PRP Records

Probable Primes Top 10000

(301352 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 ?
37512^506917+28847152598Enzo Doria02/2024
37522^506451-22339152457Enzo Doria07/2013
375326463^34460-34460^26463152405Frank Doornink03/2024
375431898^33837-33837^31898152394Frank Doornink01/2024
37552^505995-113185152320Enzo Doria07/2014
3756(8*10^152260-17)/9152260Serge Batalov11/2022
3757(4*10^152253+149)/9152253Robert Price04/2018
375833530^33643-33643^33530152250Norbert Schneider04/2024
3759578^55117-577^55117152230Jean-Louis Charton08/2012
37602^505431-505431152150Henri Lifchitz04/2005
3761(203*10^152143+1)/3152145Robert Price03/2020
376231730^33787-33787^31730152092Frank Doornink01/2024
37632^505089+217787152047Enzo Doria01/2024
376433565^33594-33594^33565152043Norbert Schneider04/2024
37652^505053+73097152037Enzo Doria04/2016
376622*10^151998+3152000Robert Price01/2020
3767(238*10^151979-1)/3151981Robert Price04/2020
3768(2^504793-7)/46765151954Lelio R Paula12/2017
37693^318465+4151947Aurel Gibier09/2024
3770350377#+797581151937Nicolas PALAU08/2017
3771(79*10^151906-529)/9151907Robert Price01/2022
37722^504618-343991151906Enzo Doria07/2015
37732^504259+211193151798Enzo Doria08/2023
37742^504212-461939151783Enzo Doria07/2015
37757*10^151772-41151773Robert Price08/2021
37762^504054-2231151736Yves Minet10/2011
377725237^34458-34458^25237151686Frank Doornink11/2023
3778(28*10^151682+191)/3151683Robert Price02/2020
37792^503817+23961151665Enzo Doria10/2023
37802^503475-933075151562Paul Bourdelais06/2021
37812^503371+26289151530Enzo Doria12/2023
37822^503361-39883151527Enzo Doria09/2015
37832^503225+382667151486Enzo Doria10/2016
3784(206*10^151483-11)/3151485Robert Price02/2022
3785(844*10^151396-7)/9151398Robert Price05/2021
3786(26*10^151391-503)/9151392Robert Price07/2018
37872^502769+1877567151349Enzo Doria08/2016
37882^502576-4019151291Yves Minet10/2011
37895*10^151257+41151258Robert Price03/2019
37902^502290-2792501151205Enzo Doria02/2016
37912^502181+1868417151172Enzo Doria04/2016
37922^502055+22583151134Enzo Doria09/2023
3793(3*23^110967+41)/22151106Anonymous12/2023
37946*10^151063-77151064Robert Price09/2021
37952^501781-1850503151052Enzo Doria08/2015
3796(5*10^151007+37)/3151008Robert Price03/2018
37973^316494+5*2^316494151007Jon Grantham08/2023
37982^501627-991151005Yves Minet02/2014
37992^501577-115333150990Enzo Doria07/2015
380025239^34298-34298^25239150983Frank Doornink12/2023
3801(19*10^150977-7)/3150978Robert Price12/2023
38028*10^150975+3150976Robert Price08/2015
38032^501512-113669150971Enzo Doria09/2014
380434180^26101+26101^34180150962Norman Luhn04/2024
3805U(1083477)/2166953150949Serge Batalov07/2024
3806(83*10^150908+493)/9150909Robert Price12/2021
380736267^14482+14482^36267150901Norman Luhn04/2024
38082*10^150818+83150819Robert Price12/2021
380948753^1240+1240^48753150814Norman Luhn04/2024
3810(12^139739+1)/13150803Paul Bourdelais09/2011
3811(31^101111-1)/30150792Alexander Zhirkov11/2010
38122^500899-500899150786Henri Lifchitz04/2005
38132^500832+1876801150766Enzo Doria07/2016
3814(23*10^150763-59)/9150764Robert Price05/2018
381546002^1891+1891^46002150735Norman Luhn04/2024
381632001^33458-33458^32001150734Frank Doornink01/2024
38172^500699+1884953150726Enzo Doria02/2017
3818(13*10^150675-37)/3150676Robert Price01/2019
3819(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
382035365^18204+18204^35365150661Norman Luhn05/2024
38222^500337-71101150617Enzo Doria04/2016
3821(74*10^150616+133)/9150617Robert Price06/2019
3823(2*10^150612-17)/3150612Serge Batalov11/2022
38244*10^150577+91150578Robert Price08/2018
38255649^40132+40132^5649150575Norbert Schneider04/2024
38262^500160+80071150564Enzo Doria06/2016
3827(2^500120+5)/9150551Lelio R Paula12/2017
3829(43*10^150515-421)/9150516Robert Price01/2019
38284695^40994+40994^4695150516Norbert Schneider11/2023
38302^499999+15981150515Norman Luhn08/2023
3831(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
3832(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
383326614^34005-34005^26614150476Frank Doornink03/2024
38342^499861-29503150474Enzo Doria08/2015
38352^499653-113533150411Enzo Doria08/2014
3836(14*10^150391-191)/3150392Robert Price10/2020
383729033^33696+33696^29033150382Norbert Schneider10/2023
38382^499534-221150375Yves Minet06/2012
383930110^33567+33567^30110150337Norbert Schneider10/2023
384026212^34023-34023^26212150331Frank Doornink03/2024
3841(28*10^150294+41)/3150295Robert Price07/2021
38422^499225+49727150282Enzo Doria09/2016
3843(695*10^150274+7)/9150276Robert Price12/2021
38442^499054-29261150231Enzo Doria07/2015
384518580^35187+35187^18580150215Norbert Schneider10/2023
3846(844*10^150196-7)/9150198Robert Price05/2021
38472^498907-933075150186Paul Bourdelais06/2021
3848(2^498898-7)/9150183Lelio R Paula10/2015
38493*10^150182+17150183Robert Price07/2018
38505*10^150175+63150176Robert Price09/2020
385129273^33618-33618^29273150154Frank Doornink06/2024
385232363^33292+33292^32363150149Norbert Schneider07/2022
385332^99753-99753^32150144Henri Lifchitz08/2024
3854(77*10^150128+67)/9150129Robert Price12/2021
3855(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
38562^498623+1866983150101Enzo Doria03/2016
385733194^33194-213^213150073Serge Batalov04/2024
385827868^33759-33759^27868150063Frank Doornink06/2024
3859(25*10^150050-403)/9150051Robert Price12/2020
3860numbpart(18140942830)150033Serge Batalov04/2017
386110^150029+4381150030Patrick De Geest05/2016
386210^150029-41150029Serge Batalov12/2014
386333185^33185+618^618150028Serge Batalov04/2024
38649*34^97952+529150013Eric Chen08/2023
386510^150000+1158603150001Patrick De Geest09/2018
386610^150000-245703150000Patrick De Geest09/2018
3867(38*10^149999+691)/9150000Robert Price10/2018
38682043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
3869(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
38702^498238-53149985Lelio R Paula12/2017
387145728^1905+1905^45728149984Hans Havermann10/2020
3872(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
38735*10^149907+23149908Robert Price03/2019
387432^99585-829149891Eric Chen11/2023
387539347^6442+6442^39347149874Hans Havermann09/2020
38762^497850+81049149868Enzo Doria07/2016
3877V(1075416)149830Serge Batalov07/2024
387837228^10575+10575^37228149816Hans Havermann10/2020
3879(5*2^497673+1)/2743149812Lelio R Paula10/2015
3880(5*2^497671+1)/373703149810Lelio R Paula10/2015
3881(2*10^149803-143)/3149803Robert Price03/2018
388233845^26604+26604^33845149763Hans Havermann09/2020
38832^497434-2784191149743Enzo Doria10/2015
3884(865*10^149737-1)/9149739Robert Price04/2020
388510^149695-7000001149695Robert Price06/2021
388638237^8214+8214^38237149681Hans Havermann09/2020
3887Phi(745791,2)/1491583149664Anonymous03/2025
3888(497167*2^497167-1)/70975149664Anonymous04/2025
3889(23*10^149655+19)/3149656Robert Price07/2019
38902^497068-113579149633Enzo Doria08/2014
38912^497037+73727149624Enzo Doria04/2016
389211*10^149618+3149620Robert Price07/2021
389334942^19067+19067^34942149562Hans Havermann09/2020
389433696^27449+27449^33696149561Hans Havermann09/2020
38952^496773+77747149544Enzo Doria05/2016
389629937^33400-33400^29937149506Frank Doornink06/2024
3897(7*10^149483-493)/9149483Robert Price04/2021
3898(206*10^149459+7)/3149461Robert Price07/2020
389934589^20940+20940^34589149459Hans Havermann09/2020
39002^496477-113485149455Enzo Doria08/2014
3901(496423*2^496423-1)/223573149439Anonymous04/2025
39023*2^496411-5149436Jon Grantham07/2023
3903((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
39042^496270-49451149393Enzo Doria10/2015
39052^496238-1865081149383Enzo Doria01/2016
390633831^26030+26030^33831149380Hans Havermann09/2020
390734131^23780+23780^34131149365Hans Havermann09/2020
3908(5*10^149335-53)/3149336Robert Price09/2020
390926043^33818-33818^26043149330Frank Doornink03/2024
39102^495968-1853699149302Enzo Doria09/2015
39112^495935-4117149292Yves Minet02/2018
39125*2^495930+3149291Jon Grantham07/2023
391335816^14709+14709^35816149267Hans Havermann09/2020
3914(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
391510^149240-40000001149240Robert Price07/2022
391610^149240-10809149240Alfred Reich08/2024
39172^495712-396765149225Enzo Doria07/2013
3918(21*2^495676-1)/4835149211Lelio R Paula10/2015
39192^495420+1880701149137Enzo Doria10/2016
392025646^33823-33823^25646149127Frank Doornink02/2024
39212^495337-1847293149112Enzo Doria07/2015
3922(2^495193-7)/5149068Lelio R Paula10/2015
39232^495163+111546435149059Paul Bourdelais10/2021
392433282^30097+30097^33282149055Hans Havermann09/2020
392537384^9705+9705^37384149050Hans Havermann09/2020
392634808^19143+19143^34808149049Hans Havermann09/2020
3927413^56963-412^56963149013Jean-Louis Charton08/2012
392830657^33212-33212^30657149007Frank Doornink06/2024
392947^89113-46^89113149006Robert Price10/2012
3930V(891190)148997Serge Batalov07/2024
39312^494916+87855148985Lelio R Paula01/2016
39326*10^148982+73148983Robert Price04/2019
39333^312155-4148936Anonymous02/2023
393410^148934+1530019148935Patrick De Geest02/2021
393510^148934-1000000001148934Robert Price11/2020
393610^148934-512057148934Patrick De Geest02/2021
393739000^6571+6571^39000148888Hans Havermann10/2020
39382^494586-2791991148886Enzo Doria02/2016
39398*10^148860-3148861Ray Chandler04/2011
394038262^7769+7769^38262148854Hans Havermann10/2020
394110^148816-500001148816Robert Price03/2022
3942(53*10^148811-287)/9148812Robert Price02/2022
39432^494333-286183148810Enzo Doria06/2015
39442^494144-264119148753Enzo Doria05/2014
39456*10^148734+47148735Robert Price06/2022
394628724^33353-33353^28724148696Frank Doornink06/2024
394736502^11823+11823^36502148663Hans Havermann11/2020
3948(5*2^493838-1)/3721148658Lelio R Paula10/2015
394964239^206+206^64239148641Hans Havermann10/2020
3950(23*2^493761-1)/555148636Lelio R Paula10/2015
3951(23*10^148627-137)/3148628Robert Price08/2021
3952(151*10^148601-1)/3148603Robert Price03/2020
39532^493636+82081148600Enzo Doria09/2016
3954((((((((((((((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
395527134^33509-33509^27134148563Frank Doornink01/2024
3956177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
3957(2*10^148460-23)/3148460Robert Price04/2018
3958(28*10^148445+101)/3148446Robert Price09/2020
39592^493065+225148428Henri Lifchitz11/2024
396036203^12556+12556^36203148391Hans Havermann10/2020
396133912^23749+23749^33912148387Hans Havermann10/2020
3962(8*10^148328+1)/9148328Serge Batalov05/2010
396334294^21117+21117^34294148309Hans Havermann10/2020
3964(71*10^148306-539)/9148307Robert Price07/2019
396530814^33039-33039^30814148304Frank Doornink06/2024
396638042^7875+7875^38042148222Hans Havermann10/2020
39675^211959-12874148153Enzo Doria05/2014
396834142^21831+21831^34142148145Hans Havermann10/2020
396910^148112+34059148113Patrick De Geest05/2021
397010^148112-70000001148112Robert Price03/2021
397110^148112-106593148112Patrick De Geest05/2021
397236303^12016+12016^36303148108Hans Havermann10/2020
3973(77*10^148089-149)/9148090Robert Price03/2022
3974(16*10^148071+41)/3148072Robert Price03/2019
3975187^65175-2148068Lelio R Paula11/2017
39762^491851+1871453148062Enzo Doria05/2016
3977(68*10^148060-257)/9148061Robert Price07/2019
3978(151*10^148020-1)/3148022Robert Price03/2020
397939153^6032+6032^39153148017Hans Havermann10/2020
398036798^10507+10507^36798147983Hans Havermann12/2020
3981(26*10^147973-23)/3147974Robert Price12/2019
39822^491521-1865323147963Enzo Doria02/2016
3983(2^491476+7)/71147948Lelio R Paula10/2015
39842*10^147928+47147929Robert Price12/2021
39852^491391-7807147924Lelio R Paula01/2013
398639736^5279+5279^39736147920Hans Havermann11/2020
39872^491370-113297147918Enzo Doria07/2014
3988(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
398944368^2155+2155^44368147899Hans Havermann12/2020
3990(17*10^147890+79)/3147891Robert Price04/2019
399194*10^147871-3147873Robert Price05/2020
399210^147843+620967147844Patrick De Geest05/2021
399310^147843-50000000001147843Robert Price12/2020
399410^147843-182891147843Patrick De Geest05/2021
399535805^13346+13346^35805147709Hans Havermann11/2020
39962^490672+255255147707Paul Bourdelais10/2021
39972^490660-17147704Lelio R Paula12/2017
3998(229*10^147699-1)/3147701Robert Price07/2020
399940656^4289+4289^40656147678Hans Havermann11/2020
4000(85*10^147676-31)/9147677Rytis Slatkevicius12/2024


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2025 12:56 (Time in France)

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