PRP Records

Probable Primes Top 10000

(291192 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(151*10^154434-7)/9154436Robert Price01/2020
2252(118*10^154428+11)/3154430Robert Price03/2022
2253(14*10^154413+139)/9154414Robert Price11/2021
2254(77*10^154389-149)/9154390Robert Price03/2022
22552^512628-114053154317Enzo Doria11/2014
22562^512529-49783154287Enzo Doria10/2015
2257(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
22582^512315-115297154223Enzo Doria06/2015
2259(47*10^154221+241)/9154222Robert Price06/2022
2260(7*10^154211+173)/9154211Robert Price01/2022
22612^512168+79561154178Enzo Doria06/2016
2262(77*10^154175+67)/9154176Robert Price12/2021
2263(5*10^154158-311)/9154158Robert Price12/2021
2264(89*10^154103-737)/9154104Robert Price01/2022
22654*10^154078-57154079Robert Price10/2018
2266(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
22677*10^154038-57154039Robert Price06/2020
22682^511658-114371154025Enzo Doria02/2015
2269(57^87719+1)/58154022Paul Bourdelais11/2017
22702^511580-1846679154001Enzo Doria07/2015
2271(259*10^153998-1)/3154000Robert Price12/2020
22722^511541-113713153990Enzo Doria09/2014
227349958^32768+49957^32768153965Kellen Shenton11/2020
227410^153935+970801153936Patrick De Geest05/2021
227510^153935-1000001153935Robert Price08/2020
2276(16*10^153868-73)/3153869Robert Price07/2020
22779*10^153851-67153852Robert Price11/2020
22782^511077-112723153850Enzo Doria06/2014
227969^83653-68^83653153826Robert Price12/2013
22802^510963-113707153816Enzo Doria09/2014
2281(154*10^153810-1)/9153812Serge Batalov12/2014
2282(181*25^109991-75077)/8153763Curtis Bright05/2015
22832*10^153746-3153747Robert Price07/2015
22842^510626+1179379153714Enzo Doria05/2016
2285(7*10^153664+113)/3153665Robert Price02/2018
22862^510420+81121153652Enzo Doria07/2016
2287(197*7^181761-1)/2153608Karsten Bonath05/2017
22882^509894-459161153494Enzo Doria05/2015
2289(74*10^153489+673)/9153490Robert Price02/2022
2290(49*10^153484-211)/9153485Robert Price06/2022
22912^509841+71657153478Enzo Doria04/2016
22929*10^153446+41153447Robert Price08/2020
22932^509533-1846723153385Enzo Doria07/2015
22942^509468-39989153366Enzo Doria09/2015
229570^83117-69^83117153360Robert Price01/2014
2296(7*10^153116-1)/3153117Robert Price08/2022
2297(112*10^153025-1)/3153027Serge Batalov12/2014
2298(19*10^153010+131)/3153011Robert Price06/2020
22992^508174-1855151152976Enzo Doria09/2015
2300181^67757-2152974Lelio R Paula12/2017
23012^508160-1864829152972Enzo Doria01/2016
230210^152960+412563152961Patrick De Geest05/2021
230310^152960-50000000001152960Robert Price12/2020
230410^152960-423749152960Patrick De Geest05/2021
2305(71*10^152933-143)/9152934Robert Price10/2021
23062^507857-1848199152881Enzo Doria07/2015
23072^507638-115361152815Enzo Doria07/2015
23082^507551-114025152789Enzo Doria11/2014
2309(6^196337+1)/7152780Paul Bourdelais02/2010
2310(22*10^152670-13)/9152671Robert Price06/2018
23112^506451-22339152457Enzo Doria07/2013
23122^505995-113185152320Enzo Doria07/2014
2313(4*10^152253+149)/9152253Robert Price04/2018
2314578^55117-577^55117152230Jean-Louis Charton08/2012
23152^505431-505431152150Henri Lifchitz04/2005
2316(203*10^152143+1)/3152145Robert Price03/2020
23172^505053+73097152037Enzo Doria04/2016
231822*10^151998+3152000Robert Price01/2020
2319(238*10^151979-1)/3151981Robert Price04/2020
2320(2^504793-7)/46765151954Lelio R Paula12/2017
2321350377#+797581151937Nicolas PALAU08/2017
2322(79*10^151906-529)/9151907Robert Price01/2022
23232^504618-343991151906Enzo Doria07/2015
23242^504212-461939151783Enzo Doria07/2015
23257*10^151772-41151773Robert Price08/2021
23262^504054-2231151736Yves Minet10/2011
2327(28*10^151682+191)/3151683Robert Price02/2020
23282^503475-933075151562Paul Bourdelais06/2021
23292^503361-39883151527Enzo Doria09/2015
23302^503225+382667151486Enzo Doria10/2016
2331(206*10^151483-11)/3151485Robert Price02/2022
2332(844*10^151396-7)/9151398Robert Price05/2021
2333(26*10^151391-503)/9151392Robert Price07/2018
23342^502769+1877567151349Enzo Doria08/2016
23352^502576-4019151291Yves Minet10/2011
23365*10^151257+41151258Robert Price03/2019
23372^502290-2792501151205Enzo Doria02/2016
23382^502181+1868417151172Enzo Doria04/2016
23396*10^151063-77151064Robert Price09/2021
23402^501781-1850503151052Enzo Doria08/2015
2341(5*10^151007+37)/3151008Robert Price03/2018
23422^501627-991151005Yves Minet02/2014
23432^501577-115333150990Enzo Doria07/2015
23448*10^150975+3150976Robert Price08/2015
23452^501512-113669150971Enzo Doria09/2014
2346(83*10^150908+493)/9150909Robert Price12/2021
23472*10^150818+83150819Robert Price12/2021
2348(12^139739+1)/13150803Paul Bourdelais09/2011
2349(31^101111-1)/30150792Alexander Zhirkov11/2010
23502^500899-500899150786Henri Lifchitz04/2005
23512^500832+1876801150766Enzo Doria07/2016
2352(23*10^150763-59)/9150764Robert Price05/2018
23532^500699+1884953150726Enzo Doria02/2017
2354(13*10^150675-37)/3150676Robert Price01/2019
2355(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
23562^500337-71101150617Enzo Doria04/2016
2357(74*10^150616+133)/9150617Robert Price06/2019
23584*10^150577+91150578Robert Price08/2018
23592^500160+80071150564Enzo Doria06/2016
2360(2^500120+5)/9150551Lelio R Paula12/2017
2361(43*10^150515-421)/9150516Robert Price01/2019
2362(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
2363(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
23642^499861-29503150474Enzo Doria08/2015
23652^499653-113533150411Enzo Doria08/2014
2366(14*10^150391-191)/3150392Robert Price10/2020
23672^499534-221150375Yves Minet06/2012
2368(28*10^150294+41)/3150295Robert Price07/2021
23692^499225+49727150282Enzo Doria09/2016
2370(695*10^150274+7)/9150276Robert Price12/2021
23712^499054-29261150231Enzo Doria07/2015
2372(844*10^150196-7)/9150198Robert Price05/2021
23732^498907-933075150186Paul Bourdelais06/2021
2374(2^498898-7)/9150183Lelio R Paula10/2015
23753*10^150182+17150183Robert Price07/2018
23765*10^150175+63150176Robert Price09/2020
237732363^33292+33292^32363150149Norbert Schneider07/2022
2378(77*10^150128+67)/9150129Robert Price12/2021
23792^498623+1866983150101Enzo Doria03/2016
2380(25*10^150050-403)/9150051Robert Price12/2020
2381numbpart(18140942830)150033Serge Batalov04/2017
238210^150029+4381150030Patrick De Geest05/2016
238310^150029-41150029Serge Batalov12/2014
238410^150000+1158603150001Patrick De Geest09/2018
238510^150000-245703150000Patrick De Geest09/2018
2386(38*10^149999+691)/9150000Robert Price10/2018
23872^498238-53149985Lelio R Paula12/2017
238845728^1905+1905^45728149984Hans Havermann10/2020
23895*10^149907+23149908Robert Price03/2019
239039347^6442+6442^39347149874Hans Havermann09/2020
23912^497850+81049149868Enzo Doria07/2016
239237228^10575+10575^37228149816Hans Havermann10/2020
2393(5*2^497673+1)/2743149812Lelio R Paula10/2015
2394(5*2^497671+1)/373703149810Lelio R Paula10/2015
2395(2*10^149803-143)/3149803Robert Price03/2018
239633845^26604+26604^33845149763Hans Havermann09/2020
23972^497434-2784191149743Enzo Doria10/2015
2398(865*10^149737-1)/9149739Robert Price04/2020
239910^149695-7000001149695Robert Price06/2021
240038237^8214+8214^38237149681Hans Havermann09/2020
2401(23*10^149655+19)/3149656Robert Price07/2019
24022^497068-113579149633Enzo Doria08/2014
24032^497037+73727149624Enzo Doria04/2016
240411*10^149618+3149620Robert Price07/2021
240534942^19067+19067^34942149562Hans Havermann09/2020
240633696^27449+27449^33696149561Hans Havermann09/2020
24072^496773+77747149544Enzo Doria05/2016
2408(7*10^149483-493)/9149483Robert Price04/2021
2409(206*10^149459+7)/3149461Robert Price07/2020
241034589^20940+20940^34589149459Hans Havermann09/2020
24112^496477-113485149455Enzo Doria08/2014
2412((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
24132^496270-49451149393Enzo Doria10/2015
24142^496238-1865081149383Enzo Doria01/2016
241533831^26030+26030^33831149380Hans Havermann09/2020
241634131^23780+23780^34131149365Hans Havermann09/2020
2417(5*10^149335-53)/3149336Robert Price09/2020
24182^495968-1853699149302Enzo Doria09/2015
24192^495935-4117149292Yves Minet02/2018
242035816^14709+14709^35816149267Hans Havermann09/2020
2421(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
242210^149240-40000001149240Robert Price07/2022
24232^495712-396765149225Enzo Doria07/2013
2424(21*2^495676-1)/4835149211Lelio R Paula10/2015
24252^495420+1880701149137Enzo Doria10/2016
24262^495337-1847293149112Enzo Doria07/2015
2427(2^495193-7)/5149068Lelio R Paula10/2015
24282^495163+111546435149059Paul Bourdelais10/2021
242933282^30097+30097^33282149055Hans Havermann09/2020
243037384^9705+9705^37384149050Hans Havermann09/2020
243134808^19143+19143^34808149049Hans Havermann09/2020
2432413^56963-412^56963149013Jean-Louis Charton08/2012
243347^89113-46^89113149006Robert Price10/2012
24342^494916+87855148985Lelio R Paula01/2016
24356*10^148982+73148983Robert Price04/2019
243610^148934+1530019148935Patrick De Geest02/2021
243710^148934-1000000001148934Robert Price11/2020
243810^148934-512057148934Patrick De Geest02/2021
243939000^6571+6571^39000148888Hans Havermann10/2020
24402^494586-2791991148886Enzo Doria02/2016
24418*10^148860-3148861Ray Chandler04/2011
244238262^7769+7769^38262148854Hans Havermann10/2020
244310^148816-500001148816Robert Price03/2022
2444(53*10^148811-287)/9148812Robert Price02/2022
24452^494333-286183148810Enzo Doria06/2015
24462^494144-264119148753Enzo Doria05/2014
24476*10^148734+47148735Robert Price06/2022
244836502^11823+11823^36502148663Hans Havermann11/2020
2449(5*2^493838-1)/3721148658Lelio R Paula10/2015
245064239^206+206^64239148641Hans Havermann10/2020
2451(23*2^493761-1)/555148636Lelio R Paula10/2015
2452(23*10^148627-137)/3148628Robert Price08/2021
2453(151*10^148601-1)/3148603Robert Price03/2020
24542^493636+82081148600Enzo Doria09/2016
2455((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2148593Serge Batalov07/2016
2456177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
2457(2*10^148460-23)/3148460Robert Price04/2018
2458(28*10^148445+101)/3148446Robert Price09/2020
245936203^12556+12556^36203148391Hans Havermann10/2020
246033912^23749+23749^33912148387Hans Havermann10/2020
2461(8*10^148328+1)/9148328Serge Batalov05/2010
246234294^21117+21117^34294148309Hans Havermann10/2020
2463(71*10^148306-539)/9148307Robert Price07/2019
246438042^7875+7875^38042148222Hans Havermann10/2020
24655^211959-12874148153Enzo Doria05/2014
246634142^21831+21831^34142148145Hans Havermann10/2020
246710^148112+34059148113Patrick De Geest05/2021
246810^148112-70000001148112Robert Price03/2021
246910^148112-106593148112Patrick De Geest05/2021
247036303^12016+12016^36303148108Hans Havermann10/2020
2471(77*10^148089-149)/9148090Robert Price03/2022
2472(16*10^148071+41)/3148072Robert Price03/2019
2473187^65175-2148068Lelio R Paula11/2017
24742^491851+1871453148062Enzo Doria05/2016
2475(68*10^148060-257)/9148061Robert Price07/2019
2476(151*10^148020-1)/3148022Robert Price03/2020
247739153^6032+6032^39153148017Hans Havermann10/2020
247836798^10507+10507^36798147983Hans Havermann12/2020
2479(26*10^147973-23)/3147974Robert Price12/2019
24802^491521-1865323147963Enzo Doria02/2016
2481(2^491476+7)/71147948Lelio R Paula10/2015
24822*10^147928+47147929Robert Price12/2021
24832^491391-7807147924Lelio R Paula01/2013
248439736^5279+5279^39736147920Hans Havermann11/2020
24852^491370-113297147918Enzo Doria07/2014
2486(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
248744368^2155+2155^44368147899Hans Havermann12/2020
2488(17*10^147890+79)/3147891Robert Price04/2019
248994*10^147871-3147873Robert Price05/2020
249010^147843+620967147844Patrick De Geest05/2021
249110^147843-50000000001147843Robert Price12/2020
249210^147843-182891147843Patrick De Geest05/2021
249335805^13346+13346^35805147709Hans Havermann11/2020
24942^490672+255255147707Paul Bourdelais10/2021
24952^490660-17147704Lelio R Paula12/2017
2496(229*10^147699-1)/3147701Robert Price07/2020
249740656^4289+4289^40656147678Hans Havermann11/2020
24982^490550+1179439147671Enzo Doria06/2016
2499(23*10^147649-59)/9147650Robert Price05/2018
25002^490303+2793653147596Enzo Doria03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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