PRP Records

Probable Primes Top 10000

(291910 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 ?
22512^527644-1856999158837Enzo Doria10/2015
2252(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
22532^527573-1863253158816Enzo Doria12/2015
22542^527553-23401158810Enzo Doria08/2013
2255(49*10^158783+437)/9158784Robert Price09/2021
225610^158755+310207158756Patrick De Geest08/2021
225710^158755-50001158755Robert Price08/2020
2258(61*10^158748-619)/9158749Robert Price03/2022
225911^152420-210158730Enzo Doria09/2012
2260(13*10^158694+401)/9158695Robert Price01/2018
22612^527052-69059158659Enzo Doria11/2015
22622^526849-113233158598Enzo Doria07/2014
2263(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
2264(299*10^158544-17)/3158546Robert Price04/2020
22652^526658-3551158540Yves Minet03/2017
22667*10^158465-11158466Robert Price06/2019
22672^526375-23115158455Enzo Doria08/2013
2268(77*10^158407-293)/9158408Robert Price09/2019
22692^526028-112793158351Enzo Doria07/2014
2270(229*10^158339-1)/3158341Robert Price07/2020
22712^525690-9221158249Lelio R Paula01/2013
22722*10^158242-7158243Robert Price10/2015
22732^525667-525667^2158242Henri Lifchitz12/2017
2274(56*10^158230+187)/9158231Robert Price10/2021
227510^158209-7000000001158209Robert Price12/2021
22762^525186-1857431158097Enzo Doria10/2015
22772^524515-23245157895Enzo Doria08/2013
22782^524499-109087157890Enzo Doria04/2014
22792^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
22802^524288+189093157827Makoto Morimoto01/2016
22812^524288-164073157827Matthias Baur03/2020
2282(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
2283(10^157792+359)/9157792Serge Batalov12/2014
22842^524154+25157787Stefano Morozzi04/2021
22852^523924+1876591157717Enzo Doria07/2016
2286(17*10^157705+67)/3157706Robert Price01/2019
2287(46^94841+1)/47157696Robert Price01/2014
22882^523774+77839157672Enzo Doria05/2016
22892^523587+2799143157616Enzo Doria04/2016
22902^523371+1872113157551Enzo Doria05/2016
22918*10^157477+27157478Robert Price09/2021
2292(8*10^157368+49)/3157369Robert Price05/2020
2293(82*10^157319+449)/9157320Robert Price11/2019
22942^522535-351457157299Enzo Doria07/2015
22952^522226+2799079157206Enzo Doria04/2016
2296(134*10^157191-11)/3157193Robert Price01/2022
22972^522134-1849451157178Enzo Doria08/2015
22989*10^157152+71157153Robert Price08/2020
22994*10^157150+93157151Robert Price08/2018
23002^521401-29593156958Enzo Doria08/2015
23017*10^156956+87156957Robert Price07/2019
23022^521348-23397156942Enzo Doria08/2013
230310^156902+34509156903Patrick De Geest08/2021
230510^156902-80000001156902Robert Price04/2021
230410^156902-69789156902Patrick De Geest08/2021
2306(98^78797+1)/99156901Paul Bourdelais12/2017
230765^86522+64156857Lelio R Paula04/2016
23088^173687-7^173687156855Jean-Louis Charton09/2004
23092^520977-1858183156830Enzo Doria10/2015
2310(8*10^156718-101)/3156719Robert Price08/2018
2311(10^156640+7)/53156639Alfred Reich07/2021
23122^520314-1849481156631Enzo Doria08/2015
2313(16*10^156563-637)/9156564Robert Price09/2022
2314(13*10^156522+89)/3156523Robert Price09/2018
2315(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
2316(2^519925-5)/3156513Stefano Morozzi08/2022
2317(4*10^156501+119)/3156502Robert Price12/2021
2318(83*10^156476-101)/9156477Robert Price08/2021
23193*10^156435-97156436Robert Price07/2018
2320(8*10^156371-77)/3156372Robert Price07/2018
232153^90679-52^90679156356Robert Price01/2013
2322(418*10^156309-31)/9156311Robert Price05/2022
23232^519106-59141156267Enzo Doria10/2015
23242^519053+6077156251Enzo Doria02/2016
23252^518968-1860989156225Enzo Doria11/2015
2326(25*10^156221-7)/9156222Robert Price05/2018
23272^518931-2782297156214Enzo Doria09/2015
23282^518608-2939156117Yves Minet09/2014
232910*27^109005+697156027Curtis Bright05/2015
2330(49*10^155933-319)/9155934Robert Price10/2021
23312^517967-113485155924Enzo Doria08/2014
2332(103*10^155904+17)/3155906Robert Price08/2020
2333(8*10^155887-719)/9155887Robert Price03/2021
23344*10^155853-39155854Robert Price09/2020
23352^517698+4429155843Lelio R Paula01/2013
23362^517543-113257155796Enzo Doria07/2014
2337(14*10^155740-143)/3155741Robert Price11/2018
233831^104309-30^104309155563Henri Lifchitz08/2013
23392^516742-39851155555Enzo Doria09/2015
2340(22*10^155543+47)/3155544Robert Price06/2021
2341(19*10^155504+131)/3155505Robert Price06/2020
23427*10^155496+61155497Robert Price08/2019
23432^516440+1878421155464Enzo Doria08/2016
23442^515863-1867237155291Enzo Doria03/2016
23452^515786-461861155268Enzo Doria07/2015
23462^515644-113247155225Enzo Doria07/2014
2347(7*10^155203+107)/3155204Robert Price02/2018
234810^155163+206871155164Patrick De Geest05/2021
234910^155163-40001155163Robert Price01/2021
2350(17*10^155133-89)/9155134Robert Price07/2018
23512^515227-114997155099Enzo Doria06/2015
2353EPrime(155025)155025Eric W. Weisstein10/2010
2352(14*10^155024-221)/9155025Robert Price04/2018
2354(4*10^155022+173)/3155023Robert Price02/2018
2355(266*10^154897+1)/3154899Robert Price04/2020
2356(115*10^154869-1)/3154871Serge Batalov12/2014
2357(86*10^154853-221)/9154854Robert Price09/2019
23582^514361+78167154839Enzo Doria05/2016
23592^514281-115033154815Enzo Doria06/2015
23602^514194-3311154788Yves Minet12/2014
2361(14*10^154773+37)/3154774Robert Price12/2018
2362(16*10^154748+131)/3154749Robert Price03/2022
23636*10^154742-31154743Robert Price07/2020
2364(14*10^154645+139)/9154646Robert Price11/2021
23655*10^154618-79154619Robert Price03/2021
2366(167*10^154595+1)/3154597Robert Price04/2021
23672^513437+1879337154560Enzo Doria09/2016
23682^513306-113201154521Enzo Doria07/2014
2369(10^154494-13)/3154494Robert Price12/2017
23702^513042-113787154442Enzo Doria09/2014
2371(151*10^154434-7)/9154436Robert Price01/2020
2372(118*10^154428+11)/3154430Robert Price03/2022
2373(14*10^154413+139)/9154414Robert Price11/2021
2374(77*10^154389-149)/9154390Robert Price03/2022
23752^512628-114053154317Enzo Doria11/2014
23762^512529-49783154287Enzo Doria10/2015
2377(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
23782^512315-115297154223Enzo Doria06/2015
2379(47*10^154221+241)/9154222Robert Price06/2022
2380(7*10^154211+173)/9154211Robert Price01/2022
23812^512168+79561154178Enzo Doria06/2016
2382(77*10^154175+67)/9154176Robert Price12/2021
2383(5*10^154158-311)/9154158Robert Price12/2021
2384(89*10^154103-737)/9154104Robert Price01/2022
23854*10^154078-57154079Robert Price10/2018
2386(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
23877*10^154038-57154039Robert Price06/2020
23882^511658-114371154025Enzo Doria02/2015
2389(57^87719+1)/58154022Paul Bourdelais11/2017
23902^511580-1846679154001Enzo Doria07/2015
2391(259*10^153998-1)/3154000Robert Price12/2020
23922^511541-113713153990Enzo Doria09/2014
239349958^32768+49957^32768153965Kellen Shenton11/2020
239410^153935+970801153936Patrick De Geest05/2021
239510^153935-1000001153935Robert Price08/2020
2396(16*10^153868-73)/3153869Robert Price07/2020
23979*10^153851-67153852Robert Price11/2020
23982^511077-112723153850Enzo Doria06/2014
239969^83653-68^83653153826Robert Price12/2013
24002^510963-113707153816Enzo Doria09/2014
2401(154*10^153810-1)/9153812Serge Batalov12/2014
2402(181*25^109991-75077)/8153763Curtis Bright05/2015
24032*10^153746-3153747Robert Price07/2015
24042^510626+1179379153714Enzo Doria05/2016
2405(7*10^153664+113)/3153665Robert Price02/2018
24062^510420+81121153652Enzo Doria07/2016
2407(197*7^181761-1)/2153608Karsten Bonath05/2017
24082^509894-459161153494Enzo Doria05/2015
2409(74*10^153489+673)/9153490Robert Price02/2022
2410(49*10^153484-211)/9153485Robert Price06/2022
24112^509841+71657153478Enzo Doria04/2016
24129*10^153446+41153447Robert Price08/2020
24132^509533-1846723153385Enzo Doria07/2015
24142^509468-39989153366Enzo Doria09/2015
241570^83117-69^83117153360Robert Price01/2014
2416(7*10^153116-1)/3153117Robert Price08/2022
2417(112*10^153025-1)/3153027Serge Batalov12/2014
2418(19*10^153010+131)/3153011Robert Price06/2020
24192^508174-1855151152976Enzo Doria09/2015
2420181^67757-2152974Lelio R Paula12/2017
24212^508160-1864829152972Enzo Doria01/2016
242210^152960+412563152961Patrick De Geest05/2021
242310^152960-50000000001152960Robert Price12/2020
242410^152960-423749152960Patrick De Geest05/2021
2425(71*10^152933-143)/9152934Robert Price10/2021
24262^507857-1848199152881Enzo Doria07/2015
24272^507638-115361152815Enzo Doria07/2015
24282^507551-114025152789Enzo Doria11/2014
2429(6^196337+1)/7152780Paul Bourdelais02/2010
2430(22*10^152670-13)/9152671Robert Price06/2018
24312^506451-22339152457Enzo Doria07/2013
24322^505995-113185152320Enzo Doria07/2014
2433(8*10^152260-17)/9152260Serge Batalov11/2022
2434(4*10^152253+149)/9152253Robert Price04/2018
2435578^55117-577^55117152230Jean-Louis Charton08/2012
24362^505431-505431152150Henri Lifchitz04/2005
2437(203*10^152143+1)/3152145Robert Price03/2020
24382^505053+73097152037Enzo Doria04/2016
243922*10^151998+3152000Robert Price01/2020
2440(238*10^151979-1)/3151981Robert Price04/2020
2441(2^504793-7)/46765151954Lelio R Paula12/2017
2442350377#+797581151937Nicolas PALAU08/2017
2443(79*10^151906-529)/9151907Robert Price01/2022
24442^504618-343991151906Enzo Doria07/2015
24452^504212-461939151783Enzo Doria07/2015
24467*10^151772-41151773Robert Price08/2021
24472^504054-2231151736Yves Minet10/2011
2448(28*10^151682+191)/3151683Robert Price02/2020
24492^503475-933075151562Paul Bourdelais06/2021
24502^503361-39883151527Enzo Doria09/2015
24512^503225+382667151486Enzo Doria10/2016
2452(206*10^151483-11)/3151485Robert Price02/2022
2453(844*10^151396-7)/9151398Robert Price05/2021
2454(26*10^151391-503)/9151392Robert Price07/2018
24552^502769+1877567151349Enzo Doria08/2016
24562^502576-4019151291Yves Minet10/2011
24575*10^151257+41151258Robert Price03/2019
24582^502290-2792501151205Enzo Doria02/2016
24592^502181+1868417151172Enzo Doria04/2016
24606*10^151063-77151064Robert Price09/2021
24612^501781-1850503151052Enzo Doria08/2015
2462(5*10^151007+37)/3151008Robert Price03/2018
24632^501627-991151005Yves Minet02/2014
24642^501577-115333150990Enzo Doria07/2015
24658*10^150975+3150976Robert Price08/2015
24662^501512-113669150971Enzo Doria09/2014
2467(83*10^150908+493)/9150909Robert Price12/2021
24682*10^150818+83150819Robert Price12/2021
2469(12^139739+1)/13150803Paul Bourdelais09/2011
2470(31^101111-1)/30150792Alexander Zhirkov11/2010
24712^500899-500899150786Henri Lifchitz04/2005
24722^500832+1876801150766Enzo Doria07/2016
2473(23*10^150763-59)/9150764Robert Price05/2018
24742^500699+1884953150726Enzo Doria02/2017
2475(13*10^150675-37)/3150676Robert Price01/2019
2476(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
24772^500337-71101150617Enzo Doria04/2016
2478(74*10^150616+133)/9150617Robert Price06/2019
2479(2*10^150612-17)/3150612Serge Batalov11/2022
24804*10^150577+91150578Robert Price08/2018
24812^500160+80071150564Enzo Doria06/2016
2482(2^500120+5)/9150551Lelio R Paula12/2017
2483(43*10^150515-421)/9150516Robert Price01/2019
2484(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
2485(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
24862^499861-29503150474Enzo Doria08/2015
24872^499653-113533150411Enzo Doria08/2014
2488(14*10^150391-191)/3150392Robert Price10/2020
24892^499534-221150375Yves Minet06/2012
2490(28*10^150294+41)/3150295Robert Price07/2021
24912^499225+49727150282Enzo Doria09/2016
2492(695*10^150274+7)/9150276Robert Price12/2021
24932^499054-29261150231Enzo Doria07/2015
2494(844*10^150196-7)/9150198Robert Price05/2021
24952^498907-933075150186Paul Bourdelais06/2021
2496(2^498898-7)/9150183Lelio R Paula10/2015
24973*10^150182+17150183Robert Price07/2018
24985*10^150175+63150176Robert Price09/2020
249932363^33292+33292^32363150149Norbert Schneider07/2022
2500(77*10^150128+67)/9150129Robert Price12/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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