PRP Records

Probable Primes Top 10000

(293016 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 ?
2251(509*10^162422+31)/9162424Robert Price08/2022
2252(91*10^162410+11)/3162412Robert Price02/2020
22532^539346+81049162360Enzo Doria07/2016
22542^539220-115499162322Enzo Doria07/2015
22552^539217-113713162321Enzo Doria09/2014
22569^170099-8^170099162316Jean-Louis Charton05/2005
22574*10^162263-39162264Robert Price09/2020
2258(115*10^162153-1)/3162155Serge Batalov12/2014
2259(10^162138+11)/3162138Serge Batalov07/2015
2260(61*10^162100-403)/9162101Robert Price10/2021
22612^538473-112723162097Enzo Doria06/2014
22622^538157+79337162002Enzo Doria06/2016
22632^538136-114749161996Enzo Doria05/2015
22642^538104+1531161986Lelio R Paula01/2013
2265(9*29^110727-1199)/14161927Curtis Bright05/2015
2266((2^179294-1)^3+2)/11161918Serge Batalov03/2023
22672^537815-22737161899Enzo Doria07/2013
22682^537804-39839161896Enzo Doria09/2015
2269(754*10^161816-7)/9161818Robert Price05/2020
22702^537458-59201161791Enzo Doria10/2015
22712*10^161766+51161767Robert Price05/2018
2272(7*10^161760+131)/3161761Robert Price06/2020
22732^537209-49849161717Enzo Doria10/2015
2274(58*10^161691+329)/9161692Robert Price05/2019
227523*10^161668-3161670Robert Price10/2021
22762^536937+1879397161635Enzo Doria09/2016
227734*10^161593-9161595Robert Price06/2020
2278(31*10^161582-1)/3161584Robert Price02/2020
22792^536569-22881161524Enzo Doria07/2013
2280(46*10^161505+593)/9161506Robert Price04/2022
228110^161253+573493161254Patrick De Geest07/2018
228210^161253-8001161253Robert Price03/2018
228397*10^161247-3161249Robert Price05/2020
22847*10^161192-9161193Robert Price10/2015
22852^535415-19161176Stefano Morozzi07/2022
22862^535269-113803161133Enzo Doria09/2014
22872^535205-23295161113Enzo Doria08/2013
2288(49*10^161105+437)/9161106Robert Price09/2021
2289(89^82609+1)/90161036Paul Bourdelais10/2017
22902^534429-19160880Stefano Morozzi07/2022
22912^534359-23229160859Enzo Doria08/2013
229210^160836-1001160836Robert Price10/2022
2293457^60454+60454^457160803Norbert Schneider07/2021
22948*10^160782+53160783Robert Price08/2020
229567^88037-66^88037160763Robert Price10/2013
2296(88*10^160761-637)/9160762Robert Price11/2020
22972^533948-1852559160735Enzo Doria08/2015
22982^533665-23335160650Enzo Doria08/2013
2299(19*10^160619+77)/3160620Robert Price05/2019
23002^533350-5160555Stefano Morozzi07/2022
2301(38*10^160508+151)/9160509Robert Price03/2022
23023^336353-2^336353160482Mike Oakes10/2007
23032*10^160339-63160340Robert Price01/2022
2304(91*10^160249+11)/3160251Robert Price02/2020
2305(772*10^160239-7)/9160241Robert Price06/2022
2306(2*10^160226+187)/9160226Robert Price06/2022
23072^532253+1868417160225Enzo Doria04/2016
23082^532108-291989160181Enzo Doria07/2015
2309(28*10^160171-79)/3160172Robert Price02/2021
2310(26*10^160166-131)/3160167Robert Price10/2019
231155*10^160145+9160147Robert Price03/2022
2312(17*10^160143+67)/3160144Robert Price01/2019
2313(394^61637-1)/393159977Jinyuan Wang04/2023
2314(19*10^159921-49)/3159922Robert Price05/2019
23152^531110-1853771159881Enzo Doria09/2015
2316(275^65536+53^65536)/2159864Kellen Shenton11/2020
23172^530992-1845299159845Enzo Doria07/2015
23182^530810+25159790Stefano Morozzi04/2021
2319(136*10^159736-1)/9159738Serge Batalov12/2014
23202^530417-113833159672Enzo Doria09/2014
23212^530406-69701159669Enzo Doria02/2016
23225*10^159656+41159657Robert Price03/2019
23238*10^159614+29159615Robert Price11/2021
23247^188858-188858^7159604Norbert Schneider05/2018
23257*10^159553-27159554Robert Price11/2022
2326(24^115597-1)/23159547Paul Bourdelais09/2017
2327(17*10^159438-377)/9159439Robert Price03/2018
2328(203*10^159381+1)/3159383Robert Price03/2020
232989*10^159258-9159260Robert Price05/2020
23302^528944-461315159229Enzo Doria07/2015
2331(13*10^159147+161)/3159148Robert Price11/2018
23322^528620-113879159131Enzo Doria10/2014
2333(47*10^159083+259)/9159084Robert Price03/2022
23342^528000-23307158944Enzo Doria08/2013
2335(29*10^158909+61)/9158910Robert Price08/2018
23362^527817+1876817158889Enzo Doria07/2016
23372^527774-49451158876Enzo Doria10/2015
23382^527745-291553158868Enzo Doria07/2015
2339(91*10^158862+11)/3158864Robert Price02/2020
23402^527644-1856999158837Enzo Doria10/2015
2341(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
23422^527573-1863253158816Enzo Doria12/2015
23432^527553-23401158810Enzo Doria08/2013
2344(49*10^158783+437)/9158784Robert Price09/2021
234510^158755+310207158756Patrick De Geest08/2021
234610^158755-50001158755Robert Price08/2020
2347(61*10^158748-619)/9158749Robert Price03/2022
234811^152420-210158730Enzo Doria09/2012
2349(13*10^158694+401)/9158695Robert Price01/2018
23502^527052-69059158659Enzo Doria11/2015
23512^526849-113233158598Enzo Doria07/2014
2352(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
2353(299*10^158544-17)/3158546Robert Price04/2020
23542^526658-3551158540Yves Minet03/2017
23557*10^158465-11158466Robert Price06/2019
23562^526375-23115158455Enzo Doria08/2013
2357(77*10^158407-293)/9158408Robert Price09/2019
23582^526028-112793158351Enzo Doria07/2014
2359(229*10^158339-1)/3158341Robert Price07/2020
23602^525690-9221158249Lelio R Paula01/2013
23612*10^158242-7158243Robert Price10/2015
23622^525667-525667^2158242Henri Lifchitz12/2017
2363(56*10^158230+187)/9158231Robert Price10/2021
236410^158209-7000000001158209Robert Price12/2021
23652^525186-1857431158097Enzo Doria10/2015
23662^524515-23245157895Enzo Doria08/2013
23672^524499-109087157890Enzo Doria04/2014
23682^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
23692^524288+189093157827Makoto Morimoto01/2016
23702^524288-164073157827Matthias Baur03/2020
2371(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
2372(10^157792+359)/9157792Serge Batalov12/2014
23732^524154+25157787Stefano Morozzi04/2021
23742^523924+1876591157717Enzo Doria07/2016
2375(17*10^157705+67)/3157706Robert Price01/2019
2376(46^94841+1)/47157696Robert Price01/2014
23772^523774+77839157672Enzo Doria05/2016
23782^523587+2799143157616Enzo Doria04/2016
23792^523371+1872113157551Enzo Doria05/2016
23808*10^157477+27157478Robert Price09/2021
2381(8*10^157368+49)/3157369Robert Price05/2020
2382(82*10^157319+449)/9157320Robert Price11/2019
23832^522535-351457157299Enzo Doria07/2015
23842^522226+2799079157206Enzo Doria04/2016
2385(134*10^157191-11)/3157193Robert Price01/2022
23862^522134-1849451157178Enzo Doria08/2015
23879*10^157152+71157153Robert Price08/2020
23884*10^157150+93157151Robert Price08/2018
23892^521401-29593156958Enzo Doria08/2015
23907*10^156956+87156957Robert Price07/2019
23912^521348-23397156942Enzo Doria08/2013
239210^156902+34509156903Patrick De Geest08/2021
239410^156902-80000001156902Robert Price04/2021
239310^156902-69789156902Patrick De Geest08/2021
2395(98^78797+1)/99156901Paul Bourdelais12/2017
239665^86522+64156857Lelio R Paula04/2016
23978^173687-7^173687156855Jean-Louis Charton09/2004
23982^520977-1858183156830Enzo Doria10/2015
2399(8*10^156718-101)/3156719Robert Price08/2018
2400(10^156640+7)/53156639Alfred Reich07/2021
24012^520314-1849481156631Enzo Doria08/2015
2402(16*10^156563-637)/9156564Robert Price09/2022
2403(13*10^156522+89)/3156523Robert Price09/2018
2405(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
2404(2^519925-5)/3156513Stefano Morozzi08/2022
2406(4*10^156501+119)/3156502Robert Price12/2021
2407(83*10^156476-101)/9156477Robert Price08/2021
24083*10^156435-97156436Robert Price07/2018
2409(8*10^156371-77)/3156372Robert Price07/2018
241053^90679-52^90679156356Robert Price01/2013
2411(418*10^156309-31)/9156311Robert Price05/2022
24122^519106-59141156267Enzo Doria10/2015
24132^519053+6077156251Enzo Doria02/2016
24142^518968-1860989156225Enzo Doria11/2015
2415(25*10^156221-7)/9156222Robert Price05/2018
24162^518931-2782297156214Enzo Doria09/2015
24172^518608-2939156117Yves Minet09/2014
241810*27^109005+697156027Curtis Bright05/2015
2419(49*10^155933-319)/9155934Robert Price10/2021
24202^517967-113485155924Enzo Doria08/2014
2421(103*10^155904+17)/3155906Robert Price08/2020
2422(8*10^155887-719)/9155887Robert Price03/2021
24234*10^155853-39155854Robert Price09/2020
24242^517698+4429155843Lelio R Paula01/2013
24252^517543-113257155796Enzo Doria07/2014
2426(14*10^155740-143)/3155741Robert Price11/2018
242731^104309-30^104309155563Henri Lifchitz08/2013
24282^516742-39851155555Enzo Doria09/2015
2429(22*10^155543+47)/3155544Robert Price06/2021
2430(19*10^155504+131)/3155505Robert Price06/2020
24317*10^155496+61155497Robert Price08/2019
24322^516440+1878421155464Enzo Doria08/2016
24332^515863-1867237155291Enzo Doria03/2016
24342^515786-461861155268Enzo Doria07/2015
24352^515644-113247155225Enzo Doria07/2014
2436(7*10^155203+107)/3155204Robert Price02/2018
243710^155163+206871155164Patrick De Geest05/2021
243810^155163-40001155163Robert Price01/2021
2439(17*10^155133-89)/9155134Robert Price07/2018
24402^515227-114997155099Enzo Doria06/2015
2442EPrime(155025)155025Eric W. Weisstein10/2010
2441(14*10^155024-221)/9155025Robert Price04/2018
2443(4*10^155022+173)/3155023Robert Price02/2018
2444(266*10^154897+1)/3154899Robert Price04/2020
2445(115*10^154869-1)/3154871Serge Batalov12/2014
2446(86*10^154853-221)/9154854Robert Price09/2019
24472^514361+78167154839Enzo Doria05/2016
24482^514281-115033154815Enzo Doria06/2015
24492^514194-3311154788Yves Minet12/2014
2450(14*10^154773+37)/3154774Robert Price12/2018
2451(16*10^154748+131)/3154749Robert Price03/2022
24526*10^154742-31154743Robert Price07/2020
2453(14*10^154645+139)/9154646Robert Price11/2021
24545*10^154618-79154619Robert Price03/2021
2455(167*10^154595+1)/3154597Robert Price04/2021
24562^513437+1879337154560Enzo Doria09/2016
24572^513306-113201154521Enzo Doria07/2014
2458(10^154494-13)/3154494Robert Price12/2017
245923462^35343+35343^23462154462Norbert Schneider04/2023
24602^513042-113787154442Enzo Doria09/2014
2461(151*10^154434-7)/9154436Robert Price01/2020
2462(118*10^154428+11)/3154430Robert Price03/2022
2463(14*10^154413+139)/9154414Robert Price11/2021
2464(77*10^154389-149)/9154390Robert Price03/2022
246510^154359+49154360Robert Price02/2023
24662^512628-114053154317Enzo Doria11/2014
24672^512529-49783154287Enzo Doria10/2015
2468(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
24692^512315-115297154223Enzo Doria06/2015
2470(47*10^154221+241)/9154222Robert Price06/2022
2471(7*10^154211+173)/9154211Robert Price01/2022
24722^512168+79561154178Enzo Doria06/2016
2473(77*10^154175+67)/9154176Robert Price12/2021
2474(5*10^154158-311)/9154158Robert Price12/2021
2475(89*10^154103-737)/9154104Robert Price01/2022
24764*10^154078-57154079Robert Price10/2018
2477(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
24787*10^154038-57154039Robert Price06/2020
24792^511658-114371154025Enzo Doria02/2015
2480(57^87719+1)/58154022Paul Bourdelais11/2017
24812^511580-1846679154001Enzo Doria07/2015
2482(259*10^153998-1)/3154000Robert Price12/2020
24832^511541-113713153990Enzo Doria09/2014
248449958^32768+49957^32768153965Kellen Shenton11/2020
248510^153935+970801153936Patrick De Geest05/2021
248610^153935-1000001153935Robert Price08/2020
2487(16*10^153868-73)/3153869Robert Price07/2020
24889*10^153851-67153852Robert Price11/2020
24892^511077-112723153850Enzo Doria06/2014
249069^83653-68^83653153826Robert Price12/2013
24912^510963-113707153816Enzo Doria09/2014
2492(154*10^153810-1)/9153812Serge Batalov12/2014
2493(181*25^109991-75077)/8153763Curtis Bright05/2015
24942*10^153746-3153747Robert Price07/2015
24952^510626+1179379153714Enzo Doria05/2016
2496(7*10^153664+113)/3153665Robert Price02/2018
24972^510420+81121153652Enzo Doria07/2016
2498(197*7^181761-1)/2153608Karsten Bonath05/2017
24992^509894-459161153494Enzo Doria05/2015
2500(74*10^153489+673)/9153490Robert Price02/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

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