PRP Records

Probable Primes Top 10000

(288949 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
20012^522535-351457157299Enzo Doria07/2015
20022^522226+2799079157206Enzo Doria04/2016
2003(134*10^157191-11)/3157193Robert Price01/2022
20042^522134-1849451157178Enzo Doria08/2015
20059*10^157152+71157153Robert Price08/2020
20064*10^157150+93157151Robert Price08/2018
20072^521401-29593156958Enzo Doria08/2015
20087*10^156956+87156957Robert Price07/2019
20092^521348-23397156942Enzo Doria08/2013
201010^156902+34509156903Patrick De Geest08/2021
201210^156902-80000001156902Robert Price04/2021
201110^156902-69789156902Patrick De Geest08/2021
2013(98^78797+1)/99156901Paul Bourdelais12/2017
201465^86522+64156857Lelio R Paula04/2016
20158^173687-7^173687156855Jean-Louis Charton09/2004
20162^520977-1858183156830Enzo Doria10/2015
2017(8*10^156718-101)/3156719Robert Price08/2018
2018(10^156640+7)/53156639Alfred Reich07/2021
20192^520314-1849481156631Enzo Doria08/2015
2020(13*10^156522+89)/3156523Robert Price09/2018
2021(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
2022(4*10^156501+119)/3156502Robert Price12/2021
2023(83*10^156476-101)/9156477Robert Price08/2021
20243*10^156435-97156436Robert Price07/2018
2025(8*10^156371-77)/3156372Robert Price07/2018
202653^90679-52^90679156356Robert Price01/2013
20272^519106-59141156267Enzo Doria10/2015
20282^519053+6077156251Enzo Doria02/2016
20292^518968-1860989156225Enzo Doria11/2015
2030(25*10^156221-7)/9156222Robert Price05/2018
20312^518931-2782297156214Enzo Doria09/2015
20322^518608-2939156117Yves Minet09/2014
203310*27^109005+697156027Curtis Bright05/2015
2034(49*10^155933-319)/9155934Robert Price10/2021
20352^517967-113485155924Enzo Doria08/2014
2036(103*10^155904+17)/3155906Robert Price08/2020
2037(8*10^155887-719)/9155887Robert Price03/2021
20384*10^155853-39155854Robert Price09/2020
20392^517698+4429155843Lelio R Paula01/2013
20402^517543-113257155796Enzo Doria07/2014
2041(14*10^155740-143)/3155741Robert Price11/2018
204231^104309-30^104309155563Henri Lifchitz08/2013
20432^516742-39851155555Enzo Doria09/2015
2044(22*10^155543+47)/3155544Robert Price06/2021
2045(19*10^155504+131)/3155505Robert Price06/2020
20467*10^155496+61155497Robert Price08/2019
20472^516440+1878421155464Enzo Doria08/2016
20482^515863-1867237155291Enzo Doria03/2016
20492^515786-461861155268Enzo Doria07/2015
20502^515644-113247155225Enzo Doria07/2014
2051(7*10^155203+107)/3155204Robert Price02/2018
205210^155163+206871155164Patrick De Geest05/2021
205310^155163-40001155163Robert Price01/2021
2054(17*10^155133-89)/9155134Robert Price07/2018
20552^515227-114997155099Enzo Doria06/2015
2057EPrime(155025)155025Eric W. Weisstein10/2010
2056(14*10^155024-221)/9155025Robert Price04/2018
2058(4*10^155022+173)/3155023Robert Price02/2018
2059(266*10^154897+1)/3154899Robert Price04/2020
2060(115*10^154869-1)/3154871Serge Batalov12/2014
2061(86*10^154853-221)/9154854Robert Price09/2019
20622^514361+78167154839Enzo Doria05/2016
20632^514281-115033154815Enzo Doria06/2015
20642^514194-3311154788Yves Minet12/2014
2065(14*10^154773+37)/3154774Robert Price12/2018
20666*10^154742-31154743Robert Price07/2020
2067(14*10^154645+139)/9154646Robert Price11/2021
20685*10^154618-79154619Robert Price03/2021
2069(167*10^154595+1)/3154597Robert Price04/2021
20702^513437+1879337154560Enzo Doria09/2016
20712^513306-113201154521Enzo Doria07/2014
2072(10^154494-13)/3154494Robert Price12/2017
20732^513042-113787154442Enzo Doria09/2014
2074(151*10^154434-7)/9154436Robert Price01/2020
2075(14*10^154413+139)/9154414Robert Price11/2021
20762^512628-114053154317Enzo Doria11/2014
20772^512529-49783154287Enzo Doria10/2015
2078(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
20792^512315-115297154223Enzo Doria06/2015
2080(7*10^154211+173)/9154211Robert Price01/2022
20812^512168+79561154178Enzo Doria06/2016
2082(77*10^154175+67)/9154176Robert Price12/2021
2083(5*10^154158-311)/9154158Robert Price12/2021
2084(89*10^154103-737)/9154104Robert Price01/2022
20854*10^154078-57154079Robert Price10/2018
2086(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
20877*10^154038-57154039Robert Price06/2020
20882^511658-114371154025Enzo Doria02/2015
2089(57^87719+1)/58154022Paul Bourdelais11/2017
20902^511580-1846679154001Enzo Doria07/2015
2091(259*10^153998-1)/3154000Robert Price12/2020
20922^511541-113713153990Enzo Doria09/2014
209349958^32768+49957^32768153965Kellen Shenton11/2020
209410^153935+970801153936Patrick De Geest05/2021
209510^153935-1000001153935Robert Price08/2020
2096(16*10^153868-73)/3153869Robert Price07/2020
20979*10^153851-67153852Robert Price11/2020
20982^511077-112723153850Enzo Doria06/2014
209969^83653-68^83653153826Robert Price12/2013
21002^510963-113707153816Enzo Doria09/2014
2101(154*10^153810-1)/9153812Serge Batalov12/2014
2102(181*25^109991-75077)/8153763Curtis Bright05/2015
21032*10^153746-3153747Robert Price07/2015
21042^510626+1179379153714Enzo Doria05/2016
2105(7*10^153664+113)/3153665Robert Price02/2018
21062^510420+81121153652Enzo Doria07/2016
2107(197*7^181761-1)/2153608Karsten Bonath05/2017
21082^509894-459161153494Enzo Doria05/2015
21092^509841+71657153478Enzo Doria04/2016
21109*10^153446+41153447Robert Price08/2020
21112^509533-1846723153385Enzo Doria07/2015
21122^509468-39989153366Enzo Doria09/2015
211370^83117-69^83117153360Robert Price01/2014
2114(112*10^153025-1)/3153027Serge Batalov12/2014
2115(19*10^153010+131)/3153011Robert Price06/2020
21162^508174-1855151152976Enzo Doria09/2015
2117181^67757-2152974Lelio R Paula12/2017
21182^508160-1864829152972Enzo Doria01/2016
211910^152960+412563152961Patrick De Geest05/2021
212010^152960-50000000001152960Robert Price12/2020
212110^152960-423749152960Patrick De Geest05/2021
2122(71*10^152933-143)/9152934Robert Price10/2021
21232^507857-1848199152881Enzo Doria07/2015
21242^507638-115361152815Enzo Doria07/2015
21252^507551-114025152789Enzo Doria11/2014
2126(6^196337+1)/7152780Paul Bourdelais02/2010
2127(22*10^152670-13)/9152671Robert Price06/2018
21282^506451-22339152457Enzo Doria07/2013
21292^505995-113185152320Enzo Doria07/2014
2130(4*10^152253+149)/9152253Robert Price04/2018
2131578^55117-577^55117152230Jean-Louis Charton08/2012
21322^505431-505431152150Henri Lifchitz04/2005
2133(203*10^152143+1)/3152145Robert Price03/2020
21342^505053+73097152037Enzo Doria04/2016
213522*10^151998+3152000Robert Price01/2020
2136(238*10^151979-1)/3151981Robert Price04/2020
2137(2^504793-7)/46765151954Lelio R Paula12/2017
2138350377#+797581151937Nicolas PALAU08/2017
21392^504618-343991151906Enzo Doria07/2015
21402^504212-461939151783Enzo Doria07/2015
21417*10^151772-41151773Robert Price08/2021
21422^504054-2231151736Yves Minet10/2011
2143(28*10^151682+191)/3151683Robert Price02/2020
21442^503475-933075151562Paul Bourdelais06/2021
21452^503361-39883151527Enzo Doria09/2015
21462^503225+382667151486Enzo Doria10/2016
2147(844*10^151396-7)/9151398Robert Price05/2021
2148(26*10^151391-503)/9151392Robert Price07/2018
21492^502769+1877567151349Enzo Doria08/2016
21502^502576-4019151291Yves Minet10/2011
21515*10^151257+41151258Robert Price03/2019
21522^502290-2792501151205Enzo Doria02/2016
21532^502181+1868417151172Enzo Doria04/2016
21546*10^151063-77151064Robert Price09/2021
21552^501781-1850503151052Enzo Doria08/2015
2156(5*10^151007+37)/3151008Robert Price03/2018
21572^501627-991151005Yves Minet02/2014
21582^501577-115333150990Enzo Doria07/2015
21598*10^150975+3150976Robert Price08/2015
21602^501512-113669150971Enzo Doria09/2014
2161(83*10^150908+493)/9150909Robert Price12/2021
21622*10^150818+83150819Robert Price12/2021
2163(12^139739+1)/13150803Paul Bourdelais09/2011
2164(31^101111-1)/30150792Alexander Zhirkov11/2010
21652^500899-500899150786Henri Lifchitz04/2005
21662^500832+1876801150766Enzo Doria07/2016
2167(23*10^150763-59)/9150764Robert Price05/2018
21682^500699+1884953150726Enzo Doria02/2017
2169(13*10^150675-37)/3150676Robert Price01/2019
2170(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
21712^500337-71101150617Enzo Doria04/2016
2172(74*10^150616+133)/9150617Robert Price06/2019
21734*10^150577+91150578Robert Price08/2018
21742^500160+80071150564Enzo Doria06/2016
2175(2^500120+5)/9150551Lelio R Paula12/2017
2176(43*10^150515-421)/9150516Robert Price01/2019
2177(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
2178(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
21792^499861-29503150474Enzo Doria08/2015
21802^499653-113533150411Enzo Doria08/2014
2181(14*10^150391-191)/3150392Robert Price10/2020
21822^499534-221150375Yves Minet06/2012
2183(28*10^150294+41)/3150295Robert Price07/2021
21842^499225+49727150282Enzo Doria09/2016
2185(695*10^150274+7)/9150276Robert Price12/2021
21862^499054-29261150231Enzo Doria07/2015
2187(844*10^150196-7)/9150198Robert Price05/2021
21882^498907-933075150186Paul Bourdelais06/2021
2189(2^498898-7)/9150183Lelio R Paula10/2015
21903*10^150182+17150183Robert Price07/2018
21915*10^150175+63150176Robert Price09/2020
2192(77*10^150128+67)/9150129Robert Price12/2021
21932^498623+1866983150101Enzo Doria03/2016
2194(25*10^150050-403)/9150051Robert Price12/2020
2195numbpart(18140942830)150033Serge Batalov04/2017
219610^150029+4381150030Patrick De Geest05/2016
219710^150029-41150029Serge Batalov12/2014
219810^150000+1158603150001Patrick De Geest09/2018
219910^150000-245703150000Patrick De Geest09/2018
2200(38*10^149999+691)/9150000Robert Price10/2018
22012^498238-53149985Lelio R Paula12/2017
220245728^1905+1905^45728149984Hans Havermann10/2020
22035*10^149907+23149908Robert Price03/2019
220439347^6442+6442^39347149874Hans Havermann09/2020
22052^497850+81049149868Enzo Doria07/2016
220637228^10575+10575^37228149816Hans Havermann10/2020
2207(5*2^497673+1)/2743149812Lelio R Paula10/2015
2208(5*2^497671+1)/373703149810Lelio R Paula10/2015
2209(2*10^149803-143)/3149803Robert Price03/2018
221033845^26604+26604^33845149763Hans Havermann09/2020
22112^497434-2784191149743Enzo Doria10/2015
2212(865*10^149737-1)/9149739Robert Price04/2020
221310^149695-7000001149695Robert Price06/2021
221438237^8214+8214^38237149681Hans Havermann09/2020
2215(23*10^149655+19)/3149656Robert Price07/2019
22162^497068-113579149633Enzo Doria08/2014
22172^497037+73727149624Enzo Doria04/2016
221811*10^149618+3149620Robert Price07/2021
221934942^19067+19067^34942149562Hans Havermann09/2020
222033696^27449+27449^33696149561Hans Havermann09/2020
22212^496773+77747149544Enzo Doria05/2016
2222(7*10^149483-493)/9149483Robert Price04/2021
2223(206*10^149459+7)/3149461Robert Price07/2020
222434589^20940+20940^34589149459Hans Havermann09/2020
22252^496477-113485149455Enzo Doria08/2014
2226((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
22272^496270-49451149393Enzo Doria10/2015
22282^496238-1865081149383Enzo Doria01/2016
222933831^26030+26030^33831149380Hans Havermann09/2020
223034131^23780+23780^34131149365Hans Havermann09/2020
2231(5*10^149335-53)/3149336Robert Price09/2020
22322^495968-1853699149302Enzo Doria09/2015
22332^495935-4117149292Yves Minet02/2018
223435816^14709+14709^35816149267Hans Havermann09/2020
2235(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
22362^495712-396765149225Enzo Doria07/2013
2237(21*2^495676-1)/4835149211Lelio R Paula10/2015
22382^495420+1880701149137Enzo Doria10/2016
22392^495337-1847293149112Enzo Doria07/2015
2240(2^495193-7)/5149068Lelio R Paula10/2015
22412^495163+111546435149059Paul Bourdelais10/2021
224233282^30097+30097^33282149055Hans Havermann09/2020
224337384^9705+9705^37384149050Hans Havermann09/2020
224434808^19143+19143^34808149049Hans Havermann09/2020
2245413^56963-412^56963149013Jean-Louis Charton08/2012
224647^89113-46^89113149006Robert Price10/2012
22472^494916+87855148985Lelio R Paula01/2016
22486*10^148982+73148983Robert Price04/2019
224910^148934+1530019148935Patrick De Geest02/2021
225010^148934-1000000001148934Robert Price11/2020


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!