PRP Records

Probable Primes Top 10000

(302606 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 ?
42512^506451-22339152457Enzo Doria07/2013
425226463^34460-34460^26463152405Frank Doornink03/2024
425331898^33837-33837^31898152394Frank Doornink01/2024
42542^505995-113185152320Enzo Doria07/2014
4255(8*10^152260-17)/9152260Serge Batalov11/2022
4256(4*10^152253+149)/9152253Robert Price04/2018
425733530^33643-33643^33530152250Norbert Schneider04/2024
4258578^55117-577^55117152230Jean-Louis Charton08/2012
42592^505431-505431152150Henri Lifchitz04/2005
4260(203*10^152143+1)/3152145Robert Price03/2020
426131730^33787-33787^31730152092Frank Doornink01/2024
42622^505089+217787152047Enzo Doria01/2024
426333565^33594-33594^33565152043Norbert Schneider04/2024
42642^505053+73097152037Enzo Doria04/2016
426522*10^151998+3152000Robert Price01/2020
4266(238*10^151979-1)/3151981Robert Price04/2020
4267(2^504793-7)/46765151954Lelio R Paula12/2017
42683^318465+4151947Aurel Gibier09/2024
4269350377#+797581151937Nicolas PALAU08/2017
4270Phi(97785,1105)151925Henri Lifchitz12/2025
4271(79*10^151906-529)/9151907Robert Price01/2022
42722^504618-343991151906Enzo Doria07/2015
42732^504259+211193151798Enzo Doria08/2023
42742^504212-461939151783Enzo Doria07/2015
42757*10^151772-41151773Robert Price08/2021
4276(47^90749-4^90749)/43151740Robert Price12/2025
42772^504054-2231151736Yves Minet10/2011
427825237^34458-34458^25237151686Frank Doornink11/2023
4279(28*10^151682+191)/3151683Robert Price02/2020
42802^503817+23961151665Enzo Doria10/2023
42812^503475-933075151562Paul Bourdelais06/2021
42822^503371+26289151530Enzo Doria12/2023
42832^503361-39883151527Enzo Doria09/2015
42842^503225+382667151486Enzo Doria10/2016
4285(206*10^151483-11)/3151485Robert Price02/2022
4286(844*10^151396-7)/9151398Robert Price05/2021
4287(26*10^151391-503)/9151392Robert Price07/2018
42882^502769+1877567151349Enzo Doria08/2016
42892^502576-4019151291Yves Minet10/2011
42905*10^151257+41151258Robert Price03/2019
42912^502290-2792501151205Enzo Doria02/2016
429217015^35734+35734^17015151185Norbert Schneider12/2025
42932^502181+1868417151172Enzo Doria04/2016
42942^502055+22583151134Enzo Doria09/2023
4295(3*23^110967+41)/22151106Anonymous12/2023
42966*10^151063-77151064Robert Price09/2021
42972^501781-1850503151052Enzo Doria08/2015
4298(2^82589933-1)%(10^151020)151020Anonymous05/2025
4299(5*10^151007+37)/3151008Robert Price03/2018
43003^316494+5*2^316494151007Jon Grantham08/2023
43012^501627-991151005Yves Minet02/2014
43022^501577-115333150990Enzo Doria07/2015
430325239^34298-34298^25239150983Frank Doornink12/2023
4304(19*10^150977-7)/3150978Robert Price12/2023
43058*10^150975+3150976Robert Price08/2015
43062^501512-113669150971Enzo Doria09/2014
430734180^26101+26101^34180150962Norman Luhn04/2024
4308U(1083477)/2166953150949Serge Batalov07/2024
4309(83*10^150908+493)/9150909Robert Price12/2021
431036267^14482+14482^36267150901Norman Luhn04/2024
43112*10^150818+83150819Robert Price12/2021
431248753^1240+1240^48753150814Norman Luhn04/2024
4313(12^139739+1)/13150803Paul Bourdelais09/2011
4314(31^101111-1)/30150792Alexander Zhirkov11/2010
43152^500899-500899150786Henri Lifchitz04/2005
43162^500832+1876801150766Enzo Doria07/2016
4317(23*10^150763-59)/9150764Robert Price05/2018
431846002^1891+1891^46002150735Norman Luhn04/2024
431932001^33458-33458^32001150734Frank Doornink01/2024
43202^500699+1884953150726Enzo Doria02/2017
4321(13*10^150675-37)/3150676Robert Price01/2019
4322(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
432335365^18204+18204^35365150661Norman Luhn05/2024
43252^500337-71101150617Enzo Doria04/2016
4324(74*10^150616+133)/9150617Robert Price06/2019
4326(2*10^150612-17)/3150612Serge Batalov11/2022
43274*10^150577+91150578Robert Price08/2018
43285649^40132+40132^5649150575Norbert Schneider04/2024
43292^500160+80071150564Enzo Doria06/2016
4330(2^500120+5)/9150551Lelio R Paula12/2017
4332(43*10^150515-421)/9150516Robert Price01/2019
43314695^40994+40994^4695150516Norbert Schneider11/2023
43332^499999+15981150515Norman Luhn08/2023
4334(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
4335(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
433626614^34005-34005^26614150476Frank Doornink03/2024
43372^499861-29503150474Enzo Doria08/2015
4338Phi(64793,-7#)150462Henri Lifchitz12/2025
43392^499653-113533150411Enzo Doria08/2014
4340(14*10^150391-191)/3150392Robert Price10/2020
434129033^33696+33696^29033150382Norbert Schneider10/2023
43422^499534-221150375Yves Minet06/2012
434330110^33567+33567^30110150337Norbert Schneider10/2023
434426212^34023-34023^26212150331Frank Doornink03/2024
4345(28*10^150294+41)/3150295Robert Price07/2021
43462^499225+49727150282Enzo Doria09/2016
4347(695*10^150274+7)/9150276Robert Price12/2021
43482^499054-29261150231Enzo Doria07/2015
434918580^35187+35187^18580150215Norbert Schneider10/2023
4350(844*10^150196-7)/9150198Robert Price05/2021
43512^498907-933075150186Paul Bourdelais06/2021
4352(2^498898-7)/9150183Lelio R Paula10/2015
43533*10^150182+17150183Robert Price07/2018
43545*10^150175+63150176Robert Price09/2020
435529273^33618-33618^29273150154Frank Doornink06/2024
435632363^33292+33292^32363150149Norbert Schneider07/2022
435732^99753-99753^32150144Henri Lifchitz08/2024
4358(77*10^150128+67)/9150129Robert Price12/2021
4359(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
43602^498623+1866983150101Enzo Doria03/2016
436133194^33194-213^213150073Serge Batalov04/2024
436227868^33759-33759^27868150063Frank Doornink06/2024
4363(25*10^150050-403)/9150051Robert Price12/2020
4364numbpart(18140942830)150033Serge Batalov04/2017
436510^150029+4381150030Patrick De Geest05/2016
436610^150029-41150029Serge Batalov12/2014
436733185^33185+618^618150028Serge Batalov04/2024
43689*34^97952+529150013Eric Chen08/2023
436910^150000+1158603150001Patrick De Geest09/2018
437010^150000-245703150000Patrick De Geest09/2018
4371(38*10^149999+691)/9150000Robert Price10/2018
43722043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
4373(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
43742^498238-53149985Lelio R Paula12/2017
437545728^1905+1905^45728149984Hans Havermann10/2020
4376(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
43775*10^149907+23149908Robert Price03/2019
437832^99585-829149891Eric Chen11/2023
437939347^6442+6442^39347149874Hans Havermann09/2020
43802^497850+81049149868Enzo Doria07/2016
4381V(1075416)149830Serge Batalov07/2024
438237228^10575+10575^37228149816Hans Havermann10/2020
4383(5*2^497673+1)/2743149812Lelio R Paula10/2015
4384(5*2^497671+1)/373703149810Lelio R Paula10/2015
4385(2*10^149803-143)/3149803Robert Price03/2018
438633845^26604+26604^33845149763Hans Havermann09/2020
43872^497434-2784191149743Enzo Doria10/2015
4388(865*10^149737-1)/9149739Robert Price04/2020
438910^149695-7000001149695Robert Price06/2021
439038237^8214+8214^38237149681Hans Havermann09/2020
4391Phi(745791,2)/1491583149664Anonymous03/2025
4392(497167*2^497167-1)/70975149664Anonymous04/2025
4393(23*10^149655+19)/3149656Robert Price07/2019
43942^497068-113579149633Enzo Doria08/2014
43952^497037+73727149624Enzo Doria04/2016
439611*10^149618+3149620Robert Price07/2021
439734942^19067+19067^34942149562Hans Havermann09/2020
439833696^27449+27449^33696149561Hans Havermann09/2020
43992^496773+77747149544Enzo Doria05/2016
440029937^33400-33400^29937149506Frank Doornink06/2024
4401(7*10^149483-493)/9149483Robert Price04/2021
4402(206*10^149459+7)/3149461Robert Price07/2020
440334589^20940+20940^34589149459Hans Havermann09/2020
44042^496477-113485149455Enzo Doria08/2014
4405(496423*2^496423-1)/223573149439Anonymous04/2025
44063*2^496411-5149436Jon Grantham07/2023
4407((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
44082^496270-49451149393Enzo Doria10/2015
44092^496238-1865081149383Enzo Doria01/2016
441033831^26030+26030^33831149380Hans Havermann09/2020
441134131^23780+23780^34131149365Hans Havermann09/2020
4412(5*10^149335-53)/3149336Robert Price09/2020
441326043^33818-33818^26043149330Frank Doornink03/2024
44142^495968-1853699149302Enzo Doria09/2015
44152^495935-4117149292Yves Minet02/2018
44165*2^495930+3149291Jon Grantham07/2023
441735816^14709+14709^35816149267Hans Havermann09/2020
4418(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
441910^149240-40000001149240Robert Price07/2022
442010^149240-10809149240Alfred Reich08/2024
44212^495712-396765149225Enzo Doria07/2013
4422(21*2^495676-1)/4835149211Lelio R Paula10/2015
44232^495420+1880701149137Enzo Doria10/2016
442425646^33823-33823^25646149127Frank Doornink02/2024
44252^495337-1847293149112Enzo Doria07/2015
4426(2^495193-7)/5149068Lelio R Paula10/2015
44272^495163+111546435149059Paul Bourdelais10/2021
442833282^30097+30097^33282149055Hans Havermann09/2020
442937384^9705+9705^37384149050Hans Havermann09/2020
443034808^19143+19143^34808149049Hans Havermann09/2020
4431413^56963-412^56963149013Jean-Louis Charton08/2012
443230657^33212-33212^30657149007Frank Doornink06/2024
443347^89113-46^89113149006Robert Price10/2012
4434V(891190)148997Serge Batalov07/2024
44352^494916+87855148985Lelio R Paula01/2016
44366*10^148982+73148983Robert Price04/2019
44373^312155-4148936Anonymous02/2023
443810^148934+1530019148935Patrick De Geest02/2021
443910^148934-1000000001148934Robert Price11/2020
444010^148934-512057148934Patrick De Geest02/2021
444139000^6571+6571^39000148888Hans Havermann10/2020
44422^494586-2791991148886Enzo Doria02/2016
4443Phi(117375,3^5)148862Henri Lifchitz12/2025
44448*10^148860-3148861Ray Chandler04/2011
444538262^7769+7769^38262148854Hans Havermann10/2020
444610^148816-500001148816Robert Price03/2022
4447(53*10^148811-287)/9148812Robert Price02/2022
44482^494333-286183148810Enzo Doria06/2015
44492^494144-264119148753Enzo Doria05/2014
44506*10^148734+47148735Robert Price06/2022
445128724^33353-33353^28724148696Frank Doornink06/2024
445236502^11823+11823^36502148663Hans Havermann11/2020
4453(5*2^493838-1)/3721148658Lelio R Paula10/2015
445464239^206+206^64239148641Hans Havermann10/2020
4455(23*2^493761-1)/555148636Lelio R Paula10/2015
4456(23*10^148627-137)/3148628Robert Price08/2021
4457(151*10^148601-1)/3148603Robert Price03/2020
44582^493636+82081148600Enzo Doria09/2016
4459((((((((((((((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
446027134^33509-33509^27134148563Frank Doornink01/2024
4461177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
4462(2*10^148460-23)/3148460Robert Price04/2018
4463(28*10^148445+101)/3148446Robert Price09/2020
44642^493065+225148428Henri Lifchitz11/2024
446536203^12556+12556^36203148391Hans Havermann10/2020
446633912^23749+23749^33912148387Hans Havermann10/2020
4467(8*10^148328+1)/9148328Serge Batalov05/2010
446834294^21117+21117^34294148309Hans Havermann10/2020
4469(71*10^148306-539)/9148307Robert Price07/2019
447030814^33039-33039^30814148304Frank Doornink06/2024
447138042^7875+7875^38042148222Hans Havermann10/2020
44725^211959-12874148153Enzo Doria05/2014
447334142^21831+21831^34142148145Hans Havermann10/2020
447410^148112+34059148113Patrick De Geest05/2021
447510^148112-70000001148112Robert Price03/2021
447610^148112-106593148112Patrick De Geest05/2021
447736303^12016+12016^36303148108Hans Havermann10/2020
4478(77*10^148089-149)/9148090Robert Price03/2022
4479(16*10^148071+41)/3148072Robert Price03/2019
4480187^65175-2148068Lelio R Paula11/2017
44812^491851+1871453148062Enzo Doria05/2016
4482(68*10^148060-257)/9148061Robert Price07/2019
4483Phi(162903,-5#)148043Henri Lifchitz12/2025
4484(151*10^148020-1)/3148022Robert Price03/2020
448539153^6032+6032^39153148017Hans Havermann10/2020
448636798^10507+10507^36798147983Hans Havermann12/2020
4487(26*10^147973-23)/3147974Robert Price12/2019
4488Phi(65997,11#)147973Henri Lifchitz12/2025
44892^491521-1865323147963Enzo Doria02/2016
4490(2^491476+7)/71147948Lelio R Paula10/2015
44912*10^147928+47147929Robert Price12/2021
44922^491391-7807147924Lelio R Paula01/2013
44932^491384+236221147922Enzo Doria05/2025
449439736^5279+5279^39736147920Hans Havermann11/2020
44952^491370-113297147918Enzo Doria07/2014
4496(3^707753)%F(707753)147912Henri Lifchitz06/2025
4497(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
449844368^2155+2155^44368147899Hans Havermann12/2020
4499(17*10^147890+79)/3147891Robert Price04/2019
450094*10^147871-3147873Robert Price05/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 08 2026 09:37 (Time in France)

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