841+71657153478Enzo Doria04/2016
18509*10^153446+41153447Robert Price08/2020
18512^509533-1846723153385Enzo Doria07/2015
18522^509468-39989153366Enzo Doria09/2015
185370^83117-69^83117153360Robert Price01/2014
1854(112*10^153025-1)/3153027Serge Batalov12/2014
1855(19*10^153010+131)/3153011Robert Price06/2020
18562^508174-1855151152976Enzo Doria09/2015
1857181^67757-2152974Lelio R Paula12/2017
18582^508160-1864829152972Enzo Doria01/2016
185910^152960-50000000001152960Robert Price12/2020
18602^507857-1848199152881Enzo Doria07/2015
18612^507638-115361152815Enzo Doria07/2015
18622^507551-114025152789Enzo Doria11/2014
1863(6^196337+1)/7152780Paul Bourdelais02/2010
1864(22*10^152670-13)/9152671Robert Price06/2018
18652^506451-22339152457Enzo Doria07/2013
18662^505995-113185152320Enzo Doria07/2014
1867(4*10^152253+149)/9152253Robert Price04/2018
1868578^55117-577^55117152230Jean-Louis Charton08/2012
18692^505431-505431152150Henri Lifchitz04/2005
1870(203*10^152143+1)/3152145Robert Price03/2020
18712^505053+73097152037Enzo Doria04/2016
187222*10^151998+3152000Robert Price01/2020
1873(238*10^151979-1)/3151981Robert Price04/2020
1874(2^504793-7)/46765151954Lelio R Paula12/2017
1875350377#+797581151937Nicolas PALAU08/2017
18762^504618-343991151906Enzo Doria07/2015
18772^504212-461939151783Enzo Doria07/2015
18782^504054-2231151736Yves Minet10/2011
1879(28*10^151682+191)/3151683Robert Price02/2020
18802^503361-39883151527Enzo Doria09/2015
18812^503225+382667151486Enzo Doria10/2016
1882(26*10^151391-503)/9151392Robert Price07/2018
18832^502769+1877567151349Enzo Doria08/2016
18842^502576-4019151291Yves Minet10/2011
18855*10^151257+41151258Robert Price03/2019
18862^502290-2792501151205Enzo Doria02/2016
18872^502181+1868417151172Enzo Doria04/2016
18882^501781-1850503151052Enzo Doria08/2015
1889(5*10^151007+37)/3151008Robert Price03/2018
18902^501627-991151005Yves Minet02/2014
18912^501577-115333150990Enzo Doria07/2015
18928*10^150975+3150976Robert Price08/2015
18932^501512-113669150971Enzo Doria09/2014
1894(12^139739+1)/13150803Paul Bourdelais09/2011
1895(31^101111-1)/30150792Alexander Zhirkov11/2010
18962^500899-500899150786Henri Lifchitz04/2005
18972^500832+1876801150766Enzo Doria07/2016
1898(23*10^150763-59)/9150764Robert Price05/2018
18992^500699+1884953150726Enzo Doria02/2017
1900(13*10^150675-37)/3150676Robert Price01/2019
1901(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
19032^500337-71101150617Enzo Doria04/2016
1902(74*10^150616+133)/9150617Robert Price06/2019
19044*10^150577+91150578Robert Price08/2018
19052^500160+80071150564Enzo Doria06/2016
1906(2^500120+5)/9150551Lelio R Paula12/2017
1907(43*10^150515-421)/9150516Robert Price01/2019
1909(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
1908(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
19102^499861-29503150474Enzo Doria08/2015
19112^499653-113533150411Enzo Doria08/2014
1912(14*10^150391-191)/3150392Robert Price10/2020
19132^499534-221150375Yves Minet06/2012
19142^499225+49727150282Enzo Doria09/2016
19152^499054-29261150231Enzo Doria07/2015
1916(2^498898-7)/9150183Lelio R Paula10/2015
19173*10^150182+17150183Robert Price07/2018
19185*10^150175+63150176Robert Price09/2020
19192^498623+1866983150101Enzo Doria03/2016
1920(25*10^150050-403)/9150051Robert Price12/2020
1921numbpart(18140942830)150033Serge Batalov04/2017
192210^150029+4381150030Patrick De Geest05/2016
192310^150029-41150029Serge Batalov12/2014
192410^150000+1158603150001Patrick De Geest09/2018
192510^150000-245703150000Patrick De Geest09/2018
1926(38*10^149999+691)/9150000Robert Price10/2018
19272^498238-53149985Lelio R Paula12/2017
192845728^1905+1905^45728149984Hans Havermann10/2020
19295*10^149907+23149908Robert Price03/2019
193039347^6442+6442^39347149874Hans Havermann09/2020
19312^497850+81049149868Enzo Doria07/2016
193237228^10575+10575^37228149816Hans Havermann10/2020
1933(5*2^497673+1)/2743149812Lelio R Paula10/2015
1934(5*2^497671+1)/373703149810Lelio R Paula10/2015
1935(2*10^149803-143)/3149803Robert Price03/2018
193633845^26604+26604^33845149763Hans Havermann09/2020
19372^497434-2784191149743Enzo Doria10/2015
1938(865*10^149737-1)/9149739Robert Price04/2020
193938237^8214+8214^38237149681Hans Havermann09/2020
1940(23*10^149655+19)/3149656Robert Price07/2019
19412^497068-113579149633Enzo Doria08/2014
19422^497037+73727149624Enzo Doria04/2016
194334942^19067+19067^34942149562Hans Havermann09/2020
194433696^27449+27449^33696149561Hans Havermann09/2020
19452^496773+77747149544Enzo Doria05/2016
1946(206*10^149459+7)/3149461Robert Price07/2020
194734589^20940+20940^34589149459Hans Havermann09/2020
19482^496477-113485149455Enzo Doria08/2014
1949((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
19502^496270-49451149393Enzo Doria10/2015
19512^496238-1865081149383Enzo Doria01/2016
195233831^26030+26030^33831149380Hans Havermann09/2020
195334131^23780+23780^34131149365Hans Havermann09/2020
1954(5*10^149335-53)/3149336Robert Price09/2020
19552^495968-1853699149302Enzo Doria09/2015
19562^495935-4117149292Yves Minet02/2018
195735816^14709+14709^35816149267Hans Havermann09/2020
19582^495712-396765149225Enzo Doria07/2013
1959(21*2^495676-1)/4835149211Lelio R Paula10/2015
19602^495420+1880701149137Enzo Doria10/2016
19612^495337-1847293149112Enzo Doria07/2015
1962(2^495193-7)/5149068Lelio R Paula10/2015
196333282^30097+30097^33282149055Hans Havermann09/2020
196437384^9705+9705^37384149050Hans Havermann09/2020
196534808^19143+19143^34808149049Hans Havermann09/2020
1966413^56963-412^56963149013Jean-Louis Charton08/2012
196747^89113-46^89113149006Robert Price10/2012
19682^494916+87855148985Lelio R Paula01/2016
19696*10^148982+73148983Robert Price04/2019
197010^148934+1530019148935Patrick De Geest02/2021
197110^148934-1000000001148934Robert Price11/2020
197210^148934-512057148934Patrick De Geest02/2021
197339000^6571+6571^39000148888Hans Havermann10/2020
19742^494586-2791991148886Enzo Doria02/2016
19758*10^148860-3148861Ray Chandler04/2011
197638262^7769+7769^38262148854Hans Havermann10/2020
19772^494333-286183148810Enzo Doria06/2015
19782^494144-264119148753Enzo Doria05/2014
197936502^11823+11823^36502148663Hans Havermann11/2020
1980(5*2^493838-1)/3721148658Lelio R Paula10/2015
198164239^206+206^64239148641Hans Havermann10/2020
1982(23*2^493761-1)/555148636Lelio R Paula10/2015
1983(151*10^148601-1)/3148603Robert Price03/2020
19842^493636+82081148600Enzo Doria09/2016
1985((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2148593Serge Batalov07/2016
1986177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
1987(2*10^148460-23)/3148460Robert Price04/2018
1988(28*10^148445+101)/3148446Robert Price09/2020
198936203^12556+12556^36203148391Hans Havermann10/2020
199033912^23749+23749^33912148387Hans Havermann10/2020
1991(8*10^148328+1)/9148328Serge Batalov05/2010
199234294^21117+21117^34294148309Hans Havermann10/2020
1993(71*10^148306-539)/9148307Robert Price07/2019
199438042^7875+7875^38042148222Hans Havermann10/2020
19955^211959-12874148153Enzo Doria05/2014
199634142^21831+21831^34142148145Hans Havermann10/2020
199710^148112-70000001148112Robert Price03/2021
199836303^12016+12016^36303148108Hans Havermann10/2020
1999(16*10^148071+41)/3148072Robert Price03/2019
2000187^65175-2148068Lelio R Paula11/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 12 2021 20:10 (Time in France)

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