PRP Records

Probable Primes Top 10000

(303369 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 ?
450125239^34298-34298^25239150983Frank Doornink12/2023
4502(19*10^150977-7)/3150978Robert Price12/2023
45038*10^150975+3150976Robert Price08/2015
45042^501512-113669150971Enzo Doria09/2014
450534180^26101+26101^34180150962Norman Luhn04/2024
4506U(1083477)/2166953150949Serge Batalov07/2024
4507(83*10^150908+493)/9150909Robert Price12/2021
450836267^14482+14482^36267150901Norman Luhn04/2024
45092*10^150818+83150819Robert Price12/2021
451048753^1240+1240^48753150814Norman Luhn04/2024
4511(12^139739+1)/13150803Paul Bourdelais09/2011
4512(31^101111-1)/30150792Alexander Zhirkov11/2010
45132^500899-500899150786Henri Lifchitz04/2005
45142^500832+1876801150766Enzo Doria07/2016
4515(23*10^150763-59)/9150764Robert Price05/2018
451646002^1891+1891^46002150735Norman Luhn04/2024
451732001^33458-33458^32001150734Frank Doornink01/2024
45182^500699+1884953150726Enzo Doria02/2017
4519(13*10^150675-37)/3150676Robert Price01/2019
4520(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
452135365^18204+18204^35365150661Norman Luhn05/2024
45232^500337-71101150617Enzo Doria04/2016
4522(74*10^150616+133)/9150617Robert Price06/2019
4524(2*10^150612-17)/3150612Serge Batalov11/2022
45254*10^150577+91150578Robert Price08/2018
45265649^40132+40132^5649150575Norbert Schneider04/2024
45272^500160+80071150564Enzo Doria06/2016
4528(2^500120+5)/9150551Lelio R Paula12/2017
4530(43*10^150515-421)/9150516Robert Price01/2019
45294695^40994+40994^4695150516Norbert Schneider11/2023
45312^499999+15981150515Norman Luhn08/2023
4532(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
4533(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
453426614^34005-34005^26614150476Frank Doornink03/2024
45352^499861-29503150474Enzo Doria08/2015
4536Phi(64793,-7#)150462Henri Lifchitz12/2025
45372^499653-113533150411Enzo Doria08/2014
4538(14*10^150391-191)/3150392Robert Price10/2020
453929033^33696+33696^29033150382Norbert Schneider10/2023
45402^499534-221150375Yves Minet06/2012
454130110^33567+33567^30110150337Norbert Schneider10/2023
454226212^34023-34023^26212150331Frank Doornink03/2024
4543(28*10^150294+41)/3150295Robert Price07/2021
45442^499225+49727150282Enzo Doria09/2016
4545(695*10^150274+7)/9150276Robert Price12/2021
45462^499054-29261150231Enzo Doria07/2015
454718580^35187+35187^18580150215Norbert Schneider10/2023
4548(844*10^150196-7)/9150198Robert Price05/2021
45492^498907-933075150186Paul Bourdelais06/2021
4550(2^498898-7)/9150183Lelio R Paula10/2015
45513*10^150182+17150183Robert Price07/2018
45525*10^150175+63150176Robert Price09/2020
455329273^33618-33618^29273150154Frank Doornink06/2024
455432363^33292+33292^32363150149Norbert Schneider07/2022
455532^99753-99753^32150144Henri Lifchitz08/2024
4556(77*10^150128+67)/9150129Robert Price12/2021
4557(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
45582^498623+1866983150101Enzo Doria03/2016
455933194^33194-213^213150073Serge Batalov04/2024
456027868^33759-33759^27868150063Frank Doornink06/2024
4561(25*10^150050-403)/9150051Robert Price12/2020
4562numbpart(18140942830)150033Serge Batalov04/2017
456310^150029+4381150030Patrick De Geest05/2016
456410^150029-41150029Serge Batalov12/2014
456533185^33185+618^618150028Serge Batalov04/2024
45669*34^97952+529150013Eric Chen08/2023
456710^150000+1158603150001Patrick De Geest09/2018
456810^150000-245703150000Patrick De Geest09/2018
4569(38*10^149999+691)/9150000Robert Price10/2018
45702043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
4571(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
45722^498238-53149985Lelio R Paula12/2017
457345728^1905+1905^45728149984Hans Havermann10/2020
4574(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
45755*10^149907+23149908Robert Price03/2019
457632^99585-829149891Eric Chen11/2023
457739347^6442+6442^39347149874Hans Havermann09/2020
45782^497850+81049149868Enzo Doria07/2016
4579V(1075416)149830Serge Batalov07/2024
458037228^10575+10575^37228149816Hans Havermann10/2020
4581(5*2^497673+1)/2743149812Lelio R Paula10/2015
4582(5*2^497671+1)/373703149810Lelio R Paula10/2015
4583(2*10^149803-143)/3149803Robert Price03/2018
458433845^26604+26604^33845149763Hans Havermann09/2020
45852^497434-2784191149743Enzo Doria10/2015
4586(865*10^149737-1)/9149739Robert Price04/2020
458710^149695-7000001149695Robert Price06/2021
458838237^8214+8214^38237149681Hans Havermann09/2020
4589Phi(745791,2)/1491583149664Anonymous03/2025
4590(497167*2^497167-1)/70975149664Anonymous04/2025
4591(23*10^149655+19)/3149656Robert Price07/2019
45922^497068-113579149633Enzo Doria08/2014
45932^497037+73727149624Enzo Doria04/2016
459411*10^149618+3149620Robert Price07/2021
459534942^19067+19067^34942149562Hans Havermann09/2020
459633696^27449+27449^33696149561Hans Havermann09/2020
45972^496773+77747149544Enzo Doria05/2016
459829937^33400-33400^29937149506Frank Doornink06/2024
4599(7*10^149483-493)/9149483Robert Price04/2021
4600(206*10^149459+7)/3149461Robert Price07/2020
460134589^20940+20940^34589149459Hans Havermann09/2020
46022^496477-113485149455Enzo Doria08/2014
4603(496423*2^496423-1)/223573149439Anonymous04/2025
46043*2^496411-5149436Jon Grantham07/2023
4605((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
46062^496270-49451149393Enzo Doria10/2015
46072^496238-1865081149383Enzo Doria01/2016
460833831^26030+26030^33831149380Hans Havermann09/2020
460934131^23780+23780^34131149365Hans Havermann09/2020
4610(5*10^149335-53)/3149336Robert Price09/2020
461126043^33818-33818^26043149330Frank Doornink03/2024
46122^495968-1853699149302Enzo Doria09/2015
46132^495935-4117149292Yves Minet02/2018
46145*2^495930+3149291Jon Grantham07/2023
461535816^14709+14709^35816149267Hans Havermann09/2020
4616(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
46173^312800+6560149244Alfred Reich04/2026
461810^149240-40000001149240Robert Price07/2022
461910^149240-10809149240Alfred Reich08/2024
46202^495712-396765149225Enzo Doria07/2013
4621(21*2^495676-1)/4835149211Lelio R Paula10/2015
46222^495420+1880701149137Enzo Doria10/2016
462325646^33823-33823^25646149127Frank Doornink02/2024
46242^495337-1847293149112Enzo Doria07/2015
4625(2^495193-7)/5149068Lelio R Paula10/2015
46262^495163+111546435149059Paul Bourdelais10/2021
462733282^30097+30097^33282149055Hans Havermann09/2020
462837384^9705+9705^37384149050Hans Havermann09/2020
462934808^19143+19143^34808149049Hans Havermann09/2020
4630413^56963-412^56963149013Jean-Louis Charton08/2012
463130657^33212-33212^30657149007Frank Doornink06/2024
463247^89113-46^89113149006Robert Price10/2012
4633V(891190)148997Serge Batalov07/2024
46342^494916+87855148985Lelio R Paula01/2016
46356*10^148982+73148983Robert Price04/2019
46363^312155-4148936Anonymous02/2023
463710^148934+1530019148935Patrick De Geest02/2021
463810^148934-1000000001148934Robert Price11/2020
463910^148934-512057148934Patrick De Geest02/2021
464039000^6571+6571^39000148888Hans Havermann10/2020
46412^494586-2791991148886Enzo Doria02/2016
4642Phi(117375,3^5)148862Henri Lifchitz12/2025
46438*10^148860-3148861Ray Chandler04/2011
464438262^7769+7769^38262148854Hans Havermann10/2020
464510^148816-500001148816Robert Price03/2022
4646(53*10^148811-287)/9148812Robert Price02/2022
46472^494333-286183148810Enzo Doria06/2015
46482^494144-264119148753Enzo Doria05/2014
46496*10^148734+47148735Robert Price06/2022
465028724^33353-33353^28724148696Frank Doornink06/2024
465136502^11823+11823^36502148663Hans Havermann11/2020
4652(5*2^493838-1)/3721148658Lelio R Paula10/2015
465364239^206+206^64239148641Hans Havermann10/2020
4654(23*2^493761-1)/555148636Lelio R Paula10/2015
4655(23*10^148627-137)/3148628Robert Price08/2021
4656(151*10^148601-1)/3148603Robert Price03/2020
46572^493636+82081148600Enzo Doria09/2016
4658((((((((((((((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
465927134^33509-33509^27134148563Frank Doornink01/2024
4660177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
4661(2*10^148460-23)/3148460Robert Price04/2018
4662(28*10^148445+101)/3148446Robert Price09/2020
46632^493065+225148428Henri Lifchitz11/2024
466436203^12556+12556^36203148391Hans Havermann10/2020
466533912^23749+23749^33912148387Hans Havermann10/2020
4666(8*10^148328+1)/9148328Serge Batalov05/2010
466734294^21117+21117^34294148309Hans Havermann10/2020
4668(71*10^148306-539)/9148307Robert Price07/2019
466930814^33039-33039^30814148304Frank Doornink06/2024
467038042^7875+7875^38042148222Hans Havermann10/2020
46715^211959-12874148153Enzo Doria05/2014
467234142^21831+21831^34142148145Hans Havermann10/2020
4673(288*21^112023-13)/5148121Eric Chen03/2026
467410^148112+34059148113Patrick De Geest05/2021
467510^148112-70000001148112Robert Price03/2021
467610^148112-106593148112Patrick De Geest05/2021
467736303^12016+12016^36303148108Hans Havermann10/2020
4678(77*10^148089-149)/9148090Robert Price03/2022
4679(16*10^148071+41)/3148072Robert Price03/2019
4680187^65175-2148068Lelio R Paula11/2017
46812^491851+1871453148062Enzo Doria05/2016
4682(68*10^148060-257)/9148061Robert Price07/2019
4683Phi(162903,-5#)148043Henri Lifchitz12/2025
4684(151*10^148020-1)/3148022Robert Price03/2020
468539153^6032+6032^39153148017Hans Havermann10/2020
468636798^10507+10507^36798147983Hans Havermann12/2020
4687(26*10^147973-23)/3147974Robert Price12/2019
4688Phi(65997,11#)147973Henri Lifchitz12/2025
46892^491521-1865323147963Enzo Doria02/2016
4690(2^491476+7)/71147948Lelio R Paula10/2015
46912*10^147928+47147929Robert Price12/2021
46922^491391-7807147924Lelio R Paula01/2013
46932^491384+236221147922Enzo Doria05/2025
469439736^5279+5279^39736147920Hans Havermann11/2020
46952^491370-113297147918Enzo Doria07/2014
4696(3^707753)%F(707753)147912Henri Lifchitz06/2025
4697(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
469844368^2155+2155^44368147899Hans Havermann12/2020
4699(17*10^147890+79)/3147891Robert Price04/2019
470094*10^147871-3147873Robert Price05/2020
470110^147843+620967147844Patrick De Geest05/2021
470210^147843-50000000001147843Robert Price12/2020
470310^147843-182891147843Patrick De Geest05/2021
470435805^13346+13346^35805147709Hans Havermann11/2020
47052^490672+255255147707Paul Bourdelais10/2021
47062^490660-17147704Lelio R Paula12/2017
4707(229*10^147699-1)/3147701Robert Price07/2020
470840656^4289+4289^40656147678Hans Havermann11/2020
4709(85*10^147676-31)/9147677Rytis Slatkevicius12/2024
47102^490550+1179439147671Enzo Doria06/2016
471127249^33292-33292^27249147662Frank Doornink06/2024
4712(23*10^147649-59)/9147650Robert Price05/2018
47132^490368-498143147616Maxim Gerspach08/2026
47142^490303+2793653147596Enzo Doria03/2016
47152^490266+255255147585Paul Bourdelais10/2021
4716199^64181-2147543Lelio R Paula11/2017
471732849^30958+30958^32849147518Hans Havermann11/2020
47182^489871-286987147466Enzo Doria07/2015
47192^489864-351899147464Enzo Doria07/2015
4720175^65724-2147422Lelio R Paula11/2017
47212^489712+1874851147419Enzo Doria06/2016
472234473^18830+18830^34473147367Hans Havermann11/2020
472363^81896-2147359Lelio R Paula10/2017
472434580^18237+18237^34580147344Hans Havermann11/2020
4725(11*10^147313-107)/3147314Robert Price09/2018
4726(397*10^147310+17)/9147312Robert Price03/2022
47272^489305-59815147296Enzo Doria10/2015
4728(2^489280-7)/6381147285Lelio R Paula09/2015
47292*10^147264-61147265Robert Price10/2021
47302*10^147260+29147261Robert Price02/2021
473133556^24457+24457^33556147258Hans Havermann11/2020
473212^136450-11147255Riley Fisher12/2024
47332^489125+80357147242Enzo Doria06/2016
473410^147240-40000001147240Robert Price07/2022
473510^147240-371331147240Alfred Reich09/2024
473610^147240-464727147240Alfred Reich09/2024
473732835^30452+30452^32835147220Hans Havermann12/2020
4738(19*10^147213-97)/3147214Robert Price10/2021
473927123^33190-33190^27123147143Frank Doornink01/2024
4740(148*10^147139-1)/3147141Robert Price03/2020
474134338^19255+19255^34338147123Hans Havermann11/2020
47422^488648-112799147098Enzo Doria07/2014
47432^488627-350317147092Enzo Doria06/2015
474433432^25075+25075^33432147076Hans Havermann12/2020
4745(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
47462^488280-2165146987Yves Minet07/2014
47472^488278+45146987Lelio R Paula12/2017
4748(3^834646)/(2^834646)146974Henri Lifchitz06/2025
474932568^32568+32561^32561146973Henri Lifchitz08/2024
47502^487927-39146881Lelio R Paula12/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2026 14:00 (Time in France)

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