PRP Records

Probable Primes Top 10000

(303335 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 ?
4501(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
4502(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
450326614^34005-34005^26614150476Frank Doornink03/2024
45042^499861-29503150474Enzo Doria08/2015
4505Phi(64793,-7#)150462Henri Lifchitz12/2025
45062^499653-113533150411Enzo Doria08/2014
4507(14*10^150391-191)/3150392Robert Price10/2020
450829033^33696+33696^29033150382Norbert Schneider10/2023
45092^499534-221150375Yves Minet06/2012
451030110^33567+33567^30110150337Norbert Schneider10/2023
451126212^34023-34023^26212150331Frank Doornink03/2024
4512(28*10^150294+41)/3150295Robert Price07/2021
45132^499225+49727150282Enzo Doria09/2016
4514(695*10^150274+7)/9150276Robert Price12/2021
45152^499054-29261150231Enzo Doria07/2015
451618580^35187+35187^18580150215Norbert Schneider10/2023
4517(844*10^150196-7)/9150198Robert Price05/2021
45182^498907-933075150186Paul Bourdelais06/2021
4519(2^498898-7)/9150183Lelio R Paula10/2015
45203*10^150182+17150183Robert Price07/2018
45215*10^150175+63150176Robert Price09/2020
452229273^33618-33618^29273150154Frank Doornink06/2024
452332363^33292+33292^32363150149Norbert Schneider07/2022
452432^99753-99753^32150144Henri Lifchitz08/2024
4525(77*10^150128+67)/9150129Robert Price12/2021
4526(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
45272^498623+1866983150101Enzo Doria03/2016
452833194^33194-213^213150073Serge Batalov04/2024
452927868^33759-33759^27868150063Frank Doornink06/2024
4530(25*10^150050-403)/9150051Robert Price12/2020
4531numbpart(18140942830)150033Serge Batalov04/2017
453210^150029+4381150030Patrick De Geest05/2016
453310^150029-41150029Serge Batalov12/2014
453433185^33185+618^618150028Serge Batalov04/2024
45359*34^97952+529150013Eric Chen08/2023
453610^150000+1158603150001Patrick De Geest09/2018
453710^150000-245703150000Patrick De Geest09/2018
4538(38*10^149999+691)/9150000Robert Price10/2018
45392043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
4540(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
45412^498238-53149985Lelio R Paula12/2017
454245728^1905+1905^45728149984Hans Havermann10/2020
4543(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
45445*10^149907+23149908Robert Price03/2019
454532^99585-829149891Eric Chen11/2023
454639347^6442+6442^39347149874Hans Havermann09/2020
45472^497850+81049149868Enzo Doria07/2016
4548V(1075416)149830Serge Batalov07/2024
454937228^10575+10575^37228149816Hans Havermann10/2020
4550(5*2^497673+1)/2743149812Lelio R Paula10/2015
4551(5*2^497671+1)/373703149810Lelio R Paula10/2015
4552(2*10^149803-143)/3149803Robert Price03/2018
455333845^26604+26604^33845149763Hans Havermann09/2020
45542^497434-2784191149743Enzo Doria10/2015
4555(865*10^149737-1)/9149739Robert Price04/2020
455610^149695-7000001149695Robert Price06/2021
455738237^8214+8214^38237149681Hans Havermann09/2020
4558Phi(745791,2)/1491583149664Anonymous03/2025
4559(497167*2^497167-1)/70975149664Anonymous04/2025
4560(23*10^149655+19)/3149656Robert Price07/2019
45612^497068-113579149633Enzo Doria08/2014
45622^497037+73727149624Enzo Doria04/2016
456311*10^149618+3149620Robert Price07/2021
456434942^19067+19067^34942149562Hans Havermann09/2020
456533696^27449+27449^33696149561Hans Havermann09/2020
45662^496773+77747149544Enzo Doria05/2016
456729937^33400-33400^29937149506Frank Doornink06/2024
4568(7*10^149483-493)/9149483Robert Price04/2021
4569(206*10^149459+7)/3149461Robert Price07/2020
457034589^20940+20940^34589149459Hans Havermann09/2020
45712^496477-113485149455Enzo Doria08/2014
4572(496423*2^496423-1)/223573149439Anonymous04/2025
45733*2^496411-5149436Jon Grantham07/2023
4574((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
45752^496270-49451149393Enzo Doria10/2015
45762^496238-1865081149383Enzo Doria01/2016
457733831^26030+26030^33831149380Hans Havermann09/2020
457834131^23780+23780^34131149365Hans Havermann09/2020
4579(5*10^149335-53)/3149336Robert Price09/2020
458026043^33818-33818^26043149330Frank Doornink03/2024
45812^495968-1853699149302Enzo Doria09/2015
45822^495935-4117149292Yves Minet02/2018
45835*2^495930+3149291Jon Grantham07/2023
458435816^14709+14709^35816149267Hans Havermann09/2020
4585(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
45863^312800+6560149244Alfred Reich04/2026
458710^149240-40000001149240Robert Price07/2022
458810^149240-10809149240Alfred Reich08/2024
45892^495712-396765149225Enzo Doria07/2013
4590(21*2^495676-1)/4835149211Lelio R Paula10/2015
45912^495420+1880701149137Enzo Doria10/2016
459225646^33823-33823^25646149127Frank Doornink02/2024
45932^495337-1847293149112Enzo Doria07/2015
4594(2^495193-7)/5149068Lelio R Paula10/2015
45952^495163+111546435149059Paul Bourdelais10/2021
459633282^30097+30097^33282149055Hans Havermann09/2020
459737384^9705+9705^37384149050Hans Havermann09/2020
459834808^19143+19143^34808149049Hans Havermann09/2020
4599413^56963-412^56963149013Jean-Louis Charton08/2012
460030657^33212-33212^30657149007Frank Doornink06/2024
460147^89113-46^89113149006Robert Price10/2012
4602V(891190)148997Serge Batalov07/2024
46032^494916+87855148985Lelio R Paula01/2016
46046*10^148982+73148983Robert Price04/2019
46053^312155-4148936Anonymous02/2023
460610^148934+1530019148935Patrick De Geest02/2021
460710^148934-1000000001148934Robert Price11/2020
460810^148934-512057148934Patrick De Geest02/2021
460939000^6571+6571^39000148888Hans Havermann10/2020
46102^494586-2791991148886Enzo Doria02/2016
4611Phi(117375,3^5)148862Henri Lifchitz12/2025
46128*10^148860-3148861Ray Chandler04/2011
461338262^7769+7769^38262148854Hans Havermann10/2020
461410^148816-500001148816Robert Price03/2022
4615(53*10^148811-287)/9148812Robert Price02/2022
46162^494333-286183148810Enzo Doria06/2015
46172^494144-264119148753Enzo Doria05/2014
46186*10^148734+47148735Robert Price06/2022
461928724^33353-33353^28724148696Frank Doornink06/2024
462036502^11823+11823^36502148663Hans Havermann11/2020
4621(5*2^493838-1)/3721148658Lelio R Paula10/2015
462264239^206+206^64239148641Hans Havermann10/2020
4623(23*2^493761-1)/555148636Lelio R Paula10/2015
4624(23*10^148627-137)/3148628Robert Price08/2021
4625(151*10^148601-1)/3148603Robert Price03/2020
46262^493636+82081148600Enzo Doria09/2016
4627((((((((((((((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
462827134^33509-33509^27134148563Frank Doornink01/2024
4629177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
4630(2*10^148460-23)/3148460Robert Price04/2018
4631(28*10^148445+101)/3148446Robert Price09/2020
46322^493065+225148428Henri Lifchitz11/2024
463336203^12556+12556^36203148391Hans Havermann10/2020
463433912^23749+23749^33912148387Hans Havermann10/2020
4635(8*10^148328+1)/9148328Serge Batalov05/2010
463634294^21117+21117^34294148309Hans Havermann10/2020
4637(71*10^148306-539)/9148307Robert Price07/2019
463830814^33039-33039^30814148304Frank Doornink06/2024
463938042^7875+7875^38042148222Hans Havermann10/2020
46405^211959-12874148153Enzo Doria05/2014
464134142^21831+21831^34142148145Hans Havermann10/2020
4642(288*21^112023-13)/5148121Eric Chen03/2026
464310^148112+34059148113Patrick De Geest05/2021
464410^148112-70000001148112Robert Price03/2021
464510^148112-106593148112Patrick De Geest05/2021
464636303^12016+12016^36303148108Hans Havermann10/2020
4647(77*10^148089-149)/9148090Robert Price03/2022
4648(16*10^148071+41)/3148072Robert Price03/2019
4649187^65175-2148068Lelio R Paula11/2017
46502^491851+1871453148062Enzo Doria05/2016
4651(68*10^148060-257)/9148061Robert Price07/2019
4652Phi(162903,-5#)148043Henri Lifchitz12/2025
4653(151*10^148020-1)/3148022Robert Price03/2020
465439153^6032+6032^39153148017Hans Havermann10/2020
465536798^10507+10507^36798147983Hans Havermann12/2020
4656(26*10^147973-23)/3147974Robert Price12/2019
4657Phi(65997,11#)147973Henri Lifchitz12/2025
46582^491521-1865323147963Enzo Doria02/2016
4659(2^491476+7)/71147948Lelio R Paula10/2015
46602*10^147928+47147929Robert Price12/2021
46612^491391-7807147924Lelio R Paula01/2013
46622^491384+236221147922Enzo Doria05/2025
466339736^5279+5279^39736147920Hans Havermann11/2020
46642^491370-113297147918Enzo Doria07/2014
4665(3^707753)%F(707753)147912Henri Lifchitz06/2025
4666(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
466744368^2155+2155^44368147899Hans Havermann12/2020
4668(17*10^147890+79)/3147891Robert Price04/2019
466994*10^147871-3147873Robert Price05/2020
467010^147843+620967147844Patrick De Geest05/2021
467110^147843-50000000001147843Robert Price12/2020
467210^147843-182891147843Patrick De Geest05/2021
467335805^13346+13346^35805147709Hans Havermann11/2020
46742^490672+255255147707Paul Bourdelais10/2021
46752^490660-17147704Lelio R Paula12/2017
4676(229*10^147699-1)/3147701Robert Price07/2020
467740656^4289+4289^40656147678Hans Havermann11/2020
4678(85*10^147676-31)/9147677Rytis Slatkevicius12/2024
46792^490550+1179439147671Enzo Doria06/2016
468027249^33292-33292^27249147662Frank Doornink06/2024
4681(23*10^147649-59)/9147650Robert Price05/2018
46822^490368-498143147616Maxim Gerspach08/2026
46832^490303+2793653147596Enzo Doria03/2016
46842^490266+255255147585Paul Bourdelais10/2021
4685199^64181-2147543Lelio R Paula11/2017
468632849^30958+30958^32849147518Hans Havermann11/2020
46872^489871-286987147466Enzo Doria07/2015
46882^489864-351899147464Enzo Doria07/2015
4689175^65724-2147422Lelio R Paula11/2017
46902^489712+1874851147419Enzo Doria06/2016
469134473^18830+18830^34473147367Hans Havermann11/2020
469263^81896-2147359Lelio R Paula10/2017
469334580^18237+18237^34580147344Hans Havermann11/2020
4694(11*10^147313-107)/3147314Robert Price09/2018
4695(397*10^147310+17)/9147312Robert Price03/2022
46962^489305-59815147296Enzo Doria10/2015
4697(2^489280-7)/6381147285Lelio R Paula09/2015
46982*10^147264-61147265Robert Price10/2021
46992*10^147260+29147261Robert Price02/2021
470033556^24457+24457^33556147258Hans Havermann11/2020
470112^136450-11147255Riley Fisher12/2024
47022^489125+80357147242Enzo Doria06/2016
470310^147240-40000001147240Robert Price07/2022
470410^147240-371331147240Alfred Reich09/2024
470510^147240-464727147240Alfred Reich09/2024
470632835^30452+30452^32835147220Hans Havermann12/2020
4707(19*10^147213-97)/3147214Robert Price10/2021
470827123^33190-33190^27123147143Frank Doornink01/2024
4709(148*10^147139-1)/3147141Robert Price03/2020
471034338^19255+19255^34338147123Hans Havermann11/2020
47112^488648-112799147098Enzo Doria07/2014
47122^488627-350317147092Enzo Doria06/2015
471333432^25075+25075^33432147076Hans Havermann12/2020
4714(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
47152^488280-2165146987Yves Minet07/2014
47162^488278+45146987Lelio R Paula12/2017
4717(3^834646)/(2^834646)146974Henri Lifchitz06/2025
471832568^32568+32561^32561146973Henri Lifchitz08/2024
47192^487927-39146881Lelio R Paula12/2017
4720(7*10^146860-13)/3146861Robert Price07/2018
4721(26*10^146856-77)/3146857Robert Price11/2019
472232948^28611+28611^32948146834Hans Havermann11/2020
472342596^2799+2799^42596146829Hans Havermann12/2020
47242^487726-1863341146821Enzo Doria12/2015
472543838^2229+2229^43838146775Hans Havermann11/2020
472635005^15594+15594^35005146775Hans Havermann11/2020
4727(167*10^146764+7)/3146766Robert Price04/2021
472853^85114+85114146761Kellen Shenton05/2022
4729(59*10^146738+157)/9146739Robert Price12/2021
4730((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
473132963^28234+28234^32963146711Hans Havermann12/2020
4732(22*10^146661-19)/3146662Robert Price04/2019
473333958^20825+20825^33958146651Hans Havermann12/2020
473426289^33178-33178^26289146640Frank Doornink03/2024
47352^487121-39523146639Enzo Doria09/2015
473661063^252+252^61063146637Hans Havermann12/2020
4737(7*2^486967+1)/39146591Lelio R Paula09/2015
473834099^19900+19900^34099146587Hans Havermann11/2020
4739(10^146606+1)/2931129793051428557705609146582Anonymous03/2026
47402^486893-79146570Yves Minet09/2017
474136818^9567+9567^36818146565Hans Havermann12/2020
47422^486840+1879141146554Enzo Doria08/2016
47432^486774-87146534Lelio R Paula12/2017
474438655^6176+6176^38655146530Hans Havermann11/2020
47458*10^146522-81146523Robert Price02/2021
474632820^29059+29059^32820146485Hans Havermann12/2020
474737261^8530+8530^37261146472Hans Havermann12/2020
474866953^154+154^66953146462Hans Havermann12/2020
474996^73877-95^73877146445Robert Price10/2015
47508*10^146421+81146422Robert Price08/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 08 2026 09:31 (Time in France)

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