PRP Records

Probable Primes Top 10000

(301692 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 ?
4001(28*10^150294+41)/3150295Robert Price07/2021
40022^499225+49727150282Enzo Doria09/2016
4003(695*10^150274+7)/9150276Robert Price12/2021
40042^499054-29261150231Enzo Doria07/2015
400518580^35187+35187^18580150215Norbert Schneider10/2023
4006(844*10^150196-7)/9150198Robert Price05/2021
40072^498907-933075150186Paul Bourdelais06/2021
4008(2^498898-7)/9150183Lelio R Paula10/2015
40093*10^150182+17150183Robert Price07/2018
40105*10^150175+63150176Robert Price09/2020
401129273^33618-33618^29273150154Frank Doornink06/2024
401232363^33292+33292^32363150149Norbert Schneider07/2022
401332^99753-99753^32150144Henri Lifchitz08/2024
4014(77*10^150128+67)/9150129Robert Price12/2021
4015(7*10^(2*75062+1)-9*10^75062-7)/9150125Robert Price12/2023
40162^498623+1866983150101Enzo Doria03/2016
401733194^33194-213^213150073Serge Batalov04/2024
401827868^33759-33759^27868150063Frank Doornink06/2024
4019(25*10^150050-403)/9150051Robert Price12/2020
4020numbpart(18140942830)150033Serge Batalov04/2017
402110^150029+4381150030Patrick De Geest05/2016
402210^150029-41150029Serge Batalov12/2014
402333185^33185+618^618150028Serge Batalov04/2024
40249*34^97952+529150013Eric Chen08/2023
402510^150000+1158603150001Patrick De Geest09/2018
402610^150000-245703150000Patrick De Geest09/2018
4027(38*10^149999+691)/9150000Robert Price10/2018
40282043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
4029(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
40302^498238-53149985Lelio R Paula12/2017
403145728^1905+1905^45728149984Hans Havermann10/2020
4032(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
40335*10^149907+23149908Robert Price03/2019
403432^99585-829149891Eric Chen11/2023
403539347^6442+6442^39347149874Hans Havermann09/2020
40362^497850+81049149868Enzo Doria07/2016
4037V(1075416)149830Serge Batalov07/2024
403837228^10575+10575^37228149816Hans Havermann10/2020
4039(5*2^497673+1)/2743149812Lelio R Paula10/2015
4040(5*2^497671+1)/373703149810Lelio R Paula10/2015
4041(2*10^149803-143)/3149803Robert Price03/2018
404233845^26604+26604^33845149763Hans Havermann09/2020
40432^497434-2784191149743Enzo Doria10/2015
4044(865*10^149737-1)/9149739Robert Price04/2020
404510^149695-7000001149695Robert Price06/2021
404638237^8214+8214^38237149681Hans Havermann09/2020
4047Phi(745791,2)/1491583149664Anonymous03/2025
4048(497167*2^497167-1)/70975149664Anonymous04/2025
4049(23*10^149655+19)/3149656Robert Price07/2019
40502^497068-113579149633Enzo Doria08/2014
40512^497037+73727149624Enzo Doria04/2016
405211*10^149618+3149620Robert Price07/2021
405334942^19067+19067^34942149562Hans Havermann09/2020
405433696^27449+27449^33696149561Hans Havermann09/2020
40552^496773+77747149544Enzo Doria05/2016
405629937^33400-33400^29937149506Frank Doornink06/2024
4057(7*10^149483-493)/9149483Robert Price04/2021
4058(206*10^149459+7)/3149461Robert Price07/2020
405934589^20940+20940^34589149459Hans Havermann09/2020
40602^496477-113485149455Enzo Doria08/2014
4061(496423*2^496423-1)/223573149439Anonymous04/2025
40623*2^496411-5149436Jon Grantham07/2023
4063((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
40642^496270-49451149393Enzo Doria10/2015
40652^496238-1865081149383Enzo Doria01/2016
406633831^26030+26030^33831149380Hans Havermann09/2020
406734131^23780+23780^34131149365Hans Havermann09/2020
4068(5*10^149335-53)/3149336Robert Price09/2020
406926043^33818-33818^26043149330Frank Doornink03/2024
40702^495968-1853699149302Enzo Doria09/2015
40712^495935-4117149292Yves Minet02/2018
40725*2^495930+3149291Jon Grantham07/2023
407335816^14709+14709^35816149267Hans Havermann09/2020
4074(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
407510^149240-40000001149240Robert Price07/2022
407610^149240-10809149240Alfred Reich08/2024
40772^495712-396765149225Enzo Doria07/2013
4078(21*2^495676-1)/4835149211Lelio R Paula10/2015
40792^495420+1880701149137Enzo Doria10/2016
408025646^33823-33823^25646149127Frank Doornink02/2024
40812^495337-1847293149112Enzo Doria07/2015
4082(2^495193-7)/5149068Lelio R Paula10/2015
40832^495163+111546435149059Paul Bourdelais10/2021
408433282^30097+30097^33282149055Hans Havermann09/2020
408537384^9705+9705^37384149050Hans Havermann09/2020
408634808^19143+19143^34808149049Hans Havermann09/2020
4087413^56963-412^56963149013Jean-Louis Charton08/2012
408830657^33212-33212^30657149007Frank Doornink06/2024
408947^89113-46^89113149006Robert Price10/2012
4090V(891190)148997Serge Batalov07/2024
40912^494916+87855148985Lelio R Paula01/2016
40926*10^148982+73148983Robert Price04/2019
40933^312155-4148936Anonymous02/2023
409410^148934+1530019148935Patrick De Geest02/2021
409510^148934-1000000001148934Robert Price11/2020
409610^148934-512057148934Patrick De Geest02/2021
409739000^6571+6571^39000148888Hans Havermann10/2020
40982^494586-2791991148886Enzo Doria02/2016
40998*10^148860-3148861Ray Chandler04/2011
410038262^7769+7769^38262148854Hans Havermann10/2020
410110^148816-500001148816Robert Price03/2022
4102(53*10^148811-287)/9148812Robert Price02/2022
41032^494333-286183148810Enzo Doria06/2015
41042^494144-264119148753Enzo Doria05/2014
41056*10^148734+47148735Robert Price06/2022
410628724^33353-33353^28724148696Frank Doornink06/2024
410736502^11823+11823^36502148663Hans Havermann11/2020
4108(5*2^493838-1)/3721148658Lelio R Paula10/2015
410964239^206+206^64239148641Hans Havermann10/2020
4110(23*2^493761-1)/555148636Lelio R Paula10/2015
4111(23*10^148627-137)/3148628Robert Price08/2021
4112(151*10^148601-1)/3148603Robert Price03/2020
41132^493636+82081148600Enzo Doria09/2016
4114((((((((((((((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
411527134^33509-33509^27134148563Frank Doornink01/2024
4116177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
4117(2*10^148460-23)/3148460Robert Price04/2018
4118(28*10^148445+101)/3148446Robert Price09/2020
41192^493065+225148428Henri Lifchitz11/2024
412036203^12556+12556^36203148391Hans Havermann10/2020
412133912^23749+23749^33912148387Hans Havermann10/2020
4122(8*10^148328+1)/9148328Serge Batalov05/2010
412334294^21117+21117^34294148309Hans Havermann10/2020
4124(71*10^148306-539)/9148307Robert Price07/2019
412530814^33039-33039^30814148304Frank Doornink06/2024
412638042^7875+7875^38042148222Hans Havermann10/2020
41275^211959-12874148153Enzo Doria05/2014
412834142^21831+21831^34142148145Hans Havermann10/2020
412910^148112+34059148113Patrick De Geest05/2021
413010^148112-70000001148112Robert Price03/2021
413110^148112-106593148112Patrick De Geest05/2021
413236303^12016+12016^36303148108Hans Havermann10/2020
4133(77*10^148089-149)/9148090Robert Price03/2022
4134(16*10^148071+41)/3148072Robert Price03/2019
4135187^65175-2148068Lelio R Paula11/2017
41362^491851+1871453148062Enzo Doria05/2016
4137(68*10^148060-257)/9148061Robert Price07/2019
4138(151*10^148020-1)/3148022Robert Price03/2020
413939153^6032+6032^39153148017Hans Havermann10/2020
414036798^10507+10507^36798147983Hans Havermann12/2020
4141(26*10^147973-23)/3147974Robert Price12/2019
41422^491521-1865323147963Enzo Doria02/2016
4143(2^491476+7)/71147948Lelio R Paula10/2015
41442*10^147928+47147929Robert Price12/2021
41452^491391-7807147924Lelio R Paula01/2013
41462^491384+236221147922Enzo Doria05/2025
414739736^5279+5279^39736147920Hans Havermann11/2020
41482^491370-113297147918Enzo Doria07/2014
4149(3^707753)%F(707753)147912Henri Lifchitz06/2025
4150(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
415144368^2155+2155^44368147899Hans Havermann12/2020
4152(17*10^147890+79)/3147891Robert Price04/2019
415394*10^147871-3147873Robert Price05/2020
415410^147843+620967147844Patrick De Geest05/2021
415510^147843-50000000001147843Robert Price12/2020
415610^147843-182891147843Patrick De Geest05/2021
415735805^13346+13346^35805147709Hans Havermann11/2020
41582^490672+255255147707Paul Bourdelais10/2021
41592^490660-17147704Lelio R Paula12/2017
4160(229*10^147699-1)/3147701Robert Price07/2020
416140656^4289+4289^40656147678Hans Havermann11/2020
4162(85*10^147676-31)/9147677Rytis Slatkevicius12/2024
41632^490550+1179439147671Enzo Doria06/2016
416427249^33292-33292^27249147662Frank Doornink06/2024
4165(23*10^147649-59)/9147650Robert Price05/2018
41662^490303+2793653147596Enzo Doria03/2016
41672^490266+255255147585Paul Bourdelais10/2021
4168199^64181-2147543Lelio R Paula11/2017
416932849^30958+30958^32849147518Hans Havermann11/2020
41702^489871-286987147466Enzo Doria07/2015
41712^489864-351899147464Enzo Doria07/2015
4172175^65724-2147422Lelio R Paula11/2017
41732^489712+1874851147419Enzo Doria06/2016
417434473^18830+18830^34473147367Hans Havermann11/2020
417563^81896-2147359Lelio R Paula10/2017
417634580^18237+18237^34580147344Hans Havermann11/2020
4177(11*10^147313-107)/3147314Robert Price09/2018
4178(397*10^147310+17)/9147312Robert Price03/2022
41792^489305-59815147296Enzo Doria10/2015
4180(2^489280-7)/6381147285Lelio R Paula09/2015
41812*10^147264-61147265Robert Price10/2021
41822*10^147260+29147261Robert Price02/2021
418333556^24457+24457^33556147258Hans Havermann11/2020
418412^136450-11147255Riley Fisher12/2024
41852^489125+80357147242Enzo Doria06/2016
418610^147240-40000001147240Robert Price07/2022
418710^147240-371331147240Alfred Reich09/2024
418810^147240-464727147240Alfred Reich09/2024
418932835^30452+30452^32835147220Hans Havermann12/2020
4190(19*10^147213-97)/3147214Robert Price10/2021
419127123^33190-33190^27123147143Frank Doornink01/2024
4192(148*10^147139-1)/3147141Robert Price03/2020
419334338^19255+19255^34338147123Hans Havermann11/2020
41942^488648-112799147098Enzo Doria07/2014
41952^488627-350317147092Enzo Doria06/2015
419633432^25075+25075^33432147076Hans Havermann12/2020
4197(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
41982^488280-2165146987Yves Minet07/2014
41992^488278+45146987Lelio R Paula12/2017
4200(3^834646)/(2^834646)146974Henri Lifchitz06/2025
420132568^32568+32561^32561146973Henri Lifchitz08/2024
42022^487927-39146881Lelio R Paula12/2017
4203(7*10^146860-13)/3146861Robert Price07/2018
4204(26*10^146856-77)/3146857Robert Price11/2019
420532948^28611+28611^32948146834Hans Havermann11/2020
420642596^2799+2799^42596146829Hans Havermann12/2020
42072^487726-1863341146821Enzo Doria12/2015
420843838^2229+2229^43838146775Hans Havermann11/2020
420935005^15594+15594^35005146775Hans Havermann11/2020
4210(167*10^146764+7)/3146766Robert Price04/2021
421153^85114+85114146761Kellen Shenton05/2022
4212(59*10^146738+157)/9146739Robert Price12/2021
4213((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
421432963^28234+28234^32963146711Hans Havermann12/2020
4215(22*10^146661-19)/3146662Robert Price04/2019
421633958^20825+20825^33958146651Hans Havermann12/2020
421726289^33178-33178^26289146640Frank Doornink03/2024
42182^487121-39523146639Enzo Doria09/2015
421961063^252+252^61063146637Hans Havermann12/2020
4220(7*2^486967+1)/39146591Lelio R Paula09/2015
422134099^19900+19900^34099146587Hans Havermann11/2020
42222^486893-79146570Yves Minet09/2017
422336818^9567+9567^36818146565Hans Havermann12/2020
42242^486840+1879141146554Enzo Doria08/2016
42252^486774-87146534Lelio R Paula12/2017
422638655^6176+6176^38655146530Hans Havermann11/2020
42278*10^146522-81146523Robert Price02/2021
422832820^29059+29059^32820146485Hans Havermann12/2020
422937261^8530+8530^37261146472Hans Havermann12/2020
423066953^154+154^66953146462Hans Havermann12/2020
423196^73877-95^73877146445Robert Price10/2015
42328*10^146421+81146422Robert Price08/2019
423333153^26090+26090^33153146420Hans Havermann11/2020
42342^486275+23961146384Enzo Doria10/2023
4235(12^135607-1)/18437127731146335Paul Vanderveen06/2025
4236(52^85259+1)/53146304Paul Bourdelais09/2017
4237179^64935+2146290Lelio R Paula10/2017
423832595^30758+30758^32595146285Hans Havermann11/2020
423934972^15157+15157^34972146205Hans Havermann12/2020
4240(16*10^146200+131)/3146201Robert Price03/2022
4241(19*10^146181-49)/3146182Robert Price05/2019
42422^485531-114621146160Enzo Doria05/2015
42432^485473-933075146142Paul Bourdelais06/2021
4244(2^485461-9)/4249146135Lelio R Paula09/2015
4245(22*10^146130-193)/9146131Robert Price07/2022
42462^485389+81887146117Enzo Doria08/2016
424732554^30773+30773^32554146108Hans Havermann11/2020
424828075^32844-32844^28075146101Frank Doornink06/2024
4249(10^146063+71)/9146063Serge Batalov07/2015
42502*10^146051-63146052Robert Price01/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 05 2025 13:49 (Time in France)

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