400 (four hundred) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal n ...

following 399 and preceding 401.

Mathematical properties

400 is the

square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...

of 20. 400 is the sum of the powers of 7 from 0 to 3, thus making it a

repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit. Example ...

in base 7 (1111). A

circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...

is divided into 400

grads The Grid Analysis and Display System (GrADS) is an interactive desktop tool that is used for easy access, manipulation, and visualization of earth science data. The format of the data may be either binary, GRIB, NetCDF, or HDF-SDS (Scientific Da ...

, which is equal to 360

degree Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathematics ...

s and 2π

radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that c ...

s. (Degrees and radians are the SI accepted units). 400 is a

self number In number theory, a self number or Devlali number in a given number base b is a natural number that cannot be written as the sum of any other natural number n and the individual digits of n. 20 is a self number (in base 10), because no such combina ...

in base 10, since there is no integer that added to the sum of its own digits results in 400. On the other hand, 400 is divisible by the sum of its own base 10 digits, making it a

Harshad number In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. Harshad numbers ...

Other fields

Four hundred is also *

The Four Hundred (oligarchy) The Athenian coup of 411 BC was the result of a revolution that took place during the Peloponnesian War between Athens and Sparta. The coup overthrew the democratic government of ancient Athens and replaced it with a short-lived oligarchy known ...

of ancient

Athens Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital and largest city of Greece. With a population close to four million, it is also the seventh largest city in the European Union. Athens dominates ...

. * An

HTTP status code This is a list of Hypertext Transfer Protocol (HTTP) response status codes. Status codes are issued by a server in response to a client's request made to the server. It includes codes from IETF Request for Comments (RFCs), other specifications, ...

for a bad client request. * The Four Hundred (sometimes The Four Hundred Club) a phrase meaning the wealthiest, most famous, or most powerful social group (see, e.g.,

Ward McAllister Samuel Ward McAllister (December 28, 1827 – January 31, 1895) was a popular arbiter of social taste in the Gilded Age of late 19th-century America. He was widely accepted as the authority as to which families could be classified as the cream o ...

), leading to the generation of such lists as the

Forbes 400 The ''Forbes'' 400 or 400 Richest Americans is a list published by ''Forbes'' magazine of the wealthiest 400 American citizens who own assets in the U.S., ranked by net worth. The 400 was started by Malcolm Forbes in 1982 and the list is publ ...

. * The

Atari 400 The Atari 8-bit family is a series of 8-bit home computers introduced by Atari, Inc. in 1979 as the Atari 400 and Atari 800. The series was successively upgraded to Atari 1200XL , Atari 600XL, Atari 800XL, Atari 65XE, Atari 130XE, Atari 800XE ...

home computer. * A former limited stop bus route which operated from

Bolton Bolton (, locally ) is a large town in Greater Manchester in North West England, formerly a part of Lancashire. A former mill town, Bolton has been a production centre for textiles since Flemish people, Flemish weavers settled in the area i ...

Stockport Stockport is a town and borough in Greater Manchester, England, south-east of Manchester, south-west of Ashton-under-Lyne and north of Macclesfield. The River Goyt and Tame merge to create the River Mersey here. Most of the town is within ...

and

Manchester Airport Manchester Airport is an international airport in Ringway, Manchester, England, south-west of Manchester city centre. In 2019, it was the third busiest airport in the United Kingdom in terms of passenger numbers and the busiest of those n ...

from 1970 to 2004, known as the Trans-Lancs Express. * in the title of the film ''Les Quatre Cent Coups'' (''

The 400 Blows ''The 400 Blows'' (french: Les Quatre Cents Coups) is a 1959 French coming-of-age drama film, and the directorial debut of François Truffaut. The film, shot in DyaliScope, stars Jean-Pierre Léaud, Albert Rémy, and Claire Maurier. One of ...

''), a French film directed by

François Truffaut François Roland Truffaut ( , ; ; 6 February 1932 – 21 October 1984) was a French film director, screenwriter, producer, actor, and film critic. He is widely regarded as one of the founders of the French New Wave. After a career of more tha ...

. * A Lebanese card game,

400 (card game) 400 is atrick-taking card game played in two partnerships with a standard deck of 52 playing cards. The object of the game is to be the first team to reach forty-one points. The game somewhat resembles Spades, but with subtle differences. It wa ...

. * the designation for a class of

Ontario Ontario ( ; ) is one of the thirteen provinces and territories of Canada.Ontario is located in the geographic eastern half of Canada, but it has historically and politically been considered to be part of Central Canada. Located in Central Ca ...

highways called

400-Series Highways The 400-series highways are a network of controlled-access highways throughout the southern portion of the Canadian province of Ontario, forming a special subset of the provincial highway system. They are analogous to the Interstate Highway ...

. * The 400, later the Twin Cities 400, a

Chicago and North Western Railway The Chicago and North Western was a Class I railroad in the Midwestern United States. It was also known as the "North Western". The railroad operated more than of track at the turn of the 20th century, and over of track in seven states befor ...

passenger train that traveled 400 miles between Minneapolis/St. Paul and

Chicago, Illinois (''City in a Garden''); I Will , image_map = , map_caption = Interactive Map of Chicago , coordinates = , coordinates_footnotes = , subdivision_type = Country , subdivision_name ...

in 400 minutes. * The yard number of the RMS ''Olympic'', the RMS ''Titanic'''s sister ship. * .400 (2 hits out of 5 at-bats) is a numerically significant annual batting average statistic in Major League Baseball, last accomplished by Ted Williams of the Boston Red Sox in 1941. * The number of days in a

Gregorian calendar The Gregorian calendar is the calendar used in most parts of the world. It was introduced in October 1582 by Pope Gregory XIII as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years dif ...

year changes according to a cycle of exactly 400 years, of which 97 are leap years and 303 are common. * The

Intertestamental period The intertestamental period (Protestant) or deuterocanonical period (Catholic and Eastern Orthodox) is the period of time between the events of the protocanonical books and the New Testament. Traditionally, it is considered to cover roughly four h ...

or period of time between the writings of the Hebrew Bible and the Christian New Testament texts is traditionally considered to be a roughly four hundred-year period. * The

Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...

is approximately 400 times the size of the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

but also is approximately 400 times further away, creating the temporary illusion in which the Sun and Moon in Earth's sky appear as if of similar size. * In

gematria Gematria (; he, גמטריא or gimatria , plural or , ''gimatriot'') is the practice of assigning a numerical value to a name, word or phrase according to an alphanumerical cipher. A single word can yield several values depending on the cipher ...

400 is the largest single number that can be represented without using the Sophit forms (see

Kaph Kaph (also spelled kaf) is the eleventh letter of the Semitic abjads, including Phoenician kāp , Hebrew kāf , Aramaic kāp , Syriac kāp̄ , and Arabic kāf (in abjadi order). The Phoenician letter gave rise to the Greek kappa (Κ), Lati ...

, Mem,

Nun A nun is a woman who vows to dedicate her life to religious service, typically living under vows of poverty, chastity, and obedience in the enclosure of a monastery or convent.''The Oxford English Dictionary'', vol. X, page 599. The term is o ...

, Pe, and Tzade). * List of highways numbered 400

Integers from 401 to 499

400s

401

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

, tetranacci number, sum of seven consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71), sum of nine consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61),

Chen prime A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingru ...

Eisenstein prime In mathematics, an Eisenstein prime is an Eisenstein integer : z = a + b\,\omega, \quad \text \quad \omega = e^, that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units , itself ...

with no imaginary part, prime index prime,

Mertens function In number theory, the Mertens function is defined for all positive integers ''n'' as : M(n) = \sum_^n \mu(k), where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive r ...

returns 0, member of the

Mian–Chowla sequence In mathematics, the Mian–Chowla sequence is an integer sequence defined recursion, recursively in the following way. The sequence starts with :a_1 = 1. Then for n>1, a_n is the smallest integer such that every pairwise sum :a_i + a_j is di ...

. *

for "Unauthorized", area code for

Rhode Island Rhode Island (, like ''road'') is a U.S. state, state in the New England region of the Northeastern United States. It is the List of U.S. states by area, smallest U.S. state by area and the List of states and territories of the United States ...

, also in the name of a retirement plan,

401(k) In the United States, a 401(k) plan is an employer-sponsored, defined-contribution, personal pension (savings) account, as defined in subsection 401(k) of the U.S. Internal Revenue Code. Periodical employee contributions come directly out of their ...

Stephen Colbert Stephen Tyrone Colbert ( ; born May 13, 1964) is an American comedian, writer, producer, political commentator, actor, and television host. He is best known for hosting the satirical Comedy Central program ''The Colbert Report'' from 2005 to ...

's Formula 401, a "man seed" based product brand his persona on ''

The Colbert Report ''The Colbert Report'' ( ) is an American late-night talk and news satire television program hosted by Stephen Colbert that aired four days a week on Comedy Central from October 17, 2005, to December 18, 2014, for 1,447 episodes. The show focuse ...

'' promotes for sale to the publi

*

Ontario Highway 401 King's Highway 401, commonly referred to as Highway 401 and also known by its official name as the Macdonald–Cartier Freeway or colloquially referred to as the four-oh-one, is a Controlled-access highway, controlled-access 400-series high ...

, colloquially referred to as the four-oh-one, is a popular Canadian highway 817.9 kilometres (508.2 mi) that stretches from

Windsor Windsor may refer to: Places Australia * Windsor, New South Wales ** Municipality of Windsor, a former local government area * Windsor, Queensland, a suburb of Brisbane, Queensland **Shire of Windsor, a former local government authority around Wi ...

to the Quebec border, passing through

Toronto Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the ancho ...

. It turns into

Quebec Autoroute 20 Autoroute 20 is a Quebec Autoroute, following the Saint Lawrence River through one of the more densely populated parts of Canada, with its central section forming the main route of the Trans-Canada Highway from the A-25 interchange to the A-8 ...

at the Quebec/Ontario border which leads to the cities of

Montreal Montreal ( ; officially Montréal, ) is the List of the largest municipalities in Canada by population, second-most populous city in Canada and List of towns in Quebec, most populous city in the Provinces and territories of Canada, Canadian ...

and

Quebec Quebec ( ; )According to the Canadian government, ''Québec'' (with the acute accent) is the official name in Canadian French and ''Quebec'' (without the accent) is the province's official name in Canadian English is one of the thirtee ...

402

402 = 2 × 3 × 67,

sphenic number In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers. Definit ...

nontotient In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotient ...

, number of graphs with 8 nodes and 9 edges *

for "Payment Required",

area code A telephone numbering plan is a type of numbering scheme used in telecommunication to assign telephone numbers to subscriber telephones or other telephony endpoints. Telephone numbers are the addresses of participants in a telephone network, rea ...

for

Nebraska Nebraska () is a state in the Midwestern region of the United States. It is bordered by South Dakota to the north; Iowa to the east and Missouri to the southeast, both across the Missouri River; Kansas to the south; Colorado to the southwe ...

403

403 = 13 × 31,

heptagonal number A heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The ''n''-th heptagonal number is given by the formula :H_n=\frac. The first few heptagonal numbers are: : 0, 1, 7, 18, 34, 55, 81, 112, ...

returns 0. * First number that is the product of an emirp pair. *

HTTP 403 HTTP 403 is an HTTP status code meaning access to the requested resource is forbidden. The server understood the request, but will not fulfill it. Specifications HTTP 403 provides a distinct error case from HTTP 401; while HTTP 401 is returned ...

, the status code for "Forbidden" * Also in the name of a retirement plan in the United States,

403(b) In the United States, a 403(b) plan is a U.S. tax-advantaged retirement savings plan available for public education organizations, some non-profit employers (only Internal Revenue Code 501(c)(3) organizations), cooperative hospital service organiza ...

. * The area code for southern Alberta.

404

404 = 2² × 101, Mertens function returns 0, nontotient,

noncototient In mathematics, a noncototient is a positive integer ''n'' that cannot be expressed as the difference between a positive integer ''m'' and the number of coprime integers below it. That is, ''m'' − φ(''m'') = ''n'', where � ...

, number of integer partitions of 20 with an alternating permutation. *

for "Not Found", perhaps the most famous HTTP status code. * Section 404 of the

Sarbanes–Oxley Act The Sarbanes–Oxley Act of 2002 is a United States federal law that mandates certain practices in financial record keeping and reporting for corporations. The act, (), also known as the "Public Company Accounting Reform and Investor Protecti ...

. * One of the three area codes of the Atlanta calling area.

405

405 = 3⁴ × 5, Mertens function returns 0,

pentagonal pyramidal number A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an -sided polygon of points. ...

; *

for "Method Not Allowed". *

Area code A telephone numbering plan is a type of numbering scheme used in telecommunication to assign telephone numbers to subscriber telephones or other telephony endpoints. Telephone numbers are the addresses of participants in a telephone network, rea ...

for central Oklahoma, including

Oklahoma City Oklahoma City (), officially the City of Oklahoma City, and often shortened to OKC, is the capital and largest city of the U.S. state of Oklahoma. The county seat of Oklahoma County, it ranks 20th among United States cities in population, a ...

and surrounding suburbs. * Interstate 405 is a major, heavily traveled freeway in

Southern California Southern California (commonly shortened to SoCal) is a geographic and Cultural area, cultural region that generally comprises the southern portion of the U.S. state of California. It includes the Los Angeles metropolitan area, the second most po ...

, known to the local as "The 405".

406

406 = 2 × 7 × 29,

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...

centered nonagonal number A centered nonagonal number (or centered enneagonal number) is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers. The centered nonagonal n ...

, nontotient *

for "Not Acceptable". *''406'' is a poem by

John Boyle O'Reilly John Boyle O'Reilly (28 June 1844 – 10 August 1890) was an Irish poet, journalist, author and activist. As a youth in Ireland, he was a member of the Irish Republican Brotherhood, or Fenians, for which he was transported to Western Australi ...

. It was believed to have been the number of one of O'Reilly's prison cells, and was the number of his first hotel room after he arrived in the United States. Hence the number had a

mystical Mysticism is popularly known as becoming one with God or the Absolute, but may refer to any kind of ecstasy or altered state of consciousness which is given a religious or spiritual meaning. It may also refer to the attainment of insight in u ...

significance to him, as intimated in the poem. *

Peugeot 406 The Peugeot 406 is a large family car that was produced by French automaker Peugeot between 1995 and 2004. Available in saloon, estate and coupé bodystyles with a choice of petrol or turbodiesel engines, the 406 replaced the Peugeot 405 in P ...

car. *

for all of

Montana Montana () is a state in the Mountain West division of the Western United States. It is bordered by Idaho to the west, North Dakota and South Dakota to the east, Wyoming to the south, and the Canadian provinces of Alberta, British Columbi ...

407

407 = 11 × 37, *sum of cubes of 4, 0 and 7 (4³ + 0³ + 7³ = 407);

narcissistic number In number theory, a narcissistic number 1 F_ : \mathbb \rightarrow \mathbb to be the following: : F_(n) = \sum_^ d_i^k. where k = \lfloor \log_ \rfloor + 1 is the number of digits in the number in base b, and : d_i = \frac is the value of each d ...

*sum of three consecutive primes (131 + 137 + 139) *Mertens function returns 0 *Harshad number *lazy caterer number *

for "Proxy Authentication Required" *Area code for

Orlando Orlando () is a city in the U.S. state of Florida and is the county seat of Orange County. In Central Florida, it is the center of the Orlando metropolitan area, which had a population of 2,509,831, according to U.S. Census Bureau figures rele ...

, Florida *Colloquial name for the Express Toll Route in Ontario

408

408 = 2³ × 3 × 17 *Sum of four consecutive primes (97 + 101 + 103 + 107) *Sum of eight consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67) *

Pell number In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , an ...

returns 0 *

Octagonal number An octagonal number is a figurate number that represents an octagon. The octagonal number for ''n'' is given by the formula 3''n''2 - 2''n'', with ''n'' > 0. The first few octagonal numbers are : 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 34 ...

Untouchable number An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. ...

*Harshad number *

for "Request Timeout" *Area code for the Silicon Valley

409

409 is a prime number,

centered triangular number A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers. The following ...

. *A family of cleaning products,

Formula 409 Formula 409 or 409 is an American brand of home and industrial cleaning products well known in the United States, but virtually unknown in other places. It includes Formula 409 All-Purpose Cleaner, Formula 409 Glass and Surface Cleaner, Formula ...

*An engine known as the Chevrolet 409, a 409 cubic inch W-series V8. *The song " 409" by

The Beach Boys The Beach Boys are an American Rock music, rock band that formed in Hawthorne, California, in 1961. The group's original lineup consisted of brothers Brian Wilson, Brian, Dennis Wilson, Dennis, and Carl Wilson, their cousin Mike Love, and frie ...

, inspired by the above engine *

for "Conflict" *A

Green Day Green Day is an American rock band formed in the East Bay of California in 1987 by lead vocalist and guitarist Billie Joe Armstrong, together with bassist and backing vocalist Mike Dirnt. For most of the band's career, they have been a powe ...

song, "409 in Your Coffeemaker", included on their album '' 1,039/Smoothed Out Slappy Hours'' *The

for a part of eastern Texas *

Venice Venice ( ; it, Venezia ; vec, Venesia or ) is a city in northeastern Italy and the capital of the Veneto Regions of Italy, region. It is built on a group of 118 small islands that are separated by canals and linked by over 400 ...

has 409 bridges. *A Bullet For My Valentine song, "Room 409", from the album ''

The Poison ''The Poison'' is the debut studio album by Welsh heavy metal band Bullet for My Valentine. The album was released on 3 October 2005 through Visible Noise Records in the UK, and on 14 February 2006 in the United States, through Trustkill R ...

'' *

Joe Paterno Joseph Vincent Paterno (; December 21, 1926 – January 22, 2012), sometimes referred to as JoePa, was an American college football player, athletic director, and coach. He was the head coach of the Penn State Nittany Lions football, Penn ...

holds the record as the winningest head coach in

NCAA FBS The NCAA Division I Football Bowl Subdivision (FBS), formerly known as Division I-A, is the highest level of college football in the United States. The FBS consists of the largest schools in the National Collegiate Athletic Association (NCAA). As ...

with 409 victories.

410s

410

410 = 2 × 5 × 41,

, sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number, number of triangle-free graphs on 8 vertices *

for "Gone". *

Area Code 410 __NOTOC__ Year 410 ( CDX) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year after the Consulship of Honorius and Theodosius (or, less frequently, year 116 ...

, a telephone area code for the US State of Maryland, representing portions of the state including the

Baltimore metropolitan area The Baltimore–Columbia–Towson Metropolitan Statistical Area, also known as Central Maryland, is a Metropolitan Statistical Area (MSA) in Maryland as defined by the United States Office of Management and Budget (OMB). As of the 2010 United Sta ...

and the Eastern Shore.

411

411 = 3 × 137,

, *

for "Length Required", slang for information (see 4-1-1) *The number of possible

FM broadcasting FM broadcasting is a method of radio broadcasting using frequency modulation (FM). Invented in 1933 by American engineer Edwin Armstrong, wide-band FM is used worldwide to provide high fidelity sound over broadcast radio. FM broadcasting is cap ...

frequencies between 87.50 and 108.00

MHz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one he ...

in 50 kHz spacing countries

412

412 = 2² × 103, nontotient, noncototient, sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), 412⁶⁴ + 1 is prime *

for "Precondition Failed" * Area code for

Pittsburgh Pittsburgh ( ) is a city in the Commonwealth (U.S. state), Commonwealth of Pennsylvania, United States, and the county seat of Allegheny County, Pennsylvania, Allegheny County. It is the most populous city in both Allegheny County and Wester ...

Pennsylvania Pennsylvania (; ( Pennsylvania Dutch: )), officially the Commonwealth of Pennsylvania, is a state spanning the Mid-Atlantic, Northeastern, Appalachian, and Great Lakes regions of the United States. It borders Delaware to its southeast, ...

. * Fictitious Police Code for "Overacting" from
St. George and the Dragonet
- Stan Freeberg

413

413 = 7 × 59,

returns 0, self number, Blum integer *HTTP 413, HTTP status code for "Request Entity Too Large" * Area code for Western Massachusetts. *An important and recurring number in the webcomic Homestuck by Andrew Hussie.

414

414 = 2 × 3² × 23, Mertens function returns 0, nontotient, Harshad number, number of balanced partitions of 31 :

\sum_^^

is prime * HTTP 414, HTTP status code for "Request-URI Too Long" * Area code for Milwaukee, Wisconsin, Milwaukee, Wisconsin. * The 414s, a group of hackers from Milwaukee, Wisconsin.

415

415 = 5 × 83, logarithmic number *HTTP 415, HTTP status code for "Unsupported Media Type" * 415 Records, a record label * 415 refers to California Penal Code, section 415, pertaining to public fighting, public disturbance, and public use of offensive words likely to provoke an immediate violent reaction. *Area code 415, a telephone area code for San Francisco, California

416

416 = 2⁵ × 13, number o
independent vertex sets
an

in the

*HTTP 416, HTTP status code for "Requested Range Not Satisfiable" *416 is also Area codes 416, 647 and 437#416 in popular culture, a nickname for the city of

, based on Area codes 416, 647 and 437, the area code it used before overlay plans added two more area codes.

417

417 = 3 × 139, Blum integer *HTTP 417, HTTP status code for "Expectation Failed". Also the area code for southwestern Missouri, including Springfield, Missouri, Springfield, and Joplin, Missouri, Joplin.

418

418 = 2 × 11 × 19, sphenic number, balanced number * the number of Abrahadabra * Hyper Text Coffee Pot Control Protocol status code for "Teapot" as an April Fools' joke.

419

A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, highly cototient number, Mertens function returns 0 *refers to the Nigerian advance fee fraud scheme (after the section of the Nigerian Criminal Code it violates)

420s

420

421

* A prime number, sum of five consecutive primes (73 + 79 + 83 + 89 + 97), centered square number, also SMTP code meaning the transmission channel will be closing * +421, Country calling code for Slovakia

422

422 = 2 × 211, Mertens function returns 0, nontotient, since 422 = 20² + 20 + 2 it is the maximum number of regions into which 2
intersecting circles divide the plane

423

423 = 3² × 47, Mertens function returns 0,

, number of secondary structures of RNA molecules with 10 nucleotides * +423, Country calling code for Liechtenstein

424

424 = 2³ × 53, sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Mertens function returns 0, refactorable number, self number

425

425 = 5² × 17, pentagonal number, centered tetrahedral number, sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0, the second number that can be expressed as the sum of two squares in three different ways (425 = 20² + 5² = 19² + 8² = 16² + 13²). * 425 is an area code in Washington (state), Washington State.

426

426 = 2 × 3 × 71, sphenic number, nontotient, untouchable number

427

427 = 7 × 61, Mertens function returns 0. 427! + 1 is prime.

428

428 = 2² × 107, Mertens function returns 0, nontotient, 428³² + 1 is prime *''428: Shibuya Scramble'', a video game

429

429 = 3 × 11 × 13, sphenic number, Catalan number

430s

430

430 = 2 × 5 × 43, sphenic number, untouchable number

431

A prime number, Sophie Germain prime, sum of seven consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73),

, prime index prime,

with no imaginary part *It is also the fourth Leyland number#Leyland number of the second kind, Leyland prime of the second kind. *The distance between Earth and the star Polaris in light years. *Area code 431 is a telephone area code for Manitoba, Canada.

432

432 = 2⁴ × 3³ = 4² × 3³, the sum of four consecutive primes (103 + 107 + 109 + 113), a Harshad number, a highly totient number, an Achilles number and the sum of totient function for first 37 integers. 432! is the first factorial that is not a

in base 10. 432 is also three-dozen sets of a dozen, making it three gross. An equilateral triangle whose area and perimeter are equal, has an area (and perimeter) equal to

\sqrt

433

A prime number, Markov number, star number. * The perfect score in the game show ''Fifteen To One'', only ever achieved once in over 2000 shows. * 433 can refer to composer John Cage's composition 4′33″ (pronounced "Four minutes, thirty-three seconds" or just "Four thirty-three").

434

434 = 2 × 7 × 31, sphenic number, sum of six consecutive primes (61 + 67 + 71 + 73 + 79 + 83), nontotient, maximal number of pieces that can be obtained by cutting an annulus with 28 cuts

435

435 = 3 × 5 × 29, sphenic number, triangular number, hexagonal number, self number, number of compositions of 16 into distinct parts * The number of members in the US House of Representatives.

436

436 = 2² × 109, nontotient, noncototient, lazy caterer number

437

437 = 19 × 23, Blum integer

438

438 = 2 × 3 × 73, sphenic number, Smith number. *The "438 match" or "438 game" has been used by cricket media to describe Fifth ODI, Australian cricket team in South Africa in 2005–06, the famous 2006 One Day International in which Australia national cricket team, Australia scored a world record 434 in their innings, only to see South Africa national cricket team, South Africa respond in their innings with 438.

439

A prime number, sum of three consecutive primes (139 + 149 + 151), sum of nine consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), strictly non-palindromic number

440s

440

440 = 2³ × 5 × 11, the sum of the first seventeen prime numbers, Harshad number, *in hertz, the Concert pitch, standard frequency to which most orchestras tune the pitch A above middle C. A few orchestras tune slightly flatter or sharper than this.

441

441 = 3² × 7² = 21² * 441 is the sum of the cubes of the first 6 natural numbers (441 = 1³ + 2³ + 3³ + 4³ + 5³ + 6³). * 441 is a centered octagonal number, a refactorable number, and a Harshad number. * 441 is the number of squares on a Super Scrabble board.

442

442 = 2 × 13 × 17 = 21² + 1, sphenic number, sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71)

443

A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, Mertens function sets new low of -9, which stands until 659. *In computing, it is the default port for HTTP Secure, HTTPS connections.

444

444 = 2² × 3 × 37, refactorable number,

, number of polyiamond, noniamonds without holes. * The title of the final track of Autechre's 1993 debut album Incunabula (album), ''Incunabula''. *The 444th Fighter Squadron "Spare", a fictional air squadron in ''Ace Combat 7: Skies Unknown''.

445

445 = 5 × 89, number of series-reduced trees with 17 nodes

446

446 = 2 × 223, nontotient, self number

447

447 = 3 × 149, number of 1's in all partitions of 22 into odd parts * The flight number of Air France Flight 447

448

448 = 2⁶ × 7, untouchable number, refactorable number, Harshad number

449

A prime number, sum of five consecutive primes (79 + 83 + 89 + 97 + 101), Chen prime, Eisenstein prime with no imaginary part, Proth prime. Also the largest number whose factorial is less than 10¹⁰⁰⁰

450s

450

450 = 2 × 3² × 5², nontotient, sum of totient function for first 38 integers, refactorable number, Harshad number, *SMTP code meaning the requested mail action was not carried out. *A perfect score in Canadian five-pin bowling. *An Area codes 450 and 579, area code in Southern Quebec.

451

451 = 11 × 41; 451 is a Wedderburn–Etherington number and a centered decagonal number; its reciprocal has period 10; 451 is the smallest number with this period reciprocal length. *The novel ''Fahrenheit 451'' refers to the temperature in Fahrenheit that author Ray Bradbury understood to be the autoignition point of paper. *HTTP status code for "HTTP 451, Unavailable For Legal Reasons" a HTTP response error when the user requests an illegal resource, such as a web page censored by a government.

452

452 = 2² × 113, number of surface-points of a tetrahedron with edge-length 15 *SMTP code meaning that the requested mail action was not carried out because of insufficient system storage

453

453 = 3 × 151, Blum integer

454

454 = 2 × 227, nontotient, a Smith number

455

455 = 5 × 7 × 13,

, tetrahedral number *''455 Rocket'' is the title of a song by Kathy Mattea *455 kHz is a standard intermediate frequency for analog superheterodyne AM broadcast band receivers. *The sum of the squares of the first 455 primes is divisible by 455.

456

456 = 2³ × 3 × 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), centered pentagonal number, icosahedral number * In the TV show Torchwood: Children of Earth, the antagonists were an alien species with the designation 456. * Number of contestants in the South Korean Netflix drama ''Squid Game''.

457

* A prime number, sum of three consecutive primes (149 + 151 + 157), self number. * The international standard frequency for radio avalanche transceivers (457 kHz).

458

458 = 2 × 229, nontotient, number of partitions of 24 into divisors of 24

459

459 = 3³ × 17, triangular matchstick number *459 West 18th Street, a residential building at that address in Manhattan's Chelsea, Manhattan, West Chelsea neighborhood, built in 2008.

460s

460

460 = 2² × 5 × 23, centered triangular number, dodecagonal number,

, sum of twelve consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61)

461

A prime number, Chen prime, sexy prime with 467, Eisenstein prime with no imaginary part, prime index prime

462

462 = 2 × 3 × 7 × 11, binomial coefficient

\tbinom 5

, stirling number of the second kind

\left\

, sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89), pronic number, sparsely totient number, idoneal number

463

A prime number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79), centered heptagonal number, *Number of days in the synodic period of Ceres (dwarf planet), Ceres *A common baseball double play (see baseball positions) *A single by Buck 65, named after the baseball term

464

464 = 2⁴ × 29, primitive abundant number, since 464 = 21² + 21 + 2 it is the maximum number of regions into which 2
intersecting circles divide the plane
maximal number of pieces that can be obtained by cutting an annulus with 29 cuts * In chess it is the number of legal positions of the kings, not counting mirrored positions. Has some importance when constructing an endgame tablebase. * Model number of the home computer Amstrad CPC 464.

465

465 = 3 × 5 × 31,

, triangular number, member of the Padovan sequence, Harshad number

466

466 = 2 × 233, noncototient, lazy caterer number

467

A prime number, safe prime, sexy prime with 461, Chen prime, Eisenstein prime with no imaginary part :

\sum_^^

is prime

468

468 = 2² × 3² × 13, sum of ten consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), refactorable number, self number, Harshad number

469

469 = 7 × 67, centered hexagonal number. 469! - 1 is prime.

470s

470

470 = 2 × 5 × 47, sphenic number, nontotient, noncototient, cake number * In golf, 470 is the minimum length in yards from the tee to the hole on a Par 5. * 470 (dinghy), 470 is an Olympic class of sailing dinghy

471

471 = 3 × 157, sum of three consecutive primes (151 + 157 + 163), perfect totient number, φ(471) = φ(σ(471)).

472

472 = 2³ × 59, nontotient, untouchable number, refactorable number, number of distinct ways to cut a 5 × 5 square into squares with integer sides *The Amstrad CPC472 was a short-lived home computer for the Spanish market.

473

473 = 11 × 43, sum of five consecutive primes (83 + 89 + 97 + 101 + 103), Blum integer

474

474 = 2 × 3 × 79, sphenic number, sum of eight consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73), nontotient, noncototient, sum of totient function for first 39 integers, untouchable number, nonagonal number

475

475 = 5² × 19, 49-polygonal number, gonal number, member of the Mian–Chowla sequence.

476

476 = 2² × 7 × 17,

, admirable number

477

477 = 3² × 53, pentagonal number

478

478 = 2 × 239, Pell number#Pell–Lucas_numbers, Companion Pell number, number of partitions of 26 that do not contain 1 as a part

479

A prime number, safe prime, sum of nine consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71), Chen prime, Eisenstein prime with no imaginary part, self number * Also an area code in area code 479, the U.S. state of Arkansas.

480s

480

480 = 2⁵ × 3 × 5, sum of a twin prime (239 + 241), sum of four consecutive primes (109 + 113 + 127 + 131), highly totient number, refactorable number, Harshad number :

\sum_^^

is prime

481

481 = 13 × 37, octagonal number, centered square number, Harshad number

482

482 = 2 × 241, nontotient, noncototient, number of series-reduced planted trees with 15 nodes

483

483 = 3 × 7 × 23, sphenic number, Smith number

484

484 = 2² × 11² = 22², palindromic square, nontotient

485

485 = 5 × 97, number of triangles (of all sizes, including holes) in Sierpiński's triangle after 5 inscriptions * RS-485

486

486 = 2 × 3⁵, Harshad number, Perrin number * Shorthand for the Intel 80486 microprocessor chip.

487

A prime number, sum of three consecutive primes (157 + 163 + 167), Chen prime, * The only primes under 7.74 × 10¹³ that divide their own decimal repetends are 3, 487, and 56598313. * Shorthand for the Intel 80487 floating point processor chip.

488

488 = 2³ × 61, nontotient, refactorable number, φ(488) = φ(σ(488)), number of surface points on a cube with edge-length 10.

489

489 = 3 × 163, octahedral number

490s

490

490 = 2 × 5 × 7², noncototient, sum of totient function for first 40 integers, partition (number theory), partition number (integer partitions of 19), self number. *The Christianity, Christian Gospel of Matthew (Gospel of Matthew, Matthew 18:21-22) says that Jesus told Saint Peter, Peter to forgive his brother "seventy times seven" times when his brother sins against hi

491

A prime number, isolated prime, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number

492

492 = 2² × 3 × 41, sum of six consecutive primes (71 + 73 + 79 + 83 + 89 + 97), refactorable number, member of a Ruth–Aaron pair with 493 under first definition

493

493 = 17 × 29, sum of seven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83), member of a Ruth–Aaron pair with 492 under first definition, the 493d centered octagonal number is also a centered square number

494

494 = 2 × 13 × 19 = eulerian number#Eulerian numbers of the second order,

\left\langle \!\! \left\langle  \right\rangle \!\! \right\rangle

, sphenic number, nontotient

495

495 is a pentatope number.

496

496 is the third perfect number, a number whose divisors add up to the actual number (1+2+4+8+16+31+62+124+248=496).

497

497 = 7 × 71, sum of five consecutive primes (89 + 97 + 101 + 103 + 107), lazy caterer number

498

498 = 2 × 3 × 83, sphenic number, untouchable number, admirable number, abundant number

499

A prime number, isolated prime, Chen prime, oeis:A059801, 4⁴⁹⁹ - 3⁴⁹⁹ is prime

References

{{Authority control Integers