PRP Records

Probable Primes Top 10000

(295158 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 ?
32512^505089+217787152047Enzo Doria01/2024
325233565^33594-33594^33565152043Norbert Schneider04/2024
32532^505053+73097152037Enzo Doria04/2016
325422*10^151998+3152000Robert Price01/2020
3255(238*10^151979-1)/3151981Robert Price04/2020
3256(2^504793-7)/46765151954Lelio R Paula12/2017
3257350377#+797581151937Nicolas PALAU08/2017
3258(79*10^151906-529)/9151907Robert Price01/2022
32592^504618-343991151906Enzo Doria07/2015
32602^504259+211193151798Enzo Doria08/2023
32612^504212-461939151783Enzo Doria07/2015
32627*10^151772-41151773Robert Price08/2021
32632^504054-2231151736Yves Minet10/2011
326425237^34458-34458^25237151686Frank Doornink11/2023
3265(28*10^151682+191)/3151683Robert Price02/2020
32662^503817+23961151665Enzo Doria10/2023
32672^503475-933075151562Paul Bourdelais06/2021
32682^503371+26289151530Enzo Doria12/2023
32692^503361-39883151527Enzo Doria09/2015
32702^503225+382667151486Enzo Doria10/2016
3271(206*10^151483-11)/3151485Robert Price02/2022
3272(844*10^151396-7)/9151398Robert Price05/2021
3273(26*10^151391-503)/9151392Robert Price07/2018
32742^502769+1877567151349Enzo Doria08/2016
32752^502576-4019151291Yves Minet10/2011
32765*10^151257+41151258Robert Price03/2019
32772^502290-2792501151205Enzo Doria02/2016
32782^502181+1868417151172Enzo Doria04/2016
32792^502055+22583151134Enzo Doria09/2023
3280(3*23^110967+41)/22151106Anonymous12/2023
32816*10^151063-77151064Robert Price09/2021
32822^501781-1850503151052Enzo Doria08/2015
3283(5*10^151007+37)/3151008Robert Price03/2018
32843^316494+5*2^316494151007Jon Grantham08/2023
32852^501627-991151005Yves Minet02/2014
32862^501577-115333150990Enzo Doria07/2015
328725239^34298-34298^25239150983Frank Doornink12/2023
3288(19*10^150977-7)/3150978Robert Price12/2023
32898*10^150975+3150976Robert Price08/2015
32902^501512-113669150971Enzo Doria09/2014
329134180^26101+26101^34180150962Norman Luhn04/2024
3292(83*10^150908+493)/9150909Robert Price12/2021
329336267^14482+14482^36267150901Norman Luhn04/2024
32942*10^150818+83150819Robert Price12/2021
329548753^1240+1240^48753150814Norman Luhn04/2024
3296(12^139739+1)/13150803Paul Bourdelais09/2011
3297(31^101111-1)/30150792Alexander Zhirkov11/2010
32982^500899-500899150786Henri Lifchitz04/2005
32992^500832+1876801150766Enzo Doria07/2016
3300(23*10^150763-59)/9150764Robert Price05/2018
330146002^1891+1891^46002150735Norman Luhn04/2024
330232001^33458-33458^32001150734Frank Doornink01/2024
33032^500699+1884953150726Enzo Doria02/2017
3304(13*10^150675-37)/3150676Robert Price01/2019
3305(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
330635365^18204+18204^35365150661Norman Luhn05/2024
33082^500337-71101150617Enzo Doria04/2016
3307(74*10^150616+133)/9150617Robert Price06/2019
3309(2*10^150612-17)/3150612Serge Batalov11/2022
33104*10^150577+91150578Robert Price08/2018
33115649^40132+40132^5649150575Norbert Schneider04/2024
33122^500160+80071150564Enzo Doria06/2016
3313(2^500120+5)/9150551Lelio R Paula12/2017
3315(43*10^150515-421)/9150516Robert Price01/2019
33144695^40994+40994^4695150516Norbert Schneider11/2023
33162^499999+15981150515Norman Luhn08/2023
3317(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
3318(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
331926614^34005-34005^26614150476Frank Doornink03/2024
33202^499861-29503150474Enzo Doria08/2015
33212^499653-113533150411Enzo Doria08/2014
3322(14*10^150391-191)/3150392Robert Price10/2020
332329033^33696+33696^29033150382Norbert Schneider10/2023
33242^499534-221150375Yves Minet06/2012
332530110^33567+33567^30110150337Norbert Schneider10/2023
332626212^34023-34023^26212150331Frank Doornink03/2024
3327(28*10^150294+41)/3150295Robert Price07/2021
33282^499225+49727150282Enzo Doria09/2016
3329(695*10^150274+7)/9150276Robert Price12/2021
33302^499054-29261150231Enzo Doria07/2015
333118580^35187+35187^18580150215Norbert Schneider10/2023
3332(844*10^150196-7)/9150198Robert Price05/2021
33332^498907-933075150186Paul Bourdelais06/2021
3334(2^498898-7)/9150183Lelio R Paula10/2015
33353*10^150182+17150183Robert Price07/2018
33365*10^150175+63150176Robert Price09/2020
333732363^33292+33292^32363150149Norbert Schneider07/2022
3338(77*10^150128+67)/9150129Robert Price12/2021
3339(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
33402^498623+1866983150101Enzo Doria03/2016
334133194^33194-213^213150073Serge Batalov04/2024
3342(25*10^150050-403)/9150051Robert Price12/2020
3343numbpart(18140942830)150033Serge Batalov04/2017
334410^150029+4381150030Patrick De Geest05/2016
334510^150029-41150029Serge Batalov12/2014
334633185^33185+618^618150028Serge Batalov04/2024
33479*34^97952+529150013Eric Chen08/2023
334810^150000+1158603150001Patrick De Geest09/2018
334910^150000-245703150000Patrick De Geest09/2018
3350(38*10^149999+691)/9150000Robert Price10/2018
33512043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
3352(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
33532^498238-53149985Lelio R Paula12/2017
335445728^1905+1905^45728149984Hans Havermann10/2020
3355(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
33565*10^149907+23149908Robert Price03/2019
335732^99585-829149891Eric Chen11/2023
335839347^6442+6442^39347149874Hans Havermann09/2020
33592^497850+81049149868Enzo Doria07/2016
336037228^10575+10575^37228149816Hans Havermann10/2020
3361(5*2^497673+1)/2743149812Lelio R Paula10/2015
3362(5*2^497671+1)/373703149810Lelio R Paula10/2015
3363(2*10^149803-143)/3149803Robert Price03/2018
336433845^26604+26604^33845149763Hans Havermann09/2020
33652^497434-2784191149743Enzo Doria10/2015
3366(865*10^149737-1)/9149739Robert Price04/2020
336710^149695-7000001149695Robert Price06/2021
336838237^8214+8214^38237149681Hans Havermann09/2020
3369(23*10^149655+19)/3149656Robert Price07/2019
33702^497068-113579149633Enzo Doria08/2014
33712^497037+73727149624Enzo Doria04/2016
337211*10^149618+3149620Robert Price07/2021
337334942^19067+19067^34942149562Hans Havermann09/2020
337433696^27449+27449^33696149561Hans Havermann09/2020
33752^496773+77747149544Enzo Doria05/2016
3376(7*10^149483-493)/9149483Robert Price04/2021
3377(206*10^149459+7)/3149461Robert Price07/2020
337834589^20940+20940^34589149459Hans Havermann09/2020
33792^496477-113485149455Enzo Doria08/2014
33803*2^496411-5149436Jon Grantham07/2023
3381((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
33822^496270-49451149393Enzo Doria10/2015
33832^496238-1865081149383Enzo Doria01/2016
338433831^26030+26030^33831149380Hans Havermann09/2020
338534131^23780+23780^34131149365Hans Havermann09/2020
3386(5*10^149335-53)/3149336Robert Price09/2020
338726043^33818-33818^26043149330Frank Doornink03/2024
33882^495968-1853699149302Enzo Doria09/2015
33892^495935-4117149292Yves Minet02/2018
33905*2^495930+3149291Jon Grantham07/2023
339135816^14709+14709^35816149267Hans Havermann09/2020
3392(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
339310^149240-40000001149240Robert Price07/2022
33942^495712-396765149225Enzo Doria07/2013
3395(21*2^495676-1)/4835149211Lelio R Paula10/2015
33962^495420+1880701149137Enzo Doria10/2016
339725646^33823-33823^25646149127Frank Doornink02/2024
33982^495337-1847293149112Enzo Doria07/2015
3399(2^495193-7)/5149068Lelio R Paula10/2015
34002^495163+111546435149059Paul Bourdelais10/2021
340133282^30097+30097^33282149055Hans Havermann09/2020
340237384^9705+9705^37384149050Hans Havermann09/2020
340334808^19143+19143^34808149049Hans Havermann09/2020
3404413^56963-412^56963149013Jean-Louis Charton08/2012
340547^89113-46^89113149006Robert Price10/2012
34062^494916+87855148985Lelio R Paula01/2016
34076*10^148982+73148983Robert Price04/2019
34083^312155-4148936Anonymous02/2023
340910^148934+1530019148935Patrick De Geest02/2021
341010^148934-1000000001148934Robert Price11/2020
341110^148934-512057148934Patrick De Geest02/2021
341239000^6571+6571^39000148888Hans Havermann10/2020
34132^494586-2791991148886Enzo Doria02/2016
34148*10^148860-3148861Ray Chandler04/2011
341538262^7769+7769^38262148854Hans Havermann10/2020
341610^148816-500001148816Robert Price03/2022
3417(53*10^148811-287)/9148812Robert Price02/2022
34182^494333-286183148810Enzo Doria06/2015
34192^494144-264119148753Enzo Doria05/2014
34206*10^148734+47148735Robert Price06/2022
342136502^11823+11823^36502148663Hans Havermann11/2020
3422(5*2^493838-1)/3721148658Lelio R Paula10/2015
342364239^206+206^64239148641Hans Havermann10/2020
3424(23*2^493761-1)/555148636Lelio R Paula10/2015
3425(23*10^148627-137)/3148628Robert Price08/2021
3426(151*10^148601-1)/3148603Robert Price03/2020
34272^493636+82081148600Enzo Doria09/2016
3428((((((((((((((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
342927134^33509-33509^27134148563Frank Doornink01/2024
3430177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
3431(2*10^148460-23)/3148460Robert Price04/2018
3432(28*10^148445+101)/3148446Robert Price09/2020
343336203^12556+12556^36203148391Hans Havermann10/2020
343433912^23749+23749^33912148387Hans Havermann10/2020
3435(8*10^148328+1)/9148328Serge Batalov05/2010
343634294^21117+21117^34294148309Hans Havermann10/2020
3437(71*10^148306-539)/9148307Robert Price07/2019
343838042^7875+7875^38042148222Hans Havermann10/2020
34395^211959-12874148153Enzo Doria05/2014
344034142^21831+21831^34142148145Hans Havermann10/2020
344110^148112+34059148113Patrick De Geest05/2021
344210^148112-70000001148112Robert Price03/2021
344310^148112-106593148112Patrick De Geest05/2021
344436303^12016+12016^36303148108Hans Havermann10/2020
3445(77*10^148089-149)/9148090Robert Price03/2022
3446(16*10^148071+41)/3148072Robert Price03/2019
3447187^65175-2148068Lelio R Paula11/2017
34482^491851+1871453148062Enzo Doria05/2016
3449(68*10^148060-257)/9148061Robert Price07/2019
3450(151*10^148020-1)/3148022Robert Price03/2020
345139153^6032+6032^39153148017Hans Havermann10/2020
345236798^10507+10507^36798147983Hans Havermann12/2020
3453(26*10^147973-23)/3147974Robert Price12/2019
34542^491521-1865323147963Enzo Doria02/2016
3455(2^491476+7)/71147948Lelio R Paula10/2015
34562*10^147928+47147929Robert Price12/2021
34572^491391-7807147924Lelio R Paula01/2013
345839736^5279+5279^39736147920Hans Havermann11/2020
34592^491370-113297147918Enzo Doria07/2014
3460(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
346144368^2155+2155^44368147899Hans Havermann12/2020
3462(17*10^147890+79)/3147891Robert Price04/2019
346394*10^147871-3147873Robert Price05/2020
346410^147843+620967147844Patrick De Geest05/2021
346510^147843-50000000001147843Robert Price12/2020
346610^147843-182891147843Patrick De Geest05/2021
346735805^13346+13346^35805147709Hans Havermann11/2020
34682^490672+255255147707Paul Bourdelais10/2021
34692^490660-17147704Lelio R Paula12/2017
3470(229*10^147699-1)/3147701Robert Price07/2020
347140656^4289+4289^40656147678Hans Havermann11/2020
34722^490550+1179439147671Enzo Doria06/2016
3473(23*10^147649-59)/9147650Robert Price05/2018
34742^490303+2793653147596Enzo Doria03/2016
34752^490266+255255147585Paul Bourdelais10/2021
3476199^64181-2147543Lelio R Paula11/2017
347732849^30958+30958^32849147518Hans Havermann11/2020
34782^489871-286987147466Enzo Doria07/2015
34792^489864-351899147464Enzo Doria07/2015
3480175^65724-2147422Lelio R Paula11/2017
34812^489712+1874851147419Enzo Doria06/2016
348234473^18830+18830^34473147367Hans Havermann11/2020
348363^81896-2147359Lelio R Paula10/2017
348434580^18237+18237^34580147344Hans Havermann11/2020
3485(11*10^147313-107)/3147314Robert Price09/2018
3486(397*10^147310+17)/9147312Robert Price03/2022
34872^489305-59815147296Enzo Doria10/2015
3488(2^489280-7)/6381147285Lelio R Paula09/2015
34892*10^147264-61147265Robert Price10/2021
34902*10^147260+29147261Robert Price02/2021
349133556^24457+24457^33556147258Hans Havermann11/2020
34922^489125+80357147242Enzo Doria06/2016
349310^147240-40000001147240Robert Price07/2022
349432835^30452+30452^32835147220Hans Havermann12/2020
3495(19*10^147213-97)/3147214Robert Price10/2021
349627123^33190-33190^27123147143Frank Doornink01/2024
3497(148*10^147139-1)/3147141Robert Price03/2020
349834338^19255+19255^34338147123Hans Havermann11/2020
34992^488648-112799147098Enzo Doria07/2014
35002^488627-350317147092Enzo Doria06/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2024 13:30 (Time in France)

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