PRP Records

Probable Primes Top 10000

(302409 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(3*23^110967+41)/22151106Anonymous12/2023
42526*10^151063-77151064Robert Price09/2021
42532^501781-1850503151052Enzo Doria08/2015
4254(2^82589933-1)%(10^151020)151020Anonymous05/2025
4255(5*10^151007+37)/3151008Robert Price03/2018
42563^316494+5*2^316494151007Jon Grantham08/2023
42572^501627-991151005Yves Minet02/2014
42582^501577-115333150990Enzo Doria07/2015
425925239^34298-34298^25239150983Frank Doornink12/2023
4260(19*10^150977-7)/3150978Robert Price12/2023
42618*10^150975+3150976Robert Price08/2015
42622^501512-113669150971Enzo Doria09/2014
426334180^26101+26101^34180150962Norman Luhn04/2024
4264U(1083477)/2166953150949Serge Batalov07/2024
4265(83*10^150908+493)/9150909Robert Price12/2021
426636267^14482+14482^36267150901Norman Luhn04/2024
42672*10^150818+83150819Robert Price12/2021
426848753^1240+1240^48753150814Norman Luhn04/2024
4269(12^139739+1)/13150803Paul Bourdelais09/2011
4270(31^101111-1)/30150792Alexander Zhirkov11/2010
42712^500899-500899150786Henri Lifchitz04/2005
42722^500832+1876801150766Enzo Doria07/2016
4273(23*10^150763-59)/9150764Robert Price05/2018
427446002^1891+1891^46002150735Norman Luhn04/2024
427532001^33458-33458^32001150734Frank Doornink01/2024
42762^500699+1884953150726Enzo Doria02/2017
4277(13*10^150675-37)/3150676Robert Price01/2019
4278(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
427935365^18204+18204^35365150661Norman Luhn05/2024
42812^500337-71101150617Enzo Doria04/2016
4280(74*10^150616+133)/9150617Robert Price06/2019
4282(2*10^150612-17)/3150612Serge Batalov11/2022
42834*10^150577+91150578Robert Price08/2018
42845649^40132+40132^5649150575Norbert Schneider04/2024
42852^500160+80071150564Enzo Doria06/2016
4286(2^500120+5)/9150551Lelio R Paula12/2017
4288(43*10^150515-421)/9150516Robert Price01/2019
42874695^40994+40994^4695150516Norbert Schneider11/2023
42892^499999+15981150515Norman Luhn08/2023
4290(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
4291(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
429226614^34005-34005^26614150476Frank Doornink03/2024
42932^499861-29503150474Enzo Doria08/2015
4294Phi(64793,-7#)150462Henri Lifchitz12/2025
42952^499653-113533150411Enzo Doria08/2014
4296(14*10^150391-191)/3150392Robert Price10/2020
429729033^33696+33696^29033150382Norbert Schneider10/2023
42982^499534-221150375Yves Minet06/2012
429930110^33567+33567^30110150337Norbert Schneider10/2023
430026212^34023-34023^26212150331Frank Doornink03/2024
4301(28*10^150294+41)/3150295Robert Price07/2021
43022^499225+49727150282Enzo Doria09/2016
4303(695*10^150274+7)/9150276Robert Price12/2021
43042^499054-29261150231Enzo Doria07/2015
430518580^35187+35187^18580150215Norbert Schneider10/2023
4306(844*10^150196-7)/9150198Robert Price05/2021
43072^498907-933075150186Paul Bourdelais06/2021
4308(2^498898-7)/9150183Lelio R Paula10/2015
43093*10^150182+17150183Robert Price07/2018
43105*10^150175+63150176Robert Price09/2020
431129273^33618-33618^29273150154Frank Doornink06/2024
431232363^33292+33292^32363150149Norbert Schneider07/2022
431332^99753-99753^32150144Henri Lifchitz08/2024
4314(77*10^150128+67)/9150129Robert Price12/2021
4315(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
43162^498623+1866983150101Enzo Doria03/2016
431733194^33194-213^213150073Serge Batalov04/2024
431827868^33759-33759^27868150063Frank Doornink06/2024
4319(25*10^150050-403)/9150051Robert Price12/2020
4320numbpart(18140942830)150033Serge Batalov04/2017
432110^150029+4381150030Patrick De Geest05/2016
432210^150029-41150029Serge Batalov12/2014
432333185^33185+618^618150028Serge Batalov04/2024
43249*34^97952+529150013Eric Chen08/2023
432510^150000+1158603150001Patrick De Geest09/2018
432610^150000-245703150000Patrick De Geest09/2018
4327(38*10^149999+691)/9150000Robert Price10/2018
43282043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
4329(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
43302^498238-53149985Lelio R Paula12/2017
433145728^1905+1905^45728149984Hans Havermann10/2020
4332(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
43335*10^149907+23149908Robert Price03/2019
433432^99585-829149891Eric Chen11/2023
433539347^6442+6442^39347149874Hans Havermann09/2020
43362^497850+81049149868Enzo Doria07/2016
4337V(1075416)149830Serge Batalov07/2024
433837228^10575+10575^37228149816Hans Havermann10/2020
4339(5*2^497673+1)/2743149812Lelio R Paula10/2015
4340(5*2^497671+1)/373703149810Lelio R Paula10/2015
4341(2*10^149803-143)/3149803Robert Price03/2018
434233845^26604+26604^33845149763Hans Havermann09/2020
43432^497434-2784191149743Enzo Doria10/2015
4344(865*10^149737-1)/9149739Robert Price04/2020
434510^149695-7000001149695Robert Price06/2021
434638237^8214+8214^38237149681Hans Havermann09/2020
4347Phi(745791,2)/1491583149664Anonymous03/2025
4348(497167*2^497167-1)/70975149664Anonymous04/2025
4349(23*10^149655+19)/3149656Robert Price07/2019
43502^497068-113579149633Enzo Doria08/2014
43512^497037+73727149624Enzo Doria04/2016
435211*10^149618+3149620Robert Price07/2021
435334942^19067+19067^34942149562Hans Havermann09/2020
435433696^27449+27449^33696149561Hans Havermann09/2020
43552^496773+77747149544Enzo Doria05/2016
435629937^33400-33400^29937149506Frank Doornink06/2024
4357(7*10^149483-493)/9149483Robert Price04/2021
4358(206*10^149459+7)/3149461Robert Price07/2020
435934589^20940+20940^34589149459Hans Havermann09/2020
43602^496477-113485149455Enzo Doria08/2014
4361(496423*2^496423-1)/223573149439Anonymous04/2025
43623*2^496411-5149436Jon Grantham07/2023
4363((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
43642^496270-49451149393Enzo Doria10/2015
43652^496238-1865081149383Enzo Doria01/2016
436633831^26030+26030^33831149380Hans Havermann09/2020
436734131^23780+23780^34131149365Hans Havermann09/2020
4368(5*10^149335-53)/3149336Robert Price09/2020
436926043^33818-33818^26043149330Frank Doornink03/2024
43702^495968-1853699149302Enzo Doria09/2015
43712^495935-4117149292Yves Minet02/2018
43725*2^495930+3149291Jon Grantham07/2023
437335816^14709+14709^35816149267Hans Havermann09/2020
4374(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
437510^149240-40000001149240Robert Price07/2022
437610^149240-10809149240Alfred Reich08/2024
43772^495712-396765149225Enzo Doria07/2013
4378(21*2^495676-1)/4835149211Lelio R Paula10/2015
43792^495420+1880701149137Enzo Doria10/2016
438025646^33823-33823^25646149127Frank Doornink02/2024
43812^495337-1847293149112Enzo Doria07/2015
4382(2^495193-7)/5149068Lelio R Paula10/2015
43832^495163+111546435149059Paul Bourdelais10/2021
438433282^30097+30097^33282149055Hans Havermann09/2020
438537384^9705+9705^37384149050Hans Havermann09/2020
438634808^19143+19143^34808149049Hans Havermann09/2020
4387413^56963-412^56963149013Jean-Louis Charton08/2012
438830657^33212-33212^30657149007Frank Doornink06/2024
438947^89113-46^89113149006Robert Price10/2012
4390V(891190)148997Serge Batalov07/2024
43912^494916+87855148985Lelio R Paula01/2016
43926*10^148982+73148983Robert Price04/2019
43933^312155-4148936Anonymous02/2023
439410^148934+1530019148935Patrick De Geest02/2021
439510^148934-1000000001148934Robert Price11/2020
439610^148934-512057148934Patrick De Geest02/2021
439739000^6571+6571^39000148888Hans Havermann10/2020
43982^494586-2791991148886Enzo Doria02/2016
4399Phi(117375,3^5)148862Henri Lifchitz12/2025
44008*10^148860-3148861Ray Chandler04/2011
440138262^7769+7769^38262148854Hans Havermann10/2020
440210^148816-500001148816Robert Price03/2022
4403(53*10^148811-287)/9148812Robert Price02/2022
44042^494333-286183148810Enzo Doria06/2015
44052^494144-264119148753Enzo Doria05/2014
44066*10^148734+47148735Robert Price06/2022
440728724^33353-33353^28724148696Frank Doornink06/2024
440836502^11823+11823^36502148663Hans Havermann11/2020
4409(5*2^493838-1)/3721148658Lelio R Paula10/2015
441064239^206+206^64239148641Hans Havermann10/2020
4411(23*2^493761-1)/555148636Lelio R Paula10/2015
4412(23*10^148627-137)/3148628Robert Price08/2021
4413(151*10^148601-1)/3148603Robert Price03/2020
44142^493636+82081148600Enzo Doria09/2016
4415((((((((((((((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
441627134^33509-33509^27134148563Frank Doornink01/2024
4417177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
4418(2*10^148460-23)/3148460Robert Price04/2018
4419(28*10^148445+101)/3148446Robert Price09/2020
44202^493065+225148428Henri Lifchitz11/2024
442136203^12556+12556^36203148391Hans Havermann10/2020
442233912^23749+23749^33912148387Hans Havermann10/2020
4423(8*10^148328+1)/9148328Serge Batalov05/2010
442434294^21117+21117^34294148309Hans Havermann10/2020
4425(71*10^148306-539)/9148307Robert Price07/2019
442630814^33039-33039^30814148304Frank Doornink06/2024
442738042^7875+7875^38042148222Hans Havermann10/2020
44285^211959-12874148153Enzo Doria05/2014
442934142^21831+21831^34142148145Hans Havermann10/2020
443010^148112+34059148113Patrick De Geest05/2021
443110^148112-70000001148112Robert Price03/2021
443210^148112-106593148112Patrick De Geest05/2021
443336303^12016+12016^36303148108Hans Havermann10/2020
4434(77*10^148089-149)/9148090Robert Price03/2022
4435(16*10^148071+41)/3148072Robert Price03/2019
4436187^65175-2148068Lelio R Paula11/2017
44372^491851+1871453148062Enzo Doria05/2016
4438(68*10^148060-257)/9148061Robert Price07/2019
4439Phi(162903,-5#)148043Henri Lifchitz12/2025
4440(151*10^148020-1)/3148022Robert Price03/2020
444139153^6032+6032^39153148017Hans Havermann10/2020
444236798^10507+10507^36798147983Hans Havermann12/2020
4443(26*10^147973-23)/3147974Robert Price12/2019
4444Phi(65997,11#)147973Henri Lifchitz12/2025
44452^491521-1865323147963Enzo Doria02/2016
4446(2^491476+7)/71147948Lelio R Paula10/2015
44472*10^147928+47147929Robert Price12/2021
44482^491391-7807147924Lelio R Paula01/2013
44492^491384+236221147922Enzo Doria05/2025
445039736^5279+5279^39736147920Hans Havermann11/2020
44512^491370-113297147918Enzo Doria07/2014
4452(3^707753)%F(707753)147912Henri Lifchitz06/2025
4453(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
445444368^2155+2155^44368147899Hans Havermann12/2020
4455(17*10^147890+79)/3147891Robert Price04/2019
445694*10^147871-3147873Robert Price05/2020
445710^147843+620967147844Patrick De Geest05/2021
445810^147843-50000000001147843Robert Price12/2020
445910^147843-182891147843Patrick De Geest05/2021
446035805^13346+13346^35805147709Hans Havermann11/2020
44612^490672+255255147707Paul Bourdelais10/2021
44622^490660-17147704Lelio R Paula12/2017
4463(229*10^147699-1)/3147701Robert Price07/2020
446440656^4289+4289^40656147678Hans Havermann11/2020
4465(85*10^147676-31)/9147677Rytis Slatkevicius12/2024
44662^490550+1179439147671Enzo Doria06/2016
446727249^33292-33292^27249147662Frank Doornink06/2024
4468(23*10^147649-59)/9147650Robert Price05/2018
44692^490303+2793653147596Enzo Doria03/2016
44702^490266+255255147585Paul Bourdelais10/2021
4471199^64181-2147543Lelio R Paula11/2017
447232849^30958+30958^32849147518Hans Havermann11/2020
44732^489871-286987147466Enzo Doria07/2015
44742^489864-351899147464Enzo Doria07/2015
4475175^65724-2147422Lelio R Paula11/2017
44762^489712+1874851147419Enzo Doria06/2016
447734473^18830+18830^34473147367Hans Havermann11/2020
447863^81896-2147359Lelio R Paula10/2017
447934580^18237+18237^34580147344Hans Havermann11/2020
4480(11*10^147313-107)/3147314Robert Price09/2018
4481(397*10^147310+17)/9147312Robert Price03/2022
44822^489305-59815147296Enzo Doria10/2015
4483(2^489280-7)/6381147285Lelio R Paula09/2015
44842*10^147264-61147265Robert Price10/2021
44852*10^147260+29147261Robert Price02/2021
448633556^24457+24457^33556147258Hans Havermann11/2020
448712^136450-11147255Riley Fisher12/2024
44882^489125+80357147242Enzo Doria06/2016
448910^147240-40000001147240Robert Price07/2022
449010^147240-371331147240Alfred Reich09/2024
449110^147240-464727147240Alfred Reich09/2024
449232835^30452+30452^32835147220Hans Havermann12/2020
4493(19*10^147213-97)/3147214Robert Price10/2021
449427123^33190-33190^27123147143Frank Doornink01/2024
4495(148*10^147139-1)/3147141Robert Price03/2020
449634338^19255+19255^34338147123Hans Havermann11/2020
44972^488648-112799147098Enzo Doria07/2014
44982^488627-350317147092Enzo Doria06/2015
449933432^25075+25075^33432147076Hans Havermann12/2020
4500(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 01 2026 12:51 (Time in France)

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