PRP Records

Probable Primes Top 10000

(302294 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 ?
425148753^1240+1240^48753150814Norman Luhn04/2024
4252(12^139739+1)/13150803Paul Bourdelais09/2011
4253(31^101111-1)/30150792Alexander Zhirkov11/2010
42542^500899-500899150786Henri Lifchitz04/2005
42552^500832+1876801150766Enzo Doria07/2016
4256(23*10^150763-59)/9150764Robert Price05/2018
425746002^1891+1891^46002150735Norman Luhn04/2024
425832001^33458-33458^32001150734Frank Doornink01/2024
42592^500699+1884953150726Enzo Doria02/2017
4260(13*10^150675-37)/3150676Robert Price01/2019
4261(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
426235365^18204+18204^35365150661Norman Luhn05/2024
42642^500337-71101150617Enzo Doria04/2016
4263(74*10^150616+133)/9150617Robert Price06/2019
4265(2*10^150612-17)/3150612Serge Batalov11/2022
42664*10^150577+91150578Robert Price08/2018
42675649^40132+40132^5649150575Norbert Schneider04/2024
42682^500160+80071150564Enzo Doria06/2016
4269(2^500120+5)/9150551Lelio R Paula12/2017
4271(43*10^150515-421)/9150516Robert Price01/2019
42704695^40994+40994^4695150516Norbert Schneider11/2023
42722^499999+15981150515Norman Luhn08/2023
4273(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
4274(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
427526614^34005-34005^26614150476Frank Doornink03/2024
42762^499861-29503150474Enzo Doria08/2015
4277Phi(64793,-7#)150462Henri Lifchitz12/2025
42782^499653-113533150411Enzo Doria08/2014
4279(14*10^150391-191)/3150392Robert Price10/2020
428029033^33696+33696^29033150382Norbert Schneider10/2023
42812^499534-221150375Yves Minet06/2012
428230110^33567+33567^30110150337Norbert Schneider10/2023
428326212^34023-34023^26212150331Frank Doornink03/2024
4284(28*10^150294+41)/3150295Robert Price07/2021
42852^499225+49727150282Enzo Doria09/2016
4286(695*10^150274+7)/9150276Robert Price12/2021
42872^499054-29261150231Enzo Doria07/2015
428818580^35187+35187^18580150215Norbert Schneider10/2023
4289(844*10^150196-7)/9150198Robert Price05/2021
42902^498907-933075150186Paul Bourdelais06/2021
4291(2^498898-7)/9150183Lelio R Paula10/2015
42923*10^150182+17150183Robert Price07/2018
42935*10^150175+63150176Robert Price09/2020
429429273^33618-33618^29273150154Frank Doornink06/2024
429532363^33292+33292^32363150149Norbert Schneider07/2022
429632^99753-99753^32150144Henri Lifchitz08/2024
4297(77*10^150128+67)/9150129Robert Price12/2021
4298(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
42992^498623+1866983150101Enzo Doria03/2016
430033194^33194-213^213150073Serge Batalov04/2024
430127868^33759-33759^27868150063Frank Doornink06/2024
4302(25*10^150050-403)/9150051Robert Price12/2020
4303numbpart(18140942830)150033Serge Batalov04/2017
430410^150029+4381150030Patrick De Geest05/2016
430510^150029-41150029Serge Batalov12/2014
430633185^33185+618^618150028Serge Batalov04/2024
43079*34^97952+529150013Eric Chen08/2023
430810^150000+1158603150001Patrick De Geest09/2018
430910^150000-245703150000Patrick De Geest09/2018
4310(38*10^149999+691)/9150000Robert Price10/2018
43112043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
4312(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
43132^498238-53149985Lelio R Paula12/2017
431445728^1905+1905^45728149984Hans Havermann10/2020
4315(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
43165*10^149907+23149908Robert Price03/2019
431732^99585-829149891Eric Chen11/2023
431839347^6442+6442^39347149874Hans Havermann09/2020
43192^497850+81049149868Enzo Doria07/2016
4320V(1075416)149830Serge Batalov07/2024
432137228^10575+10575^37228149816Hans Havermann10/2020
4322(5*2^497673+1)/2743149812Lelio R Paula10/2015
4323(5*2^497671+1)/373703149810Lelio R Paula10/2015
4324(2*10^149803-143)/3149803Robert Price03/2018
432533845^26604+26604^33845149763Hans Havermann09/2020
43262^497434-2784191149743Enzo Doria10/2015
4327(865*10^149737-1)/9149739Robert Price04/2020
432810^149695-7000001149695Robert Price06/2021
432938237^8214+8214^38237149681Hans Havermann09/2020
4330Phi(745791,2)/1491583149664Anonymous03/2025
4331(497167*2^497167-1)/70975149664Anonymous04/2025
4332(23*10^149655+19)/3149656Robert Price07/2019
43332^497068-113579149633Enzo Doria08/2014
43342^497037+73727149624Enzo Doria04/2016
433511*10^149618+3149620Robert Price07/2021
433634942^19067+19067^34942149562Hans Havermann09/2020
433733696^27449+27449^33696149561Hans Havermann09/2020
43382^496773+77747149544Enzo Doria05/2016
433929937^33400-33400^29937149506Frank Doornink06/2024
4340(7*10^149483-493)/9149483Robert Price04/2021
4341(206*10^149459+7)/3149461Robert Price07/2020
434234589^20940+20940^34589149459Hans Havermann09/2020
43432^496477-113485149455Enzo Doria08/2014
4344(496423*2^496423-1)/223573149439Anonymous04/2025
43453*2^496411-5149436Jon Grantham07/2023
4346((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
43472^496270-49451149393Enzo Doria10/2015
43482^496238-1865081149383Enzo Doria01/2016
434933831^26030+26030^33831149380Hans Havermann09/2020
435034131^23780+23780^34131149365Hans Havermann09/2020
4351(5*10^149335-53)/3149336Robert Price09/2020
435226043^33818-33818^26043149330Frank Doornink03/2024
43532^495968-1853699149302Enzo Doria09/2015
43542^495935-4117149292Yves Minet02/2018
43555*2^495930+3149291Jon Grantham07/2023
435635816^14709+14709^35816149267Hans Havermann09/2020
4357(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
435810^149240-40000001149240Robert Price07/2022
435910^149240-10809149240Alfred Reich08/2024
43602^495712-396765149225Enzo Doria07/2013
4361(21*2^495676-1)/4835149211Lelio R Paula10/2015
43622^495420+1880701149137Enzo Doria10/2016
436325646^33823-33823^25646149127Frank Doornink02/2024
43642^495337-1847293149112Enzo Doria07/2015
4365(2^495193-7)/5149068Lelio R Paula10/2015
43662^495163+111546435149059Paul Bourdelais10/2021
436733282^30097+30097^33282149055Hans Havermann09/2020
436837384^9705+9705^37384149050Hans Havermann09/2020
436934808^19143+19143^34808149049Hans Havermann09/2020
4370413^56963-412^56963149013Jean-Louis Charton08/2012
437130657^33212-33212^30657149007Frank Doornink06/2024
437247^89113-46^89113149006Robert Price10/2012
4373V(891190)148997Serge Batalov07/2024
43742^494916+87855148985Lelio R Paula01/2016
43756*10^148982+73148983Robert Price04/2019
43763^312155-4148936Anonymous02/2023
437710^148934+1530019148935Patrick De Geest02/2021
437810^148934-1000000001148934Robert Price11/2020
437910^148934-512057148934Patrick De Geest02/2021
438039000^6571+6571^39000148888Hans Havermann10/2020
43812^494586-2791991148886Enzo Doria02/2016
4382Phi(117375,3^5)148862Henri Lifchitz12/2025
43838*10^148860-3148861Ray Chandler04/2011
438438262^7769+7769^38262148854Hans Havermann10/2020
438510^148816-500001148816Robert Price03/2022
4386(53*10^148811-287)/9148812Robert Price02/2022
43872^494333-286183148810Enzo Doria06/2015
43882^494144-264119148753Enzo Doria05/2014
43896*10^148734+47148735Robert Price06/2022
439028724^33353-33353^28724148696Frank Doornink06/2024
439136502^11823+11823^36502148663Hans Havermann11/2020
4392(5*2^493838-1)/3721148658Lelio R Paula10/2015
439364239^206+206^64239148641Hans Havermann10/2020
4394(23*2^493761-1)/555148636Lelio R Paula10/2015
4395(23*10^148627-137)/3148628Robert Price08/2021
4396(151*10^148601-1)/3148603Robert Price03/2020
43972^493636+82081148600Enzo Doria09/2016
4398((((((((((((((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
439927134^33509-33509^27134148563Frank Doornink01/2024
4400177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
4401(2*10^148460-23)/3148460Robert Price04/2018
4402(28*10^148445+101)/3148446Robert Price09/2020
44032^493065+225148428Henri Lifchitz11/2024
440436203^12556+12556^36203148391Hans Havermann10/2020
440533912^23749+23749^33912148387Hans Havermann10/2020
4406(8*10^148328+1)/9148328Serge Batalov05/2010
440734294^21117+21117^34294148309Hans Havermann10/2020
4408(71*10^148306-539)/9148307Robert Price07/2019
440930814^33039-33039^30814148304Frank Doornink06/2024
441038042^7875+7875^38042148222Hans Havermann10/2020
44115^211959-12874148153Enzo Doria05/2014
441234142^21831+21831^34142148145Hans Havermann10/2020
441310^148112+34059148113Patrick De Geest05/2021
441410^148112-70000001148112Robert Price03/2021
441510^148112-106593148112Patrick De Geest05/2021
441636303^12016+12016^36303148108Hans Havermann10/2020
4417(77*10^148089-149)/9148090Robert Price03/2022
4418(16*10^148071+41)/3148072Robert Price03/2019
4419187^65175-2148068Lelio R Paula11/2017
44202^491851+1871453148062Enzo Doria05/2016
4421(68*10^148060-257)/9148061Robert Price07/2019
4422Phi(162903,-5#)148043Henri Lifchitz12/2025
4423(151*10^148020-1)/3148022Robert Price03/2020
442439153^6032+6032^39153148017Hans Havermann10/2020
442536798^10507+10507^36798147983Hans Havermann12/2020
4426(26*10^147973-23)/3147974Robert Price12/2019
4427Phi(65997,11#)147973Henri Lifchitz12/2025
44282^491521-1865323147963Enzo Doria02/2016
4429(2^491476+7)/71147948Lelio R Paula10/2015
44302*10^147928+47147929Robert Price12/2021
44312^491391-7807147924Lelio R Paula01/2013
44322^491384+236221147922Enzo Doria05/2025
443339736^5279+5279^39736147920Hans Havermann11/2020
44342^491370-113297147918Enzo Doria07/2014
4435(3^707753)%F(707753)147912Henri Lifchitz06/2025
4436(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
443744368^2155+2155^44368147899Hans Havermann12/2020
4438(17*10^147890+79)/3147891Robert Price04/2019
443994*10^147871-3147873Robert Price05/2020
444010^147843+620967147844Patrick De Geest05/2021
444110^147843-50000000001147843Robert Price12/2020
444210^147843-182891147843Patrick De Geest05/2021
444335805^13346+13346^35805147709Hans Havermann11/2020
44442^490672+255255147707Paul Bourdelais10/2021
44452^490660-17147704Lelio R Paula12/2017
4446(229*10^147699-1)/3147701Robert Price07/2020
444740656^4289+4289^40656147678Hans Havermann11/2020
4448(85*10^147676-31)/9147677Rytis Slatkevicius12/2024
44492^490550+1179439147671Enzo Doria06/2016
445027249^33292-33292^27249147662Frank Doornink06/2024
4451(23*10^147649-59)/9147650Robert Price05/2018
44522^490303+2793653147596Enzo Doria03/2016
44532^490266+255255147585Paul Bourdelais10/2021
4454199^64181-2147543Lelio R Paula11/2017
445532849^30958+30958^32849147518Hans Havermann11/2020
44562^489871-286987147466Enzo Doria07/2015
44572^489864-351899147464Enzo Doria07/2015
4458175^65724-2147422Lelio R Paula11/2017
44592^489712+1874851147419Enzo Doria06/2016
446034473^18830+18830^34473147367Hans Havermann11/2020
446163^81896-2147359Lelio R Paula10/2017
446234580^18237+18237^34580147344Hans Havermann11/2020
4463(11*10^147313-107)/3147314Robert Price09/2018
4464(397*10^147310+17)/9147312Robert Price03/2022
44652^489305-59815147296Enzo Doria10/2015
4466(2^489280-7)/6381147285Lelio R Paula09/2015
44672*10^147264-61147265Robert Price10/2021
44682*10^147260+29147261Robert Price02/2021
446933556^24457+24457^33556147258Hans Havermann11/2020
447012^136450-11147255Riley Fisher12/2024
44712^489125+80357147242Enzo Doria06/2016
447210^147240-40000001147240Robert Price07/2022
447310^147240-371331147240Alfred Reich09/2024
447410^147240-464727147240Alfred Reich09/2024
447532835^30452+30452^32835147220Hans Havermann12/2020
4476(19*10^147213-97)/3147214Robert Price10/2021
447727123^33190-33190^27123147143Frank Doornink01/2024
4478(148*10^147139-1)/3147141Robert Price03/2020
447934338^19255+19255^34338147123Hans Havermann11/2020
44802^488648-112799147098Enzo Doria07/2014
44812^488627-350317147092Enzo Doria06/2015
448233432^25075+25075^33432147076Hans Havermann12/2020
4483(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
44842^488280-2165146987Yves Minet07/2014
44852^488278+45146987Lelio R Paula12/2017
4486(3^834646)/(2^834646)146974Henri Lifchitz06/2025
448732568^32568+32561^32561146973Henri Lifchitz08/2024
44882^487927-39146881Lelio R Paula12/2017
4489(7*10^146860-13)/3146861Robert Price07/2018
4490(26*10^146856-77)/3146857Robert Price11/2019
449132948^28611+28611^32948146834Hans Havermann11/2020
449242596^2799+2799^42596146829Hans Havermann12/2020
44932^487726-1863341146821Enzo Doria12/2015
449443838^2229+2229^43838146775Hans Havermann11/2020
449535005^15594+15594^35005146775Hans Havermann11/2020
4496(167*10^146764+7)/3146766Robert Price04/2021
449753^85114+85114146761Kellen Shenton05/2022
4498(59*10^146738+157)/9146739Robert Price12/2021
4499((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
450032963^28234+28234^32963146711Hans Havermann12/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 05 2026 14:32 (Time in France)

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