400 (four hundred) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

following 399 and preceding 401.

Mathematical properties

circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...

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 ...

Integers from 401 to 499

400s

401

401 is a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), 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 ...

, tetranacci number,

Chen prime In mathematics, 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 a ...

, prime index prime *

Eisenstein prime In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form : z = a + b\omega , where and are integers and : \omega = \frac ...

with no imaginary part * 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) *

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 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 distinct, for ...

402

402 = 2 × 3 × 67,

sphenic number In number theory, a sphenic number (from , '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. Definition A sphenic ...

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 nontotie ...

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

, number of graphs with 8 nodes and 9 edges *

HTTP status code Hypertext Transfer Protocol (HTTP) response 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, and some additional codes use ...

for "Payment Required". *The

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 landlocked U.S. state, state in the Midwestern United States, Midwestern region of the United States. It borders South Dakota to the north; Iowa to the east and Missouri to the southeast, both across the Missouri River; Ka ...

403

403 = 13 × 31, heptagonal number,

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, if it was correct. Specifications HTTP 403 provides a distinct error case from HTTP 401; whil ...

, 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 organiz ...

. * The area code for southern Alberta.

404

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

noncototient In number theory, a noncototient is a positive integer that cannot be expressed as the difference between a positive integer and the number of coprime integers below it. That is, , where stands for Euler's totient function In number theory ...

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

HTTP 404 In computer network communications, the HTTP 404, 404 not found, 404, 404 error, page not found, or file not found error message is a hypertext transfer protocol (HTTP) standard response code, to indicate that the browser was able to comm ...

status code is usually sent from a web page if a user attempts to reach a broken or dead link. It has since become one of the most commonly reached, and thus most recognizable errors on the World Wide Web. * 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 Protectio ...

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

405

405 = 3⁴ × 5, Mertens function returns 0,

, pentagonal pyramidal number; *

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 List of capitals in the United States, capital and List of municipalities in Oklahoma, most populous city of the U.S. state of Oklahoma. The county seat ...

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 List of regions of California, region that generally comprises the southern portion of the U.S. state of California. Its densely populated coastal reg ...

, known to the local as "The 405". * Sum of all numbers in a standard (3x3)x(3x3)

Sudoku Sudoku (; ; originally called Number Place) is a logic puzzle, logic-based, combinatorics, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and ...

406

406 = 2 × 7 × 29,

, 28th

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 ...

, even nontotient, Narayana's cow number *

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 ...

significance to him, as intimated in the poem. * Peugeot 406 car. *

for all of

Montana Montana ( ) is a landlocked U.S. state, state in the Mountain states, Mountain West subregion of the Western United States. It is bordered by Idaho to the west, North Dakota to the east, South Dakota to the southeast, Wyoming to the south, an ...

407

407 = 11 × 37, *Sum of cubes of 4, 0 and 7 (4³ + 0³ + 7³ = 407); narcissistic number *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 commonly refers to: * Orlando, Florida, a city in the United States Orlando may also refer to: People * Orlando (given name), a masculine name, includes a list of people with the name * Orlando (surname), includes a list of people wit ...

, 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 In mathematics, an octagonal number is a figurate number. The ''n''th octagonal number ''o'n'' is the number of dots in a pattern of dots consisting of the outlines of regular octagons with sides up to ''n'' dots, when the octagons are overlai ...

Untouchable number In mathematics, an untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer. That is, these numbers are not in the image of the aliquot sum function. Their study goes back at l ...

*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. This is also t ...

. *A family of cleaning products, Formula 409 *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 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 their f ...

, inspired by the above engine *

for "Conflict" *A

Green Day Green Day is an American Rock music, rock band formed in Rodeo, California, in 1987 by lead vocalist and guitarist Billie Joe Armstrong and bassist and backing vocalist Mike Dirnt, with drummer Tré Cool joining in 1990. In 1994, their majo ...

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

for the corner of southeastern Texas *

Venice Venice ( ; ; , formerly ) is a city in northeastern Italy and the capital of the Veneto Regions of Italy, region. It is built on a group of 118 islands that are separated by expanses of open water and by canals; portions of the city are li ...

has 409 bridges. *A

Bullet For My Valentine Bullet for My Valentine, often abbreviated as BFMV, are a Welsh heavy metal band from Bridgend, formed in 1998. The band is currently composed of Matthew Tuck (vocals, rhythm guitar), Michael Paget (lead guitar), Jason Bowld (drums) and J ...

song, "Room 409", from the album '' The Poison'' *

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 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, 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). It is part of the larger ...

and the Eastern Shore.

411

411 = 3 × 137, self number, *

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

FM broadcasting FM broadcasting is a method of radio broadcasting that uses frequency modulation (FM) of the radio broadcast carrier wave. Invented in 1933 by American engineer Edwin Armstrong, wide-band FM is used worldwide to transmit high fidelity, high-f ...

frequencies between 87.50 and 108.00

MHz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base u ...

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 Allegheny County, Pennsylvania, United States, and its county seat. It is the List of municipalities in Pennsylvania#Municipalities, second-most populous city in Pennsylvania (after Philadelphia) and the List of Un ...

Pennsylvania Pennsylvania, officially the Commonwealth of Pennsylvania, is a U.S. state, state spanning the Mid-Atlantic (United States), Mid-Atlantic, Northeastern United States, Northeastern, Appalachian, and Great Lakes region, Great Lakes regions o ...

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

Stan Freberg Stan Freberg (born Stanley Friberg; August 7, 1926 – April 7, 2015) was an American actor, author, comedian, musician, puppeteer, radio personality and advertising creative director. His best-known works include " St. George and the Dragonet ...

413

413 = 7 × 59,

returns 0, self number,

Blum integer In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/talks/ ...

for "Request Entity Too Large" * Area code for

Western Massachusetts Western Massachusetts, known colloquially as "western Mass," is a region in Massachusetts, one of the six U.S. states that make up the New England region of the United States. Western Massachusetts has diverse topography; 22 colleges and univ ...

. *An important and recurring number in the

webcomic Webcomics (also known as online comics or Internet comics) are comics published on the internet, such as on a website or a mobile app. While many webcomics are published exclusively online, others are also published in magazines, newspapers, or ...

Homestuck ''Homestuck'' is an Internet fiction series created by American author and artist Andrew Hussie. The fourth and best-known of Hussie's four ''MS Paint Adventures'', it originally ran from April 13, 2009, to April 13, 2016. Though normally describ ...

by Andrew Hussie.

414

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

\sum_^^

is prime *

for "Request-URI Too Long" *

for

Milwaukee Milwaukee is the List of cities in Wisconsin, most populous city in the U.S. state of Wisconsin. Located on the western shore of Lake Michigan, it is the List of United States cities by population, 31st-most populous city in the United States ...

, Wisconsin. *

The 414s The 414s were a group of computer hackers from Milwaukee who broke into dozens of high-profile computer systems, including ones at Los Alamos National Laboratory, Sloan-Kettering Cancer Center, and Security Pacific National Bank, in 1982 and 1 ...

, a group of hackers from Milwaukee, Wisconsin.

415

415 = 5 × 83, logarithmic number *

for "Unsupported Media Type" *

415 Records 415 Records was a San Francisco record label created in 1978. The label focused its efforts on local punk rock and new wave music acts of the late 1970s through the late 1980s, including The Offs, The Nuns, The Units, Romeo Void, and Wire Tra ...

, a record label * 415 refers to California

Penal Code A criminal code or penal code is a document that compiles all, or a significant amount of, a particular jurisdiction's criminal law. Typically a criminal code will contain Crime, offences that are recognised in the jurisdiction, penalties that ...

, 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

*

for "Requested Range Not Satisfiable" *416 is also a nickname for the city of

Toronto Toronto ( , locally pronounced or ) is the List of the largest municipalities in Canada by population, most populous city in Canada. It is the capital city of the Provinces and territories of Canada, Canadian province of Ontario. With a p ...

, based on the area code it used before

overlay plan In telecommunications, an area code overlay complex is a telephone numbering plan that assigns multiple area codes to the same geographic numbering plan area (NPA). Area code overlays are implemented in territories of the North American Numbe ...

s added two more area codes.

417

417 = 3 × 139,

for "Expectation Failed". Also the area code for southwestern Missouri, including Springfield, and Joplin.

418

418 = 2 × 11 × 19;

, balanced number. It is also the fourth 71- gonal number. * The sum of the integers between 13 and 31, inclusive. * The product of its digits as well as the sum of its prime factors are both 32. Also, 131, a strong concatenation of 13 and 31, is the 32nd prime number (while the 32nd composite number is 48). * The sum of the 84 digits of the 22nd unique prime in

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of th ...

(having a very distinct set of digits than all other known terms in the

sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is cal ...

). * The number of Abrahadabra *

Hyper Text Coffee Pot Control Protocol The Hyper Text Coffee Pot Control Protocol (HTCPCP) is a facetious communication protocol for controlling, monitoring, and diagnosing coffee pots. It is specified in , published on 1 April 1998 as an April Fools' Day RFC, as part of an April F ...

status code for "Teapot" as an April Fools' joke.

419

A prime number,

Sophie Germain prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +&nbs ...

, 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) *The Area Code for Toledo, OH and other surrounding areas.

420s

420

421

* A prime number, sum of five consecutive primes (73 + 79 + 83 + 89 + 97),

centered square number In elementary number theory, a centered square number is a Centered polygonal number, centered figurate number that gives the number of dots in a Square (geometry), square with a dot in the center and all other dots surrounding the center dot i ...

, also

SMTP The Simple Mail Transfer Protocol (SMTP) is an Internet standard communication protocol for electronic mail transmission. Mail servers and other message transfer agents use SMTP to send and receive mail messages. User-level email clients typi ...

code meaning the transmission channel will be closing *

Country calling code Telephone country codes are telephone number prefixes for reaching subscribers in foreign countries or areas by international direct dialing (IDD). Country codes are defined by the International Telecommunication Union (ITU) in ITU-T standards ...

for

Slovakia Slovakia, officially the Slovak Republic, is a landlocked country in Central Europe. It is bordered by Poland to the north, Ukraine to the east, Hungary to the south, Austria to the west, and the Czech Republic to the northwest. Slovakia's m ...

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 *

for

Liechtenstein Liechtenstein (, ; ; ), officially the Principality of Liechtenstein ( ), is a Landlocked country#Doubly landlocked, doubly landlocked Swiss Standard German, German-speaking microstate in the Central European Alps, between Austria in the east ...

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 A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n with \tau(n)=\sigma_0(n)=\prod_^(e_i+1) for n=\prod_^np_i^. The first few refact ...

, self number

425

425 = 5² × 17,

pentagonal number A pentagonal number is a figurate number that extends the concept of triangular number, triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotational ...

centered tetrahedral number In mathematics, a centered tetrahedral number is a centered figurate number that represents a tetrahedron In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangul ...

, 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.

426

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

untouchable number In mathematics, an untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer. That is, these numbers are not in the image of the aliquot sum function. Their study goes back at l ...

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 The Catalan numbers are a sequence of natural numbers that occur in various Enumeration, counting problems, often involving recursion, recursively defined objects. They are named after Eugène Charles Catalan, Eugène Catalan, though they were p ...

430s

430

430 = 2 × 5 × 43, number of primes below 3000, sphenic number, untouchable number

431

A prime number,

, 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 prime of the second kind. *

Area code 431 Year 431 ( CDXXXI) was a common year starting on Thursday of the Julian calendar. At the time, it was known as the Year of the Consulship of Bassus and Antiochus (or, less frequently, year 1184 ''Ab urbe condita''). The denomination 431 for ...

is a telephone area code for

Manitoba Manitoba is a Provinces and territories of Canada, province of Canada at the Centre of Canada, longitudinal centre of the country. It is Canada's Population of Canada by province and territory, fifth-most populous province, with a population ...

, 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 A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation :x^2 + y^2 + z^2 = 3xyz,\, studied by . The first few Markov numbers are :1 (number), 1, 2 (number), ...

star number In mathematics, a star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on. The ''n''th star number is given by the formula ''Sn'' = 6''n''(''n' ...

. * 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 John Milton Cage Jr. (September 5, 1912 – August 12, 1992) was an American composer and music theorist. A pioneer of indeterminacy in music, electroacoustic music, and Extended technique, non-standard use of musical instruments, Cage was one ...

's composition

4′33″ ''4′33″'' is a Modernism (music), modernist composition by American experimental music, experimental composer John Cage. It was composed in 1952 for any instrument or combination of instruments; the score instructs performers not to play t ...

(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, 29th

hexagonal number A hexagonal number is a figurate number. The ''n''th hexagonal number ''h'n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so ...

, self number, number of compositions of 16 into distinct parts * The number of members in the

US House of Representatives The United States House of Representatives is a chamber of the bicameral United States Congress; it is the lower house, with the U.S. Senate being the upper house. Together, the House and Senate have the authority under Article One of th ...

436

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

437

437 = 19 × 23,

438

438 = 2 × 3 × 73, sphenic number,

Smith number In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free, the ...

. *The "438 match" or "438 game" has been used by cricket media to describe the famous 2006 One Day International in which

Australia Australia, officially the Commonwealth of Australia, is a country comprising mainland Australia, the mainland of the Australia (continent), Australian continent, the island of Tasmania and list of islands of Australia, numerous smaller isl ...

scored a world record 434 in their innings, only to see

South Africa South Africa, officially the Republic of South Africa (RSA), is the Southern Africa, southernmost country in Africa. Its Provinces of South Africa, nine provinces are bounded to the south by of coastline that stretches along the Atlantic O ...

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

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 centered octagonal number is a centered number, centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are th ...

, 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

HTTPS Hypertext Transfer Protocol Secure (HTTPS) is an extension of the Hypertext Transfer Protocol (HTTP). It uses encryption for secure communication over a computer network, and is widely used on the Internet. In HTTPS, the communication protoc ...

connections.

444

444 = 2² × 3 × 37, refactorable number,

, number of noniamonds without holes, and 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". Ex ...

. * The title of the final track of

Autechre Autechre ( ) are an English electronic music duo consisting of Rob Brown and Sean Booth, both from Rochdale, Greater Manchester. Formed in 1987, they are among the best known acts signed to UK electronic label Warp Records, through which all o ...

's 1993 debut 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 Air France Flight 447 was a scheduled international passenger flight from Rio de Janeiro/Galeão International Airport, Rio de Janeiro, Brazil, to Charles de Gaulle Airport, Paris, France. On 1 June 2009, inconsistent airspeed indications and mi ...

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 In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times ...

is less than 10¹⁰⁰⁰

450s

450

450 = 2 × 3² × 5², nontotient, sum of totient function for first 38 integers, refactorable number, Harshad number, *

code meaning the requested mail action was not carried out. *A perfect score in Canadian

five-pin bowling Five-pin bowling is a bowling variant which is played in Canada, where many bowling alleys offer it, either alone or in combination with ten-pin bowling. It was devised around 1909 by Thomas F. Ryan in Toronto, Ontario, at his Toronto Bowling Clu ...

. *An

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 Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics, defined as the reciprocal of length. Common units used for this measurement include the reciprocal metre or inverse metre (symbo ...

. *The novel ''

Fahrenheit 451 ''Fahrenheit 451'' is a 1953 Dystopian fiction, dystopian novel by American writer Ray Bradbury. It presents a future American society where books have been outlawed and "firemen" Book burning, burn any that are found. The novel follows in the ...

'' refers to the temperature in

Fahrenheit The Fahrenheit scale () is a scale of temperature, temperature scale based on one proposed in 1724 by the German-Polish physicist Daniel Gabriel Fahrenheit (1686–1736). It uses the degree Fahrenheit (symbol: °F) as the unit. Several accou ...

that author

Ray Bradbury Ray Douglas Bradbury ( ; August 22, 1920June 5, 2012) was an American author and screenwriter. One of the most celebrated 20th-century American writers, he worked in a variety of genres, including fantasy, science fiction, Horror fiction, horr ...

understood to be the autoignition point of

paper Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, Textile, rags, poaceae, grasses, Feces#Other uses, herbivore dung, or other vegetable sources in water. Once the water is dra ...

. **By extension, The numbers "451", and sometimes "0451", are often included as the first security code a player encounters in

Immersive sim An immersive sim (simulation) is a video game genre that emphasizes player choice. Its core, defining trait is the use of simulated systems that respond to a variety of player actions which, combined with a comparatively broad array of player a ...

video games as a reference to the

System Shock ''System Shock'' is a 1994 first-person action-adventure game, action-adventure video game developed by LookingGlass Technologies and published by Origin Systems. It was directed by Doug Church with Warren Spector serving as producer. The game ...

series of games which first included the code as their own reference to Bradbury's novel. *

for " 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,

454

454 = 2 × 227, nontotient, a

455

455 = 5 × 7 × 13,

tetrahedral number A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid (geometry), pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular ...

*''455 Rocket'' is the title of a song by

Kathy Mattea Kathleen Alice Mattea (born June 21, 1959) is an American country music and bluegrass singer. Active since 1984 as a recording artist, she has charted more than 30 singles on the ''Billboard'' Hot Country Songs charts, including four that reac ...

*455 kHz is a standard

intermediate frequency In communications and electronic engineering, an intermediate frequency (IF) is a frequency to which a carrier wave is shifted as an intermediate step in Transmission (telecommunications), transmission or reception. The intermediate frequency is ...

for analog

superheterodyne A superheterodyne receiver, often shortened to superhet, is a type of radio receiver that uses frequency mixing to convert a received signal to a fixed intermediate frequency (IF) which can be more conveniently processed than the original car ...

AM broadcast AM broadcasting is radio broadcasting using amplitude modulation (AM) transmissions. It was the first method developed for making audio radio transmissions, and is still used worldwide, primarily for medium wave (also known as "AM band") transmi ...

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 In mathematics, a centered pentagonal number is a centered polygonal number, centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered p ...

, icosahedral number * In the TV show '' Torchwood: Children of Earth'', the antagonists were an alien species with the designation 456. * One of the two values of the

magical formula In ceremonial magic, a magical formula or a word of power is a word that is believed to have specific supernatural effects. They are words whose meaning illustrates principles and degrees of understanding that are often difficult to relay ...

IPSOS Ipsos Group S.A. (; derived from the Latin expression, ) is a multinational market research and consulting firm with headquarters in Paris, France. The company was founded in 1975 by Didier Truchot, Chairman of the company, and has been publ ...

, the other being 696. * Number of contestants in the South Korean

Netflix Netflix is an American subscription video on-demand over-the-top streaming service. The service primarily distributes original and acquired films and television shows from various genres, and it is available internationally in multiple lang ...

drama ''

Squid Game ''Squid Game'' () is a South Korean Utopian and dystopian fiction, dystopian Survival film, survival Thriller (genre)#Television, thriller horror television series created, written and directed by Hwang Dong-hyuk for Netflix. The series revol ...

''.

457

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

avalanche transceiver An avalanche transceiver or avalanche beacon is a type of emergency locator beacon, a radio transceiver (a transmitter and receiver in one unit) operating at 457 kHz for the purpose of finding people buried under snow. They are widely carrie ...

s (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 Manhattan ( ) is the most densely populated and geographically smallest of the Boroughs of New York City, five boroughs of New York City. Coextensive with New York County, Manhattan is the County statistics of the United States#Smallest, larg ...

's 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 In number theory, sexy primes are prime numbers that differ from each other by . For example, the numbers and are a pair of sexy primes, because both are prime and 11 - 5 = 6. The term "sexy prime" is a pun stemming from the Latin word for six ...

with 467, Eisenstein prime with no imaginary part, prime index prime

462

462 = 2 × 3 × 7 × 11,

binomial coefficient In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ...

\tbinom 5

, stirling number of the second kind

\left\

, sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89),

pronic number A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular 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 A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by ...

. This number is the first of seven consecutive primes that are one less than a multiple of 4 (from 463 to 503). *Number of days in the

synodic period The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, ...

of Ceres *A common baseball

double play In baseball and softball, a double play (denoted as DP in baseball statistics) is the act of making two outs during the same continuous play. Double plays can occur any time there is at least one baserunner and fewer than two outs. In Major Le ...

(see

baseball positions In the sport of baseball, each of the nine players on a team is assigned a particular fielding position when it is their turn to play defense. Each position conventionally has an associated number, for use in scorekeeping by the official scorer ...

) *A single by

Buck 65 Richard Terfry (born March 4, 1972), better known by his stage name Buck 65, is a Canadian alternative hip hop rapper. Underpinned by an extensive background in abstract hip hop, his more recent music has extensively incorporated blues, country ...

, 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 Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arran ...

it is the number of legal positions of the kings, not counting mirrored positions. Has some importance when constructing an

endgame tablebase In chess, the endgame tablebase, or simply the tablebase, is a computerised database containing precalculated evaluations of chess endgame, endgame positions. Tablebases are used to analyse finished games, as well as by chess engines to evaluate ...

. * Model number of the home computer

Amstrad CPC 464 The CPC 464 is the first personal home computer built by Amstrad. Released in 1984, it was the first entry in the Amstrad CPC family of home computers. The CPC 464 was one of the bestselling and best produced microcomputers, with more than 2 mil ...

465

465 = 3 × 5 × 31,

, 30th

, member of the Padovan sequence, Harshad number

466

466 = 2 × 233, noncototient, lazy caterer number.

467

A prime number,

safe prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +&nbs ...

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 In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered polygonal number, centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot ...

. 469! - 1 is prime.

470s

470

470 = 2 × 5 × 47, sphenic number, nontotient, noncototient, cake number * In

golf Golf is a club-and-ball sport in which players use various Golf club, clubs to hit a Golf ball, ball into a series of holes on a golf course, course in as few strokes as possible. Golf, unlike most ball games, cannot and does not use a standa ...

, 470 is the minimum length in yards from the tee to the hole on a Par 5. * 470 is an Olympic class of sailing

dinghy A dinghy is a type of small boat, often carried or Towing, towed by a Watercraft, larger vessel for use as a Ship's tender, tender. Utility dinghies are usually rowboats or have an outboard motor. Some are rigged for sailing but they diffe ...

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),

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- gonal number, member of the Mian–Chowla sequence.

476

476 = 2² × 7 × 17,

, admirable number

477

477 = 3² × 53,

478

478 = 2 × 239, 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 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,

largely composite number A highly composite number is a positive integer that has more divisors than all smaller positive integers. If ''d''(''n'') denotes the number of divisors of a positive integer ''n'', then a positive integer ''N'' is highly composite if ''d''(' ...

\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 RS-485, also known as TIA-485(-A) or EIA-485, is a standard, originally introduced in 1983, defining the electrical characteristics of drivers and receivers for use in serial communications systems. Electrical signaling is balanced, and Telecomm ...

486

486 = 2 × 3⁵, Harshad number,

Perrin number In mathematics, the Perrin numbers are a doubly infinite constant-recursive sequence, constant-recursive integer sequence with Characteristic equation (calculus), characteristic equation . The Perrin numbers, named after the French engineer , bear ...

* Shorthand for the

Intel 80486 The Intel 486, officially named i486 and also known as 80486, is a microprocessor introduced in 1989. It is a higher-performance follow-up to the i386, Intel 386. It represents the fourth generation of binary compatible CPUs following the Inte ...

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 In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The th octahedral number O_n can be obtained by the formula:. :O_n=. The first few octahedral ...

490s

490

490 = 2 × 5 × 7², noncototient, sum of totient function for first 40 integers, number of

integer partition In number theory and combinatorics, a partition of a non-negative integer , also called an integer partition, is a way of writing as a summation, sum of positive integers. Two sums that differ only in the order of their summands are considered ...

s of 19, self number. *A (possibly arbitrary) large number in the

Christian A Christian () is a person who follows or adheres to Christianity, a Monotheism, monotheistic Abrahamic religion based on the life and teachings of Jesus in Christianity, Jesus Christ. Christians form the largest religious community in the wo ...

Gospel of Matthew The Gospel of Matthew is the first book of the New Testament of the Bible and one of the three synoptic Gospels. It tells the story of who the author believes is Israel's messiah (Christ (title), Christ), Jesus, resurrection of Jesus, his res ...

. In Matthew 18:21–35,

Jesus Jesus (AD 30 or 33), also referred to as Jesus Christ, Jesus of Nazareth, and many Names and titles of Jesus in the New Testament, other names and titles, was a 1st-century Jewish preacher and religious leader. He is the Jesus in Chris ...

tells the

Parable of the Unforgiving Servant The Parable of the Unforgiving Servant (also known as ''Unforgiving Creditor'', ''Ungrateful Servant'', ''Unmerciful Servant'', or ''Wicked Servant'' but not to be confused with the parable of the Two Debtors) is a parables of Jesus, parable of J ...

, instructing

Peter Peter may refer to: People * List of people named Peter, a list of people and fictional characters with the given name * Peter (given name) ** Saint Peter (died 60s), apostle of Jesus, leader of the early Christian Church * Peter (surname), a su ...

to forgive his brother "seventy times seven" times when his brother sins against hi

491

A prime number, isolated 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 =

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

, sphenic number, nontotient

495

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, 4⁴⁹⁹ - 3⁴⁹⁹ is prime

References

{{Authority control Integers