PRP Records

Probable Primes Top 10000

(302900 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 ?
4251(209246*34^99997-81)/11153148Eric Chen08/2023
4252(7*10^153116-1)/3153117Robert Price08/2022
4253(112*10^153025-1)/3153027Serge Batalov12/2014
425431912^33975-33975^31912153022Frank Doornink01/2024
4255(19*10^153010+131)/3153011Robert Price06/2020
42562^508174-1855151152976Enzo Doria09/2015
4257181^67757-2152974Lelio R Paula12/2017
42582^508160-1864829152972Enzo Doria01/2016
425910^152960+412563152961Patrick De Geest05/2021
426010^152960-50000000001152960Robert Price12/2020
426110^152960-423749152960Patrick De Geest05/2021
4262(71*10^152933-143)/9152934Robert Price10/2021
426332109^33932-33932^32109152919Frank Doornink02/2024
42642^507857-1848199152881Enzo Doria07/2015
42652^507638-115361152815Enzo Doria07/2015
42662^507551-114025152789Enzo Doria11/2014
4267(6^196337+1)/7152780Paul Bourdelais02/2010
4268(22*10^152670-13)/9152671Robert Price06/2018
426986*17^124075+13152670Eric Chen01/2026
42702^507085+28517152648Enzo Doria01/2024
42712^506917+28847152598Enzo Doria02/2024
42722^506451-22339152457Enzo Doria07/2013
427326463^34460-34460^26463152405Frank Doornink03/2024
427431898^33837-33837^31898152394Frank Doornink01/2024
42752^505995-113185152320Enzo Doria07/2014
4276(8*10^152260-17)/9152260Serge Batalov11/2022
4277(4*10^152253+149)/9152253Robert Price04/2018
427833530^33643-33643^33530152250Norbert Schneider04/2024
4279578^55117-577^55117152230Jean-Louis Charton08/2012
42802^505431-505431152150Henri Lifchitz04/2005
4281(203*10^152143+1)/3152145Robert Price03/2020
428231730^33787-33787^31730152092Frank Doornink01/2024
42832^505089+217787152047Enzo Doria01/2024
428433565^33594-33594^33565152043Norbert Schneider04/2024
42852^505053+73097152037Enzo Doria04/2016
428622*10^151998+3152000Robert Price01/2020
4287(238*10^151979-1)/3151981Robert Price04/2020
4288(2^504793-7)/46765151954Lelio R Paula12/2017
42893^318465+4151947Aurel Gibier09/2024
4290350377#+797581151937Nicolas PALAU08/2017
4291Phi(97785,1105)151925Henri Lifchitz12/2025
4292(79*10^151906-529)/9151907Robert Price01/2022
42932^504618-343991151906Enzo Doria07/2015
42942^504259+211193151798Enzo Doria08/2023
42952^504212-461939151783Enzo Doria07/2015
42967*10^151772-41151773Robert Price08/2021
4297(47^90749-4^90749)/43151740Robert Price12/2025
42982^504054-2231151736Yves Minet10/2011
429925237^34458-34458^25237151686Frank Doornink11/2023
4300(28*10^151682+191)/3151683Robert Price02/2020
43012^503817+23961151665Enzo Doria10/2023
43022^503475-933075151562Paul Bourdelais06/2021
43032^503371+26289151530Enzo Doria12/2023
43042^503361-39883151527Enzo Doria09/2015
43052^503225+382667151486Enzo Doria10/2016
4306(206*10^151483-11)/3151485Robert Price02/2022
4307(844*10^151396-7)/9151398Robert Price05/2021
4308(26*10^151391-503)/9151392Robert Price07/2018
43092^502769+1877567151349Enzo Doria08/2016
43102^502576-4019151291Yves Minet10/2011
43115*10^151257+41151258Robert Price03/2019
43122^502290-2792501151205Enzo Doria02/2016
431317015^35734+35734^17015151185Norbert Schneider12/2025
43142^502181+1868417151172Enzo Doria04/2016
43152^502055+22583151134Enzo Doria09/2023
4316(3*23^110967+41)/22151106Anonymous12/2023
43176*10^151063-77151064Robert Price09/2021
43182^501781-1850503151052Enzo Doria08/2015
4319(2^82589933-1)%(10^151020)151020Anonymous05/2025
4320(5*10^151007+37)/3151008Robert Price03/2018
43213^316494+5*2^316494151007Jon Grantham08/2023
43222^501627-991151005Yves Minet02/2014
43232^501577-115333150990Enzo Doria07/2015
432425239^34298-34298^25239150983Frank Doornink12/2023
4325(19*10^150977-7)/3150978Robert Price12/2023
43268*10^150975+3150976Robert Price08/2015
43272^501512-113669150971Enzo Doria09/2014
432834180^26101+26101^34180150962Norman Luhn04/2024
4329U(1083477)/2166953150949Serge Batalov07/2024
4330(83*10^150908+493)/9150909Robert Price12/2021
433136267^14482+14482^36267150901Norman Luhn04/2024
43322*10^150818+83150819Robert Price12/2021
433348753^1240+1240^48753150814Norman Luhn04/2024
4334(12^139739+1)/13150803Paul Bourdelais09/2011
4335(31^101111-1)/30150792Alexander Zhirkov11/2010
43362^500899-500899150786Henri Lifchitz04/2005
43372^500832+1876801150766Enzo Doria07/2016
4338(23*10^150763-59)/9150764Robert Price05/2018
433946002^1891+1891^46002150735Norman Luhn04/2024
434032001^33458-33458^32001150734Frank Doornink01/2024
43412^500699+1884953150726Enzo Doria02/2017
4342(13*10^150675-37)/3150676Robert Price01/2019
4343(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
434435365^18204+18204^35365150661Norman Luhn05/2024
43462^500337-71101150617Enzo Doria04/2016
4345(74*10^150616+133)/9150617Robert Price06/2019
4347(2*10^150612-17)/3150612Serge Batalov11/2022
43484*10^150577+91150578Robert Price08/2018
43495649^40132+40132^5649150575Norbert Schneider04/2024
43502^500160+80071150564Enzo Doria06/2016
4351(2^500120+5)/9150551Lelio R Paula12/2017
4353(43*10^150515-421)/9150516Robert Price01/2019
43524695^40994+40994^4695150516Norbert Schneider11/2023
43542^499999+15981150515Norman Luhn08/2023
4355(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
4356(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
435726614^34005-34005^26614150476Frank Doornink03/2024
43582^499861-29503150474Enzo Doria08/2015
4359Phi(64793,-7#)150462Henri Lifchitz12/2025
43602^499653-113533150411Enzo Doria08/2014
4361(14*10^150391-191)/3150392Robert Price10/2020
436229033^33696+33696^29033150382Norbert Schneider10/2023
43632^499534-221150375Yves Minet06/2012
436430110^33567+33567^30110150337Norbert Schneider10/2023
436526212^34023-34023^26212150331Frank Doornink03/2024
4366(28*10^150294+41)/3150295Robert Price07/2021
43672^499225+49727150282Enzo Doria09/2016
4368(695*10^150274+7)/9150276Robert Price12/2021
43692^499054-29261150231Enzo Doria07/2015
437018580^35187+35187^18580150215Norbert Schneider10/2023
4371(844*10^150196-7)/9150198Robert Price05/2021
43722^498907-933075150186Paul Bourdelais06/2021
4373(2^498898-7)/9150183Lelio R Paula10/2015
43743*10^150182+17150183Robert Price07/2018
43755*10^150175+63150176Robert Price09/2020
437629273^33618-33618^29273150154Frank Doornink06/2024
437732363^33292+33292^32363150149Norbert Schneider07/2022
437832^99753-99753^32150144Henri Lifchitz08/2024
4379(77*10^150128+67)/9150129Robert Price12/2021
4380(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
43812^498623+1866983150101Enzo Doria03/2016
438233194^33194-213^213150073Serge Batalov04/2024
438327868^33759-33759^27868150063Frank Doornink06/2024
4384(25*10^150050-403)/9150051Robert Price12/2020
4385numbpart(18140942830)150033Serge Batalov04/2017
438610^150029+4381150030Patrick De Geest05/2016
438710^150029-41150029Serge Batalov12/2014
438833185^33185+618^618150028Serge Batalov04/2024
43899*34^97952+529150013Eric Chen08/2023
439010^150000+1158603150001Patrick De Geest09/2018
439110^150000-245703150000Patrick De Geest09/2018
4392(38*10^149999+691)/9150000Robert Price10/2018
43932043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
4394(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
43952^498238-53149985Lelio R Paula12/2017
439645728^1905+1905^45728149984Hans Havermann10/2020
4397(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
43985*10^149907+23149908Robert Price03/2019
439932^99585-829149891Eric Chen11/2023
440039347^6442+6442^39347149874Hans Havermann09/2020
44012^497850+81049149868Enzo Doria07/2016
4402V(1075416)149830Serge Batalov07/2024
440337228^10575+10575^37228149816Hans Havermann10/2020
4404(5*2^497673+1)/2743149812Lelio R Paula10/2015
4405(5*2^497671+1)/373703149810Lelio R Paula10/2015
4406(2*10^149803-143)/3149803Robert Price03/2018
440733845^26604+26604^33845149763Hans Havermann09/2020
44082^497434-2784191149743Enzo Doria10/2015
4409(865*10^149737-1)/9149739Robert Price04/2020
441010^149695-7000001149695Robert Price06/2021
441138237^8214+8214^38237149681Hans Havermann09/2020
4412Phi(745791,2)/1491583149664Anonymous03/2025
4413(497167*2^497167-1)/70975149664Anonymous04/2025
4414(23*10^149655+19)/3149656Robert Price07/2019
44152^497068-113579149633Enzo Doria08/2014
44162^497037+73727149624Enzo Doria04/2016
441711*10^149618+3149620Robert Price07/2021
441834942^19067+19067^34942149562Hans Havermann09/2020
441933696^27449+27449^33696149561Hans Havermann09/2020
44202^496773+77747149544Enzo Doria05/2016
442129937^33400-33400^29937149506Frank Doornink06/2024
4422(7*10^149483-493)/9149483Robert Price04/2021
4423(206*10^149459+7)/3149461Robert Price07/2020
442434589^20940+20940^34589149459Hans Havermann09/2020
44252^496477-113485149455Enzo Doria08/2014
4426(496423*2^496423-1)/223573149439Anonymous04/2025
44273*2^496411-5149436Jon Grantham07/2023
4428((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
44292^496270-49451149393Enzo Doria10/2015
44302^496238-1865081149383Enzo Doria01/2016
443133831^26030+26030^33831149380Hans Havermann09/2020
443234131^23780+23780^34131149365Hans Havermann09/2020
4433(5*10^149335-53)/3149336Robert Price09/2020
443426043^33818-33818^26043149330Frank Doornink03/2024
44352^495968-1853699149302Enzo Doria09/2015
44362^495935-4117149292Yves Minet02/2018
44375*2^495930+3149291Jon Grantham07/2023
443835816^14709+14709^35816149267Hans Havermann09/2020
4439(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
44403^312800+6560149244Alfred Reich04/2026
444110^149240-40000001149240Robert Price07/2022
444210^149240-10809149240Alfred Reich08/2024
44432^495712-396765149225Enzo Doria07/2013
4444(21*2^495676-1)/4835149211Lelio R Paula10/2015
44452^495420+1880701149137Enzo Doria10/2016
444625646^33823-33823^25646149127Frank Doornink02/2024
44472^495337-1847293149112Enzo Doria07/2015
4448(2^495193-7)/5149068Lelio R Paula10/2015
44492^495163+111546435149059Paul Bourdelais10/2021
445033282^30097+30097^33282149055Hans Havermann09/2020
445137384^9705+9705^37384149050Hans Havermann09/2020
445234808^19143+19143^34808149049Hans Havermann09/2020
4453413^56963-412^56963149013Jean-Louis Charton08/2012
445430657^33212-33212^30657149007Frank Doornink06/2024
445547^89113-46^89113149006Robert Price10/2012
4456V(891190)148997Serge Batalov07/2024
44572^494916+87855148985Lelio R Paula01/2016
44586*10^148982+73148983Robert Price04/2019
44593^312155-4148936Anonymous02/2023
446010^148934+1530019148935Patrick De Geest02/2021
446110^148934-1000000001148934Robert Price11/2020
446210^148934-512057148934Patrick De Geest02/2021
446339000^6571+6571^39000148888Hans Havermann10/2020
44642^494586-2791991148886Enzo Doria02/2016
4465Phi(117375,3^5)148862Henri Lifchitz12/2025
44668*10^148860-3148861Ray Chandler04/2011
446738262^7769+7769^38262148854Hans Havermann10/2020
446810^148816-500001148816Robert Price03/2022
4469(53*10^148811-287)/9148812Robert Price02/2022
44702^494333-286183148810Enzo Doria06/2015
44712^494144-264119148753Enzo Doria05/2014
44726*10^148734+47148735Robert Price06/2022
447328724^33353-33353^28724148696Frank Doornink06/2024
447436502^11823+11823^36502148663Hans Havermann11/2020
4475(5*2^493838-1)/3721148658Lelio R Paula10/2015
447664239^206+206^64239148641Hans Havermann10/2020
4477(23*2^493761-1)/555148636Lelio R Paula10/2015
4478(23*10^148627-137)/3148628Robert Price08/2021
4479(151*10^148601-1)/3148603Robert Price03/2020
44802^493636+82081148600Enzo Doria09/2016
4481((((((((((((((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
448227134^33509-33509^27134148563Frank Doornink01/2024
4483177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
4484(2*10^148460-23)/3148460Robert Price04/2018
4485(28*10^148445+101)/3148446Robert Price09/2020
44862^493065+225148428Henri Lifchitz11/2024
448736203^12556+12556^36203148391Hans Havermann10/2020
448833912^23749+23749^33912148387Hans Havermann10/2020
4489(8*10^148328+1)/9148328Serge Batalov05/2010
449034294^21117+21117^34294148309Hans Havermann10/2020
4491(71*10^148306-539)/9148307Robert Price07/2019
449230814^33039-33039^30814148304Frank Doornink06/2024
449338042^7875+7875^38042148222Hans Havermann10/2020
44945^211959-12874148153Enzo Doria05/2014
449534142^21831+21831^34142148145Hans Havermann10/2020
4496(288*21^112023-13)/5148121Eric Chen03/2026
449710^148112+34059148113Patrick De Geest05/2021
449810^148112-70000001148112Robert Price03/2021
449910^148112-106593148112Patrick De Geest05/2021
450036303^12016+12016^36303148108Hans Havermann10/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 03 2026 16:20 (Time in France)

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