PRP Records

Probable Primes Top 10000

(290974 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 ?
2001919^54919-918^54919162743Jean-Louis Charton01/2013
2002(203*10^162689+1)/3162691Robert Price03/2020
20033*10^162620-59162621Robert Price09/2018
20043^340694-112960162553Enzo Doria07/2014
20052^539807-114081162499Enzo Doria12/2014
2006414^62093+62093^414162498Norbert Schneider03/2022
20072^539654-114893162453Enzo Doria05/2015
20089*10^162449-71162450Robert Price11/2020
20092^539617-1851583162441Enzo Doria08/2015
2010(91*10^162410+11)/3162412Robert Price02/2020
20112^539346+81049162360Enzo Doria07/2016
20122^539220-115499162322Enzo Doria07/2015
20132^539217-113713162321Enzo Doria09/2014
20149^170099-8^170099162316Jean-Louis Charton05/2005
20154*10^162263-39162264Robert Price09/2020
2016(115*10^162153-1)/3162155Serge Batalov12/2014
2017(10^162138+11)/3162138Serge Batalov07/2015
2018(61*10^162100-403)/9162101Robert Price10/2021
20192^538473-112723162097Enzo Doria06/2014
20202^538157+79337162002Enzo Doria06/2016
20212^538136-114749161996Enzo Doria05/2015
20222^538104+1531161986Lelio R Paula01/2013
2023(9*29^110727-1199)/14161927Curtis Bright05/2015
20242^537815-22737161899Enzo Doria07/2013
20252^537804-39839161896Enzo Doria09/2015
2026(754*10^161816-7)/9161818Robert Price05/2020
20272^537458-59201161791Enzo Doria10/2015
20282*10^161766+51161767Robert Price05/2018
2029(7*10^161760+131)/3161761Robert Price06/2020
20302^537209-49849161717Enzo Doria10/2015
2031(58*10^161691+329)/9161692Robert Price05/2019
203223*10^161668-3161670Robert Price10/2021
20332^536937+1879397161635Enzo Doria09/2016
203434*10^161593-9161595Robert Price06/2020
2035(31*10^161582-1)/3161584Robert Price02/2020
20362^536569-22881161524Enzo Doria07/2013
2037(46*10^161505+593)/9161506Robert Price04/2022
203810^161253+573493161254Patrick De Geest07/2018
203910^161253-8001161253Robert Price03/2018
204097*10^161247-3161249Robert Price05/2020
20417*10^161192-9161193Robert Price10/2015
20422^535415-19161176Stefano Morozzi07/2022
20432^535269-113803161133Enzo Doria09/2014
20442^535205-23295161113Enzo Doria08/2013
2045(49*10^161105+437)/9161106Robert Price09/2021
2046(89^82609+1)/90161036Paul Bourdelais10/2017
20472^534429-19160880Stefano Morozzi07/2022
20482^534359-23229160859Enzo Doria08/2013
2049457^60454+60454^457160803Norbert Schneider07/2021
20508*10^160782+53160783Robert Price08/2020
205167^88037-66^88037160763Robert Price10/2013
2052(88*10^160761-637)/9160762Robert Price11/2020
20532^533948-1852559160735Enzo Doria08/2015
20542^533665-23335160650Enzo Doria08/2013
2055(19*10^160619+77)/3160620Robert Price05/2019
20562^533350-5160555Stefano Morozzi07/2022
2057(38*10^160508+151)/9160509Robert Price03/2022
20583^336353-2^336353160482Mike Oakes10/2007
20592*10^160339-63160340Robert Price01/2022
2060(91*10^160249+11)/3160251Robert Price02/2020
2061(772*10^160239-7)/9160241Robert Price06/2022
2062(2*10^160226+187)/9160226Robert Price06/2022
20632^532253+1868417160225Enzo Doria04/2016
20642^532108-291989160181Enzo Doria07/2015
2065(28*10^160171-79)/3160172Robert Price02/2021
2066(26*10^160166-131)/3160167Robert Price10/2019
206755*10^160145+9160147Robert Price03/2022
2068(17*10^160143+67)/3160144Robert Price01/2019
2069(19*10^159921-49)/3159922Robert Price05/2019
20702^531110-1853771159881Enzo Doria09/2015
2071(275^65536+53^65536)/2159864Kellen Shenton11/2020
20722^530992-1845299159845Enzo Doria07/2015
20732^530810+25159790Stefano Morozzi04/2021
2074(136*10^159736-1)/9159738Serge Batalov12/2014
20752^530417-113833159672Enzo Doria09/2014
20762^530406-69701159669Enzo Doria02/2016
20775*10^159656+41159657Robert Price03/2019
20788*10^159614+29159615Robert Price11/2021
20797^188858-188858^7159604Norbert Schneider05/2018
2080(24^115597-1)/23159547Paul Bourdelais09/2017
2081(17*10^159438-377)/9159439Robert Price03/2018
2082(203*10^159381+1)/3159383Robert Price03/2020
208389*10^159258-9159260Robert Price05/2020
20842^528944-461315159229Enzo Doria07/2015
2085(13*10^159147+161)/3159148Robert Price11/2018
20862^528620-113879159131Enzo Doria10/2014
2087(47*10^159083+259)/9159084Robert Price03/2022
20882^528000-23307158944Enzo Doria08/2013
2089(29*10^158909+61)/9158910Robert Price08/2018
20902^527817+1876817158889Enzo Doria07/2016
20912^527774-49451158876Enzo Doria10/2015
20922^527745-291553158868Enzo Doria07/2015
2093(91*10^158862+11)/3158864Robert Price02/2020
20942^527644-1856999158837Enzo Doria10/2015
2095(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
20962^527573-1863253158816Enzo Doria12/2015
20972^527553-23401158810Enzo Doria08/2013
2098(49*10^158783+437)/9158784Robert Price09/2021
209910^158755+310207158756Patrick De Geest08/2021
210010^158755-50001158755Robert Price08/2020
2101(61*10^158748-619)/9158749Robert Price03/2022
210211^152420-210158730Enzo Doria09/2012
2103(13*10^158694+401)/9158695Robert Price01/2018
21042^527052-69059158659Enzo Doria11/2015
21052^526849-113233158598Enzo Doria07/2014
2106(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
2107(299*10^158544-17)/3158546Robert Price04/2020
21082^526658-3551158540Yves Minet03/2017
21097*10^158465-11158466Robert Price06/2019
21102^526375-23115158455Enzo Doria08/2013
2111(77*10^158407-293)/9158408Robert Price09/2019
21122^526028-112793158351Enzo Doria07/2014
2113(229*10^158339-1)/3158341Robert Price07/2020
21142^525690-9221158249Lelio R Paula01/2013
21152*10^158242-7158243Robert Price10/2015
21162^525667-525667^2158242Henri Lifchitz12/2017
2117(56*10^158230+187)/9158231Robert Price10/2021
211810^158209-7000000001158209Robert Price12/2021
21192^525186-1857431158097Enzo Doria10/2015
21202^524515-23245157895Enzo Doria08/2013
21212^524499-109087157890Enzo Doria04/2014
21222^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
21232^524288+189093157827Makoto Morimoto01/2016
21242^524288-164073157827Matthias Baur03/2020
2125(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
2126(10^157792+359)/9157792Serge Batalov12/2014
21272^524154+25157787Stefano Morozzi04/2021
21282^523924+1876591157717Enzo Doria07/2016
2129(17*10^157705+67)/3157706Robert Price01/2019
2130(46^94841+1)/47157696Robert Price01/2014
21312^523774+77839157672Enzo Doria05/2016
21322^523587+2799143157616Enzo Doria04/2016
21332^523371+1872113157551Enzo Doria05/2016
21348*10^157477+27157478Robert Price09/2021
2135(8*10^157368+49)/3157369Robert Price05/2020
2136(82*10^157319+449)/9157320Robert Price11/2019
21372^522535-351457157299Enzo Doria07/2015
21382^522226+2799079157206Enzo Doria04/2016
2139(134*10^157191-11)/3157193Robert Price01/2022
21402^522134-1849451157178Enzo Doria08/2015
21419*10^157152+71157153Robert Price08/2020
21424*10^157150+93157151Robert Price08/2018
21432^521401-29593156958Enzo Doria08/2015
21447*10^156956+87156957Robert Price07/2019
21452^521348-23397156942Enzo Doria08/2013
214610^156902+34509156903Patrick De Geest08/2021
214810^156902-80000001156902Robert Price04/2021
214710^156902-69789156902Patrick De Geest08/2021
2149(98^78797+1)/99156901Paul Bourdelais12/2017
215065^86522+64156857Lelio R Paula04/2016
21518^173687-7^173687156855Jean-Louis Charton09/2004
21522^520977-1858183156830Enzo Doria10/2015
2153(8*10^156718-101)/3156719Robert Price08/2018
2154(10^156640+7)/53156639Alfred Reich07/2021
21552^520314-1849481156631Enzo Doria08/2015
2156(13*10^156522+89)/3156523Robert Price09/2018
2157(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
2158(4*10^156501+119)/3156502Robert Price12/2021
2159(83*10^156476-101)/9156477Robert Price08/2021
21603*10^156435-97156436Robert Price07/2018
2161(8*10^156371-77)/3156372Robert Price07/2018
216253^90679-52^90679156356Robert Price01/2013
2163(418*10^156309-31)/9156311Robert Price05/2022
21642^519106-59141156267Enzo Doria10/2015
21652^519053+6077156251Enzo Doria02/2016
21662^518968-1860989156225Enzo Doria11/2015
2167(25*10^156221-7)/9156222Robert Price05/2018
21682^518931-2782297156214Enzo Doria09/2015
21692^518608-2939156117Yves Minet09/2014
217010*27^109005+697156027Curtis Bright05/2015
2171(49*10^155933-319)/9155934Robert Price10/2021
21722^517967-113485155924Enzo Doria08/2014
2173(103*10^155904+17)/3155906Robert Price08/2020
2174(8*10^155887-719)/9155887Robert Price03/2021
21754*10^155853-39155854Robert Price09/2020
21762^517698+4429155843Lelio R Paula01/2013
21772^517543-113257155796Enzo Doria07/2014
2178(14*10^155740-143)/3155741Robert Price11/2018
217931^104309-30^104309155563Henri Lifchitz08/2013
21802^516742-39851155555Enzo Doria09/2015
2181(22*10^155543+47)/3155544Robert Price06/2021
2182(19*10^155504+131)/3155505Robert Price06/2020
21837*10^155496+61155497Robert Price08/2019
21842^516440+1878421155464Enzo Doria08/2016
21852^515863-1867237155291Enzo Doria03/2016
21862^515786-461861155268Enzo Doria07/2015
21872^515644-113247155225Enzo Doria07/2014
2188(7*10^155203+107)/3155204Robert Price02/2018
218910^155163+206871155164Patrick De Geest05/2021
219010^155163-40001155163Robert Price01/2021
2191(17*10^155133-89)/9155134Robert Price07/2018
21922^515227-114997155099Enzo Doria06/2015
2194EPrime(155025)155025Eric W. Weisstein10/2010
2193(14*10^155024-221)/9155025Robert Price04/2018
2195(4*10^155022+173)/3155023Robert Price02/2018
2196(266*10^154897+1)/3154899Robert Price04/2020
2197(115*10^154869-1)/3154871Serge Batalov12/2014
2198(86*10^154853-221)/9154854Robert Price09/2019
21992^514361+78167154839Enzo Doria05/2016
22002^514281-115033154815Enzo Doria06/2015
22012^514194-3311154788Yves Minet12/2014
2202(14*10^154773+37)/3154774Robert Price12/2018
2203(16*10^154748+131)/3154749Robert Price03/2022
22046*10^154742-31154743Robert Price07/2020
2205(14*10^154645+139)/9154646Robert Price11/2021
22065*10^154618-79154619Robert Price03/2021
2207(167*10^154595+1)/3154597Robert Price04/2021
22082^513437+1879337154560Enzo Doria09/2016
22092^513306-113201154521Enzo Doria07/2014
2210(10^154494-13)/3154494Robert Price12/2017
22112^513042-113787154442Enzo Doria09/2014
2212(151*10^154434-7)/9154436Robert Price01/2020
2213(118*10^154428+11)/3154430Robert Price03/2022
2214(14*10^154413+139)/9154414Robert Price11/2021
2215(77*10^154389-149)/9154390Robert Price03/2022
22162^512628-114053154317Enzo Doria11/2014
22172^512529-49783154287Enzo Doria10/2015
2218(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
22192^512315-115297154223Enzo Doria06/2015
2220(47*10^154221+241)/9154222Robert Price06/2022
2221(7*10^154211+173)/9154211Robert Price01/2022
22222^512168+79561154178Enzo Doria06/2016
2223(77*10^154175+67)/9154176Robert Price12/2021
2224(5*10^154158-311)/9154158Robert Price12/2021
2225(89*10^154103-737)/9154104Robert Price01/2022
22264*10^154078-57154079Robert Price10/2018
2227(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
22287*10^154038-57154039Robert Price06/2020
22292^511658-114371154025Enzo Doria02/2015
2230(57^87719+1)/58154022Paul Bourdelais11/2017
22312^511580-1846679154001Enzo Doria07/2015
2232(259*10^153998-1)/3154000Robert Price12/2020
22332^511541-113713153990Enzo Doria09/2014
223449958^32768+49957^32768153965Kellen Shenton11/2020
223510^153935+970801153936Patrick De Geest05/2021
223610^153935-1000001153935Robert Price08/2020
2237(16*10^153868-73)/3153869Robert Price07/2020
22389*10^153851-67153852Robert Price11/2020
22392^511077-112723153850Enzo Doria06/2014
224069^83653-68^83653153826Robert Price12/2013
22412^510963-113707153816Enzo Doria09/2014
2242(154*10^153810-1)/9153812Serge Batalov12/2014
2243(181*25^109991-75077)/8153763Curtis Bright05/2015
22442*10^153746-3153747Robert Price07/2015
22452^510626+1179379153714Enzo Doria05/2016
2246(7*10^153664+113)/3153665Robert Price02/2018
22472^510420+81121153652Enzo Doria07/2016
2248(197*7^181761-1)/2153608Karsten Bonath05/2017
22492^509894-459161153494Enzo Doria05/2015
2250(74*10^153489+673)/9153490Robert Price02/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 08 2022 12:00 (Time in France)

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