PRP Records

Probable Primes Top 10000

(303327 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(14*10^150391-191)/3150392Robert Price10/2020
450229033^33696+33696^29033150382Norbert Schneider10/2023
45032^499534-221150375Yves Minet06/2012
450430110^33567+33567^30110150337Norbert Schneider10/2023
450526212^34023-34023^26212150331Frank Doornink03/2024
4506(28*10^150294+41)/3150295Robert Price07/2021
45072^499225+49727150282Enzo Doria09/2016
4508(695*10^150274+7)/9150276Robert Price12/2021
45092^499054-29261150231Enzo Doria07/2015
451018580^35187+35187^18580150215Norbert Schneider10/2023
4511(844*10^150196-7)/9150198Robert Price05/2021
45122^498907-933075150186Paul Bourdelais06/2021
4513(2^498898-7)/9150183Lelio R Paula10/2015
45143*10^150182+17150183Robert Price07/2018
45155*10^150175+63150176Robert Price09/2020
451629273^33618-33618^29273150154Frank Doornink06/2024
451732363^33292+33292^32363150149Norbert Schneider07/2022
451832^99753-99753^32150144Henri Lifchitz08/2024
4519(77*10^150128+67)/9150129Robert Price12/2021
4520(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
45212^498623+1866983150101Enzo Doria03/2016
452233194^33194-213^213150073Serge Batalov04/2024
452327868^33759-33759^27868150063Frank Doornink06/2024
4524(25*10^150050-403)/9150051Robert Price12/2020
4525numbpart(18140942830)150033Serge Batalov04/2017
452610^150029+4381150030Patrick De Geest05/2016
452710^150029-41150029Serge Batalov12/2014
452833185^33185+618^618150028Serge Batalov04/2024
45299*34^97952+529150013Eric Chen08/2023
453010^150000+1158603150001Patrick De Geest09/2018
453110^150000-245703150000Patrick De Geest09/2018
4532(38*10^149999+691)/9150000Robert Price10/2018
45332043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
4534(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
45352^498238-53149985Lelio R Paula12/2017
453645728^1905+1905^45728149984Hans Havermann10/2020
4537(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
45385*10^149907+23149908Robert Price03/2019
453932^99585-829149891Eric Chen11/2023
454039347^6442+6442^39347149874Hans Havermann09/2020
45412^497850+81049149868Enzo Doria07/2016
4542V(1075416)149830Serge Batalov07/2024
454337228^10575+10575^37228149816Hans Havermann10/2020
4544(5*2^497673+1)/2743149812Lelio R Paula10/2015
4545(5*2^497671+1)/373703149810Lelio R Paula10/2015
4546(2*10^149803-143)/3149803Robert Price03/2018
454733845^26604+26604^33845149763Hans Havermann09/2020
45482^497434-2784191149743Enzo Doria10/2015
4549(865*10^149737-1)/9149739Robert Price04/2020
455010^149695-7000001149695Robert Price06/2021
455138237^8214+8214^38237149681Hans Havermann09/2020
4552Phi(745791,2)/1491583149664Anonymous03/2025
4553(497167*2^497167-1)/70975149664Anonymous04/2025
4554(23*10^149655+19)/3149656Robert Price07/2019
45552^497068-113579149633Enzo Doria08/2014
45562^497037+73727149624Enzo Doria04/2016
455711*10^149618+3149620Robert Price07/2021
455834942^19067+19067^34942149562Hans Havermann09/2020
455933696^27449+27449^33696149561Hans Havermann09/2020
45602^496773+77747149544Enzo Doria05/2016
456129937^33400-33400^29937149506Frank Doornink06/2024
4562(7*10^149483-493)/9149483Robert Price04/2021
4563(206*10^149459+7)/3149461Robert Price07/2020
456434589^20940+20940^34589149459Hans Havermann09/2020
45652^496477-113485149455Enzo Doria08/2014
4566(496423*2^496423-1)/223573149439Anonymous04/2025
45673*2^496411-5149436Jon Grantham07/2023
4568((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
45692^496270-49451149393Enzo Doria10/2015
45702^496238-1865081149383Enzo Doria01/2016
457133831^26030+26030^33831149380Hans Havermann09/2020
457234131^23780+23780^34131149365Hans Havermann09/2020
4573(5*10^149335-53)/3149336Robert Price09/2020
457426043^33818-33818^26043149330Frank Doornink03/2024
45752^495968-1853699149302Enzo Doria09/2015
45762^495935-4117149292Yves Minet02/2018
45775*2^495930+3149291Jon Grantham07/2023
457835816^14709+14709^35816149267Hans Havermann09/2020
4579(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
45803^312800+6560149244Alfred Reich04/2026
458110^149240-40000001149240Robert Price07/2022
458210^149240-10809149240Alfred Reich08/2024
45832^495712-396765149225Enzo Doria07/2013
4584(21*2^495676-1)/4835149211Lelio R Paula10/2015
45852^495420+1880701149137Enzo Doria10/2016
458625646^33823-33823^25646149127Frank Doornink02/2024
45872^495337-1847293149112Enzo Doria07/2015
4588(2^495193-7)/5149068Lelio R Paula10/2015
45892^495163+111546435149059Paul Bourdelais10/2021
459033282^30097+30097^33282149055Hans Havermann09/2020
459137384^9705+9705^37384149050Hans Havermann09/2020
459234808^19143+19143^34808149049Hans Havermann09/2020
4593413^56963-412^56963149013Jean-Louis Charton08/2012
459430657^33212-33212^30657149007Frank Doornink06/2024
459547^89113-46^89113149006Robert Price10/2012
4596V(891190)148997Serge Batalov07/2024
45972^494916+87855148985Lelio R Paula01/2016
45986*10^148982+73148983Robert Price04/2019
45993^312155-4148936Anonymous02/2023
460010^148934+1530019148935Patrick De Geest02/2021
460110^148934-1000000001148934Robert Price11/2020
460210^148934-512057148934Patrick De Geest02/2021
460339000^6571+6571^39000148888Hans Havermann10/2020
46042^494586-2791991148886Enzo Doria02/2016
4605Phi(117375,3^5)148862Henri Lifchitz12/2025
46068*10^148860-3148861Ray Chandler04/2011
460738262^7769+7769^38262148854Hans Havermann10/2020
460810^148816-500001148816Robert Price03/2022
4609(53*10^148811-287)/9148812Robert Price02/2022
46102^494333-286183148810Enzo Doria06/2015
46112^494144-264119148753Enzo Doria05/2014
46126*10^148734+47148735Robert Price06/2022
461328724^33353-33353^28724148696Frank Doornink06/2024
461436502^11823+11823^36502148663Hans Havermann11/2020
4615(5*2^493838-1)/3721148658Lelio R Paula10/2015
461664239^206+206^64239148641Hans Havermann10/2020
4617(23*2^493761-1)/555148636Lelio R Paula10/2015
4618(23*10^148627-137)/3148628Robert Price08/2021
4619(151*10^148601-1)/3148603Robert Price03/2020
46202^493636+82081148600Enzo Doria09/2016
4621((((((((((((((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
462227134^33509-33509^27134148563Frank Doornink01/2024
4623177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
4624(2*10^148460-23)/3148460Robert Price04/2018
4625(28*10^148445+101)/3148446Robert Price09/2020
46262^493065+225148428Henri Lifchitz11/2024
462736203^12556+12556^36203148391Hans Havermann10/2020
462833912^23749+23749^33912148387Hans Havermann10/2020
4629(8*10^148328+1)/9148328Serge Batalov05/2010
463034294^21117+21117^34294148309Hans Havermann10/2020
4631(71*10^148306-539)/9148307Robert Price07/2019
463230814^33039-33039^30814148304Frank Doornink06/2024
463338042^7875+7875^38042148222Hans Havermann10/2020
46345^211959-12874148153Enzo Doria05/2014
463534142^21831+21831^34142148145Hans Havermann10/2020
4636(288*21^112023-13)/5148121Eric Chen03/2026
463710^148112+34059148113Patrick De Geest05/2021
463810^148112-70000001148112Robert Price03/2021
463910^148112-106593148112Patrick De Geest05/2021
464036303^12016+12016^36303148108Hans Havermann10/2020
4641(77*10^148089-149)/9148090Robert Price03/2022
4642(16*10^148071+41)/3148072Robert Price03/2019
4643187^65175-2148068Lelio R Paula11/2017
46442^491851+1871453148062Enzo Doria05/2016
4645(68*10^148060-257)/9148061Robert Price07/2019
4646Phi(162903,-5#)148043Henri Lifchitz12/2025
4647(151*10^148020-1)/3148022Robert Price03/2020
464839153^6032+6032^39153148017Hans Havermann10/2020
464936798^10507+10507^36798147983Hans Havermann12/2020
4650(26*10^147973-23)/3147974Robert Price12/2019
4651Phi(65997,11#)147973Henri Lifchitz12/2025
46522^491521-1865323147963Enzo Doria02/2016
4653(2^491476+7)/71147948Lelio R Paula10/2015
46542*10^147928+47147929Robert Price12/2021
46552^491391-7807147924Lelio R Paula01/2013
46562^491384+236221147922Enzo Doria05/2025
465739736^5279+5279^39736147920Hans Havermann11/2020
46582^491370-113297147918Enzo Doria07/2014
4659(3^707753)%F(707753)147912Henri Lifchitz06/2025
4660(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
466144368^2155+2155^44368147899Hans Havermann12/2020
4662(17*10^147890+79)/3147891Robert Price04/2019
466394*10^147871-3147873Robert Price05/2020
466410^147843+620967147844Patrick De Geest05/2021
466510^147843-50000000001147843Robert Price12/2020
466610^147843-182891147843Patrick De Geest05/2021
466735805^13346+13346^35805147709Hans Havermann11/2020
46682^490672+255255147707Paul Bourdelais10/2021
46692^490660-17147704Lelio R Paula12/2017
4670(229*10^147699-1)/3147701Robert Price07/2020
467140656^4289+4289^40656147678Hans Havermann11/2020
4672(85*10^147676-31)/9147677Rytis Slatkevicius12/2024
46732^490550+1179439147671Enzo Doria06/2016
467427249^33292-33292^27249147662Frank Doornink06/2024
4675(23*10^147649-59)/9147650Robert Price05/2018
46762^490303+2793653147596Enzo Doria03/2016
46772^490266+255255147585Paul Bourdelais10/2021
4678199^64181-2147543Lelio R Paula11/2017
467932849^30958+30958^32849147518Hans Havermann11/2020
46802^489871-286987147466Enzo Doria07/2015
46812^489864-351899147464Enzo Doria07/2015
4682175^65724-2147422Lelio R Paula11/2017
46832^489712+1874851147419Enzo Doria06/2016
468434473^18830+18830^34473147367Hans Havermann11/2020
468563^81896-2147359Lelio R Paula10/2017
468634580^18237+18237^34580147344Hans Havermann11/2020
4687(11*10^147313-107)/3147314Robert Price09/2018
4688(397*10^147310+17)/9147312Robert Price03/2022
46892^489305-59815147296Enzo Doria10/2015
4690(2^489280-7)/6381147285Lelio R Paula09/2015
46912*10^147264-61147265Robert Price10/2021
46922*10^147260+29147261Robert Price02/2021
469333556^24457+24457^33556147258Hans Havermann11/2020
469412^136450-11147255Riley Fisher12/2024
46952^489125+80357147242Enzo Doria06/2016
469610^147240-40000001147240Robert Price07/2022
469710^147240-371331147240Alfred Reich09/2024
469810^147240-464727147240Alfred Reich09/2024
469932835^30452+30452^32835147220Hans Havermann12/2020
4700(19*10^147213-97)/3147214Robert Price10/2021
470127123^33190-33190^27123147143Frank Doornink01/2024
4702(148*10^147139-1)/3147141Robert Price03/2020
470334338^19255+19255^34338147123Hans Havermann11/2020
47042^488648-112799147098Enzo Doria07/2014
47052^488627-350317147092Enzo Doria06/2015
470633432^25075+25075^33432147076Hans Havermann12/2020
4707(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
47082^488280-2165146987Yves Minet07/2014
47092^488278+45146987Lelio R Paula12/2017
4710(3^834646)/(2^834646)146974Henri Lifchitz06/2025
471132568^32568+32561^32561146973Henri Lifchitz08/2024
47122^487927-39146881Lelio R Paula12/2017
4713(7*10^146860-13)/3146861Robert Price07/2018
4714(26*10^146856-77)/3146857Robert Price11/2019
471532948^28611+28611^32948146834Hans Havermann11/2020
471642596^2799+2799^42596146829Hans Havermann12/2020
47172^487726-1863341146821Enzo Doria12/2015
471843838^2229+2229^43838146775Hans Havermann11/2020
471935005^15594+15594^35005146775Hans Havermann11/2020
4720(167*10^146764+7)/3146766Robert Price04/2021
472153^85114+85114146761Kellen Shenton05/2022
4722(59*10^146738+157)/9146739Robert Price12/2021
4723((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
472432963^28234+28234^32963146711Hans Havermann12/2020
4725(22*10^146661-19)/3146662Robert Price04/2019
472633958^20825+20825^33958146651Hans Havermann12/2020
472726289^33178-33178^26289146640Frank Doornink03/2024
47282^487121-39523146639Enzo Doria09/2015
472961063^252+252^61063146637Hans Havermann12/2020
4730(7*2^486967+1)/39146591Lelio R Paula09/2015
473134099^19900+19900^34099146587Hans Havermann11/2020
4732(10^146606+1)/2931129793051428557705609146582Anonymous03/2026
47332^486893-79146570Yves Minet09/2017
473436818^9567+9567^36818146565Hans Havermann12/2020
47352^486840+1879141146554Enzo Doria08/2016
47362^486774-87146534Lelio R Paula12/2017
473738655^6176+6176^38655146530Hans Havermann11/2020
47388*10^146522-81146523Robert Price02/2021
473932820^29059+29059^32820146485Hans Havermann12/2020
474037261^8530+8530^37261146472Hans Havermann12/2020
474166953^154+154^66953146462Hans Havermann12/2020
474296^73877-95^73877146445Robert Price10/2015
47438*10^146421+81146422Robert Price08/2019
474433153^26090+26090^33153146420Hans Havermann11/2020
47452^486275+23961146384Enzo Doria10/2023
4746(12^135607-1)/18437127731146335Paul Vanderveen06/2025
4747(52^85259+1)/53146304Paul Bourdelais09/2017
4748179^64935+2146290Lelio R Paula10/2017
474932595^30758+30758^32595146285Hans Havermann11/2020
475034972^15157+15157^34972146205Hans Havermann12/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 24 2026 09:36 (Time in France)

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