PRP Records

Probable Primes Top 10000

(290751 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 ?
20017*10^161192-9161193Robert Price10/2015
20022^535269-113803161133Enzo Doria09/2014
20032^535205-23295161113Enzo Doria08/2013
2004(49*10^161105+437)/9161106Robert Price09/2021
2005(89^82609+1)/90161036Paul Bourdelais10/2017
20062^534359-23229160859Enzo Doria08/2013
2007457^60454+60454^457160803Norbert Schneider07/2021
20088*10^160782+53160783Robert Price08/2020
200967^88037-66^88037160763Robert Price10/2013
2010(88*10^160761-637)/9160762Robert Price11/2020
20112^533948-1852559160735Enzo Doria08/2015
20122^533665-23335160650Enzo Doria08/2013
2013(19*10^160619+77)/3160620Robert Price05/2019
2014(38*10^160508+151)/9160509Robert Price03/2022
20153^336353-2^336353160482Mike Oakes10/2007
20162*10^160339-63160340Robert Price01/2022
2017(91*10^160249+11)/3160251Robert Price02/2020
2018(772*10^160239-7)/9160241Robert Price06/2022
2019(2*10^160226+187)/9160226Robert Price06/2022
20202^532253+1868417160225Enzo Doria04/2016
20212^532108-291989160181Enzo Doria07/2015
2022(28*10^160171-79)/3160172Robert Price02/2021
2023(26*10^160166-131)/3160167Robert Price10/2019
202455*10^160145+9160147Robert Price03/2022
2025(17*10^160143+67)/3160144Robert Price01/2019
2026(19*10^159921-49)/3159922Robert Price05/2019
20272^531110-1853771159881Enzo Doria09/2015
2028(275^65536+53^65536)/2159864Kellen Shenton11/2020
20292^530992-1845299159845Enzo Doria07/2015
20302^530810+25159790Stefano Morozzi04/2021
2031(136*10^159736-1)/9159738Serge Batalov12/2014
20322^530417-113833159672Enzo Doria09/2014
20332^530406-69701159669Enzo Doria02/2016
20345*10^159656+41159657Robert Price03/2019
20358*10^159614+29159615Robert Price11/2021
20367^188858-188858^7159604Norbert Schneider05/2018
2037(24^115597-1)/23159547Paul Bourdelais09/2017
2038(17*10^159438-377)/9159439Robert Price03/2018
2039(203*10^159381+1)/3159383Robert Price03/2020
204089*10^159258-9159260Robert Price05/2020
20412^528944-461315159229Enzo Doria07/2015
2042(13*10^159147+161)/3159148Robert Price11/2018
20432^528620-113879159131Enzo Doria10/2014
2044(47*10^159083+259)/9159084Robert Price03/2022
20452^528000-23307158944Enzo Doria08/2013
2046(29*10^158909+61)/9158910Robert Price08/2018
20472^527817+1876817158889Enzo Doria07/2016
20482^527774-49451158876Enzo Doria10/2015
20492^527745-291553158868Enzo Doria07/2015
2050(91*10^158862+11)/3158864Robert Price02/2020
20512^527644-1856999158837Enzo Doria10/2015
2052(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
20532^527573-1863253158816Enzo Doria12/2015
20542^527553-23401158810Enzo Doria08/2013
2055(49*10^158783+437)/9158784Robert Price09/2021
205610^158755+310207158756Patrick De Geest08/2021
205710^158755-50001158755Robert Price08/2020
2058(61*10^158748-619)/9158749Robert Price03/2022
205911^152420-210158730Enzo Doria09/2012
2060(13*10^158694+401)/9158695Robert Price01/2018
20612^527052-69059158659Enzo Doria11/2015
20622^526849-113233158598Enzo Doria07/2014
2063(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
2064(299*10^158544-17)/3158546Robert Price04/2020
20652^526658-3551158540Yves Minet03/2017
20667*10^158465-11158466Robert Price06/2019
20672^526375-23115158455Enzo Doria08/2013
2068(77*10^158407-293)/9158408Robert Price09/2019
20692^526028-112793158351Enzo Doria07/2014
2070(229*10^158339-1)/3158341Robert Price07/2020
20712^525690-9221158249Lelio R Paula01/2013
20722*10^158242-7158243Robert Price10/2015
20732^525667-525667^2158242Henri Lifchitz12/2017
2074(56*10^158230+187)/9158231Robert Price10/2021
207510^158209-7000000001158209Robert Price12/2021
20762^525186-1857431158097Enzo Doria10/2015
20772^524515-23245157895Enzo Doria08/2013
20782^524499-109087157890Enzo Doria04/2014
20792^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
20802^524288+189093157827Makoto Morimoto01/2016
20812^524288-164073157827Matthias Baur03/2020
2082(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
2083(10^157792+359)/9157792Serge Batalov12/2014
20842^524154+25157787Stefano Morozzi04/2021
20852^523924+1876591157717Enzo Doria07/2016
2086(17*10^157705+67)/3157706Robert Price01/2019
2087(46^94841+1)/47157696Robert Price01/2014
20882^523774+77839157672Enzo Doria05/2016
20892^523587+2799143157616Enzo Doria04/2016
20902^523371+1872113157551Enzo Doria05/2016
20918*10^157477+27157478Robert Price09/2021
2092(8*10^157368+49)/3157369Robert Price05/2020
2093(82*10^157319+449)/9157320Robert Price11/2019
20942^522535-351457157299Enzo Doria07/2015
20952^522226+2799079157206Enzo Doria04/2016
2096(134*10^157191-11)/3157193Robert Price01/2022
20972^522134-1849451157178Enzo Doria08/2015
20989*10^157152+71157153Robert Price08/2020
20994*10^157150+93157151Robert Price08/2018
21002^521401-29593156958Enzo Doria08/2015
21017*10^156956+87156957Robert Price07/2019
21022^521348-23397156942Enzo Doria08/2013
210310^156902+34509156903Patrick De Geest08/2021
210510^156902-80000001156902Robert Price04/2021
210410^156902-69789156902Patrick De Geest08/2021
2106(98^78797+1)/99156901Paul Bourdelais12/2017
210765^86522+64156857Lelio R Paula04/2016
21088^173687-7^173687156855Jean-Louis Charton09/2004
21092^520977-1858183156830Enzo Doria10/2015
2110(8*10^156718-101)/3156719Robert Price08/2018
2111(10^156640+7)/53156639Alfred Reich07/2021
21122^520314-1849481156631Enzo Doria08/2015
2113(13*10^156522+89)/3156523Robert Price09/2018
2114(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
2115(4*10^156501+119)/3156502Robert Price12/2021
2116(83*10^156476-101)/9156477Robert Price08/2021
21173*10^156435-97156436Robert Price07/2018
2118(8*10^156371-77)/3156372Robert Price07/2018
211953^90679-52^90679156356Robert Price01/2013
2120(418*10^156309-31)/9156311Robert Price05/2022
21212^519106-59141156267Enzo Doria10/2015
21222^519053+6077156251Enzo Doria02/2016
21232^518968-1860989156225Enzo Doria11/2015
2124(25*10^156221-7)/9156222Robert Price05/2018
21252^518931-2782297156214Enzo Doria09/2015
21262^518608-2939156117Yves Minet09/2014
212710*27^109005+697156027Curtis Bright05/2015
2128(49*10^155933-319)/9155934Robert Price10/2021
21292^517967-113485155924Enzo Doria08/2014
2130(103*10^155904+17)/3155906Robert Price08/2020
2131(8*10^155887-719)/9155887Robert Price03/2021
21324*10^155853-39155854Robert Price09/2020
21332^517698+4429155843Lelio R Paula01/2013
21342^517543-113257155796Enzo Doria07/2014
2135(14*10^155740-143)/3155741Robert Price11/2018
213631^104309-30^104309155563Henri Lifchitz08/2013
21372^516742-39851155555Enzo Doria09/2015
2138(22*10^155543+47)/3155544Robert Price06/2021
2139(19*10^155504+131)/3155505Robert Price06/2020
21407*10^155496+61155497Robert Price08/2019
21412^516440+1878421155464Enzo Doria08/2016
21422^515863-1867237155291Enzo Doria03/2016
21432^515786-461861155268Enzo Doria07/2015
21442^515644-113247155225Enzo Doria07/2014
2145(7*10^155203+107)/3155204Robert Price02/2018
214610^155163+206871155164Patrick De Geest05/2021
214710^155163-40001155163Robert Price01/2021
2148(17*10^155133-89)/9155134Robert Price07/2018
21492^515227-114997155099Enzo Doria06/2015
2151EPrime(155025)155025Eric W. Weisstein10/2010
2150(14*10^155024-221)/9155025Robert Price04/2018
2152(4*10^155022+173)/3155023Robert Price02/2018
2153(266*10^154897+1)/3154899Robert Price04/2020
2154(115*10^154869-1)/3154871Serge Batalov12/2014
2155(86*10^154853-221)/9154854Robert Price09/2019
21562^514361+78167154839Enzo Doria05/2016
21572^514281-115033154815Enzo Doria06/2015
21582^514194-3311154788Yves Minet12/2014
2159(14*10^154773+37)/3154774Robert Price12/2018
2160(16*10^154748+131)/3154749Robert Price03/2022
21616*10^154742-31154743Robert Price07/2020
2162(14*10^154645+139)/9154646Robert Price11/2021
21635*10^154618-79154619Robert Price03/2021
2164(167*10^154595+1)/3154597Robert Price04/2021
21652^513437+1879337154560Enzo Doria09/2016
21662^513306-113201154521Enzo Doria07/2014
2167(10^154494-13)/3154494Robert Price12/2017
21682^513042-113787154442Enzo Doria09/2014
2169(151*10^154434-7)/9154436Robert Price01/2020
2170(118*10^154428+11)/3154430Robert Price03/2022
2171(14*10^154413+139)/9154414Robert Price11/2021
2172(77*10^154389-149)/9154390Robert Price03/2022
21732^512628-114053154317Enzo Doria11/2014
21742^512529-49783154287Enzo Doria10/2015
2175(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
21762^512315-115297154223Enzo Doria06/2015
2177(47*10^154221+241)/9154222Robert Price06/2022
2178(7*10^154211+173)/9154211Robert Price01/2022
21792^512168+79561154178Enzo Doria06/2016
2180(77*10^154175+67)/9154176Robert Price12/2021
2181(5*10^154158-311)/9154158Robert Price12/2021
2182(89*10^154103-737)/9154104Robert Price01/2022
21834*10^154078-57154079Robert Price10/2018
2184(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
21857*10^154038-57154039Robert Price06/2020
21862^511658-114371154025Enzo Doria02/2015
2187(57^87719+1)/58154022Paul Bourdelais11/2017
21882^511580-1846679154001Enzo Doria07/2015
2189(259*10^153998-1)/3154000Robert Price12/2020
21902^511541-113713153990Enzo Doria09/2014
219149958^32768+49957^32768153965Kellen Shenton11/2020
219210^153935+970801153936Patrick De Geest05/2021
219310^153935-1000001153935Robert Price08/2020
2194(16*10^153868-73)/3153869Robert Price07/2020
21959*10^153851-67153852Robert Price11/2020
21962^511077-112723153850Enzo Doria06/2014
219769^83653-68^83653153826Robert Price12/2013
21982^510963-113707153816Enzo Doria09/2014
2199(154*10^153810-1)/9153812Serge Batalov12/2014
2200(181*25^109991-75077)/8153763Curtis Bright05/2015
22012*10^153746-3153747Robert Price07/2015
22022^510626+1179379153714Enzo Doria05/2016
2203(7*10^153664+113)/3153665Robert Price02/2018
22042^510420+81121153652Enzo Doria07/2016
2205(197*7^181761-1)/2153608Karsten Bonath05/2017
22062^509894-459161153494Enzo Doria05/2015
2207(74*10^153489+673)/9153490Robert Price02/2022
2208(49*10^153484-211)/9153485Robert Price06/2022
22092^509841+71657153478Enzo Doria04/2016
22109*10^153446+41153447Robert Price08/2020
22112^509533-1846723153385Enzo Doria07/2015
22122^509468-39989153366Enzo Doria09/2015
221370^83117-69^83117153360Robert Price01/2014
2214(112*10^153025-1)/3153027Serge Batalov12/2014
2215(19*10^153010+131)/3153011Robert Price06/2020
22162^508174-1855151152976Enzo Doria09/2015
2217181^67757-2152974Lelio R Paula12/2017
22182^508160-1864829152972Enzo Doria01/2016
221910^152960+412563152961Patrick De Geest05/2021
222010^152960-50000000001152960Robert Price12/2020
222110^152960-423749152960Patrick De Geest05/2021
2222(71*10^152933-143)/9152934Robert Price10/2021
22232^507857-1848199152881Enzo Doria07/2015
22242^507638-115361152815Enzo Doria07/2015
22252^507551-114025152789Enzo Doria11/2014
2226(6^196337+1)/7152780Paul Bourdelais02/2010
2227(22*10^152670-13)/9152671Robert Price06/2018
22282^506451-22339152457Enzo Doria07/2013
22292^505995-113185152320Enzo Doria07/2014
2230(4*10^152253+149)/9152253Robert Price04/2018
2231578^55117-577^55117152230Jean-Louis Charton08/2012
22322^505431-505431152150Henri Lifchitz04/2005
2233(203*10^152143+1)/3152145Robert Price03/2020
22342^505053+73097152037Enzo Doria04/2016
223522*10^151998+3152000Robert Price01/2020
2236(238*10^151979-1)/3151981Robert Price04/2020
2237(2^504793-7)/46765151954Lelio R Paula12/2017
2238350377#+797581151937Nicolas PALAU08/2017
2239(79*10^151906-529)/9151907Robert Price01/2022
22402^504618-343991151906Enzo Doria07/2015
22412^504212-461939151783Enzo Doria07/2015
22427*10^151772-41151773Robert Price08/2021
22432^504054-2231151736Yves Minet10/2011
2244(28*10^151682+191)/3151683Robert Price02/2020
22452^503475-933075151562Paul Bourdelais06/2021
22462^503361-39883151527Enzo Doria09/2015
22472^503225+382667151486Enzo Doria10/2016
2248(206*10^151483-11)/3151485Robert Price02/2022
2249(844*10^151396-7)/9151398Robert Price05/2021
2250(26*10^151391-503)/9151392Robert Price07/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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