400 (number) - AbsoluteAstronomy.com

400 is the natural number

Natural number

In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

following 399 and preceding 401. (For the year 400 AD, see 400)

Mathematical properties

400 is the square

Square number

In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...

of 20

20 (number)

20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems....

.

A circle

Circle

A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....

is divided into 400 grads

Grad (angle)

The gradian is a unit of plane angle, equivalent to of a turn. It is also known as gon, grad, or grade . One grad equals of a degree or of a radian...

, which is equal to 360 degree

Degree (angle)

A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

s and 2π radian

Radian

Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

s. (Degrees and radians are the SI

International System of Units

The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

accepted units).

400 is a self number

Self number

A self number, Colombian number or Devlali number is an integer which, in a given base, cannot be generated by any other integer added to the sum of that other integer's digits. For example, 21 is not a self number, since it can be generated by the sum of 15 and the digits comprising 15, that is,...

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

Harshad number

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 were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...

Other fields

Four hundred is also

The Four Hundred (oligarchy) of ancient Athens
Athens
Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...

.
an HTTP status code 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
Ward McAllister
Samuel Ward McAllister was the self-appointed arbiter of New York society from the 1860s to the early 1890s.-Life and career:...

), leading to the generation of such lists as the Forbes 400
Forbes 400
The Forbes 400 or 400 Richest Americans is a list published by Forbes Magazine magazine of the wealthiest 400 Americans, ranked by net worth. The list is published annually in September, and 2010 marks the 29th issue. The 400 was started by Malcom Forbes in 1982 and treats those in the list like...
The Atari 400
Atari 8-bit family
The Atari 8-bit family is a series of 8-bit home computers manufactured from 1979 to 1992. All are based on the MOS Technology 6502 CPU and were the first home computers designed with custom coprocessor chips...

home computer.
A former limited stop bus route which operated from Bolton
Bolton
Bolton is a town in Greater Manchester, in the North West of England. Close to the West Pennine Moors, it is north west of the city of Manchester. Bolton is surrounded by several smaller towns and villages which together form the Metropolitan Borough of Bolton, of which Bolton is the...

to Stockport
Stockport
Stockport is a town in Greater Manchester, England. It lies on elevated ground southeast of Manchester city centre, at the point where the rivers Goyt and Tame join and create the River Mersey. Stockport is the largest settlement in the metropolitan borough of the same name...

and Manchester Airport 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
The 400 Blows is a 1959 French film directed by François Truffaut. One of the defining films of the French New Wave, it displays many of the characteristic traits of the movement. The story revolves around Antoine Doinel, an ordinary adolescent in Paris, who is thought by his parents and teachers...

), a French film directed by François Truffaut
François Truffaut
François Roland Truffaut was an influential film critic and filmmaker and one of the founders of the French New Wave. In a film career lasting over a quarter of a century, he remains an icon of the French film industry. He was also a screenwriter, producer, and actor working on over twenty-five...

.
A Lebanese card game. 400 (card game)
400 (card game)
400 is a Lebanese trick-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 designation for a class of Ontario
Ontario
Ontario is a province of Canada, located in east-central Canada. It is Canada's most populous province and second largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa....

highways called 400-Series Highways
400-series highways (Ontario)
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 System in the United States or the British Motorway...

.
The 400
Twin Cities 400
The 400 was a named passenger train operated by the Chicago and North Western Railway between Chicago and Saint Paul, with a final stop in Minneapolis...

, later the Twin Cities 400, a Chicago and North Western Railway
Chicago and North Western Railway
The Chicago and North Western Transportation Company was a Class I railroad in the Midwest United States. It was also known as the North Western. The railroad operated more than of track as of the turn of the 20th century, and over of track in seven states before retrenchment in the late 1970s...

passenger train that traveled 400 miles between Minneapolis/St. Paul and Chicago, Illinois in 400 minutes.
The yard number of the RMS Olympic
RMS Olympic
RMS Olympic was the lead ship of the Olympic-class ocean liners built for the White Star Line, which also included Titanic and Britannic...

, 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
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...

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

Integers from 401 to 499

401 prime number

Prime number

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

, 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

Chen prime

A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes. The even number 2p + 2 therefore satisfies Chen's theorem....

, Eisenstein prime

Eisenstein prime

In mathematics, an Eisenstein prime is an Eisenstein integerz = a + b\,\omega\qquadthat is irreducible in the ring-theoretic sense: its only Eisenstein divisors are the units , a + bω itself and its associates.The associates and the complex conjugate...

with no imaginary part, Mertens function returns 0, member of the Mian–Chowla sequence. Also HTTP status code for an unauthorized request, area code for Rhode Island

Rhode Island

The state of Rhode Island and Providence Plantations, more commonly referred to as Rhode Island , is a state in the New England region of the United States. It is the smallest U.S. state by area...

, also in the name of a retirement plan, 401(k)

401(k)

A 401 is a type of retirement savings account in the United States, which takes its name from subsection of the Internal Revenue Code . A contributor can begin to withdraw funds after reaching the age of 59 1/2 years...

. Stephen Colbert

Stephen Colbert

Stephen Tyrone Colbert is an American political satirist, writer, comedian, television host, and actor. He is the host of Comedy Central's The Colbert Report, a satirical news show in which Colbert portrays a caricatured version of conservative political pundits.Colbert originally studied to be an...

's Formula 401, a "man seed" based product brand his persona on The Colbert Report promotes for sale to the public http://www.wikiality.com/Stephen_Colbert%27s_Formula_400_Series.
----
402 = 2 × 3 × 67, sphenic number

Sphenic number

In number theory, a sphenic number is a positive integer which is the product of three distinct prime numbers.Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic.All...

, nontotient

Nontotient

In number theory, a nontotient is a positive integer n which is not in the range of Euler's totient function φ, that is, for which φ = n has no solution. In other words, n is a nontotient if there is no integer x that has exactly n coprimes below it. All odd numbers are nontotients, except 1,...

, Harshad number

Harshad number

, also HTTP status code for payment required, area code

Area code 402

Image:Area_code_NE.png|right|Map of Nebraska area codes in blue poly 50 20 272 25 291 37 298 32 323 30 340 38 353 50 347 36 354 16 346 7 350 1 47 0 Area code 605...

for Nebraska

Nebraska

Nebraska is a state on the Great Plains of the Midwestern United States. The state's capital is Lincoln and its largest city is Omaha, on the Missouri River....

----
403 = 13 × 31, Mertens function returns 0. Also, HTTP status code for forbidden; also in the name of a retirement plan in the United States, 403(b). The area code

Area code 403

Area code 403 is a telephone area code in the Canadian province of Alberta, encompassing the southern half of the province, including the Calgary area...

for southern Alberta.
----
404 = 2² × 101, Mertens function returns 0, nontotient, noncototient

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 = n, where φ stands for Euler's totient function, has no solution for m...

. Also, HTTP status code for "Not found", perhaps the most famous HTTP status code. Section 404 of the Sarbanes–Oxley Act. One of the three area codes of the Atlanta calling area

Area code 404

Area code 404 covers Atlanta and its immediate neighbors, roughly within Interstate 285.Originally, it covered all of Georgia when the area code system was first created in the 1940s and implemented in 1951. On July 1, 1954, area code 912 was assigned to southern and middle Georgia...

.
----
405 = 3⁴ × 5, Mertens function returns 0, Harshad number; HTTP error code for "Method not allowed". Area code

Area code 405

Area code 405 serves the U.S. state of Oklahoma. It covers the Oklahoma City Metropolitan Area including cities such as Oklahoma City, Edmond, El Reno, Norman, Stillwater, Shawnee, Chickasha, Tuttle, and Moore....

for central Oklahoma, including Oklahoma City

Oklahoma city

Oklahoma City is the capital and largest city of the U.S. state of Oklahoma.Oklahoma City may also refer to:*Oklahoma City metropolitan area*Downtown Oklahoma City*Uptown Oklahoma City*Oklahoma City bombing*Oklahoma City National Memorial...

and surrounding suburbs.
----

406 = 2 × 7 × 29, sphenic number

Sphenic number

, triangular number

Triangular number

A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...

, centered nonagonal number

Centered nonagonal number

A centered nonagonal 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...

, nontotient, and HTTP error code for "Not acceptable".

406 is a poem by John Boyle O'Reilly

John Boyle O'Reilly

John Boyle O'Reilly was an Irish-born poet, journalist and fiction writer. As a youth in Ireland, he was a member of the Irish Republican Brotherhood, or Fenians, for which he was transported to Western Australia...

. 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

Mysticism is the knowledge of, and especially the personal experience of, states of consciousness, i.e. levels of being, beyond normal human perception, including experience and even communion with a supreme being.-Classical origins:...

significance to him, as intimated in the poem.

See also the Peugeot 406

Peugeot 406

The Peugeot 406 was a large family car made by the French automaker Peugeot from 1995 to 2004. Available in saloon, estate and coupé bodystyles with a choice of petrol or turbodiesel engines, the 406 replaced the Peugeot 405 in Peugeot's lineup, and was itself replaced by the Peugeot 407...

car.
----
407 = 11 × 37,

sum of cubes of 4, 0 and 7 (4³ + 0³ + 7³ = 407); narcissistic number
Narcissistic number
In recreational number theory, a narcissistic number is a number that is the sum of its own digits each raised to the power of the number of digits. This definition depends on the base b of the number system used, e.g...
sum of three consecutive primes (131 + 137 + 139)
Mertens function returns 0
Harshad number
Harshad number
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 were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...
HTTP error code for Proxy authentication required
Area code for Orlando
Orlando, Florida
Orlando is a city in the central region of the U.S. state of Florida. It is the county seat of Orange County, and the center of the Greater Orlando metropolitan area. According to the 2010 US Census, the city had a population of 238,300, making Orlando the 79th largest city in the United States...

, Florida

----
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
Pell number
In mathematics, the Pell numbers are an infinite sequence of integers that have been known since ancient times, the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1/1, 3/2, 7/5, 17/12, and 41/29, so the sequence of Pell numbers...
Mertens function returns 0
Octagonal number
Untouchable number
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 ....
Harshad number
HTTP error code for Request timeout
Area code for the Silicon Valley

----
409 is a prime number, Chen prime, centered triangular number

Centered triangular number

A centered triangular number is a centered figurate number that represents a triangle with a dot in the center and all other dots surrounding the center in successive triangular layers...

A family of cleaning products, Formula 409
Formula 409
Formula 409 is a Clorox Company brand of home cleaning products that includes Formula 409 All-Purpose Cleaner, Formula 409 Glass and Surface Cleaner, Formula 409 Carpet Cleaner, and many others....
An engine known as the Chevrolet 409, a 409 cubic inch W-series V8.
The song 409
409 (song)
"409" is a song written by Brian Wilson, Mike Love and Gary Usher for the American rock and roll band, The Beach Boys. The song features Mike Love singing lead vocals. It was originally released as the b-side of the "Surfin' Safari" single...

by The Beach Boys
The Beach Boys
The Beach Boys are an American rock band, formed in 1961 in Hawthorne, California. The group was initially composed of brothers Brian, Dennis and Carl Wilson, their cousin Mike Love, and friend Al Jardine. Managed by the Wilsons' father Murry, The Beach Boys signed to Capitol Records in 1962...

, which was inspired by the above engine.
HTTP error code for Conflict
Green Day
Green Day
Green Day is an American punk rock band formed in 1987. The band consists of lead vocalist and guitarist Billie Joe Armstrong, bassist and backing vocalist Mike Dirnt, and drummer Tre Cool...

have made a song, 409 in Your Coffeemaker, included on their album 1,039/Smoothed Out Slappy Hours
1,039/Smoothed out Slappy Hours
-Track listing:-Origin of tracks:* Tracks 1–10 from 39/Smooth * Tracks 11–14 from the extended play Slappy * Tracks 15–18 from the extended play 1,000 Hours...

.
The area code
Area code 409
Image:Areacode409.svg|right|Map of Texas in blue and area code 409 in redpoly 121 10 199 10 199 69 179 69 173 80 187 88 183 106 162 103 170 116 156 116 141 123 126 110 117 116 Area code 806...

for a part of eastern Texas.
Bullet For My Valentine
Bullet for My Valentine
Bullet for My Valentine are a Welsh heavy metal band from Bridgend, formed in 1998. The band is composed of Matt Tuck , Michael Paget , Jason James , and Michael Thomas . They were formed under the name Jeff Killed John and started their music career by covering songs by Metallica and Nirvana...

has released a song, "Room 409", from the album The Poison
The Poison
The Poison is the debut album by Welsh heavy metal band Bullet for My Valentine. The album was released on October 3, 2005 through Visible Noise Records in the UK, and on February 14, 2006 in the United States through Trustkill Records...

410s

410 = 2 × 5 × 41, sphenic number

Sphenic number

, sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number, HTTP error code for "gone".

Area Code 410, a telephone area code for the US State of Maryland, representing portions of the state including the Baltimore
Baltimore
Baltimore is the largest independent city in the United States and the largest city and cultural center of the US state of Maryland. The city is located in central Maryland along the tidal portion of the Patapsco River, an arm of the Chesapeake Bay. Baltimore is sometimes referred to as Baltimore...

metropolitan area and the Eastern Shore.

----
411 = 3 × 137, self number

Self number

, HTTP error code for "Length required", slang for information (see 4-1-1

4-1-1

4-1-1 is the telephone number for local directory assistance in the United States and Canada. One exception is the Pacific Northwest, which used 1-1-3 until the mid-1980s. Until the early 1980s, 4-1-1 calls were free in most states....

)
----
412 = 2² × 103, nontotient, noncototient, sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), HTTP error code for "Precondition failed", Area code for Pittsburgh, Pennsylvania

Pennsylvania

The Commonwealth of Pennsylvania is a U.S. state that is located in the Northeastern and Mid-Atlantic regions of the United States. The state borders Delaware and Maryland to the south, West Virginia to the southwest, Ohio to the west, New York and Ontario, Canada, to the north, and New Jersey to...

.
----
413 = 7 × 59, Mertens function returns 0, self number, HTTP error code for "Request entity too large", area code for Western Massachusetts

Western Massachusetts

Western Massachusetts is a loosely defined geographical region of the U.S. state of Massachusetts which contains the Berkshires, the Pioneer Valley, and some or all of the Swift River Valley. The region is always considered to include Berkshire, Franklin, Hampshire, and Hampden counties, and the...

.
----
414 = 2 × 3² × 23, Mertens function returns 0, nontotient, Harshad number

Harshad number

, HTTP error code for "Request URI too long", Area code for Milwaukee

Milwaukee, Wisconsin

Milwaukee is the largest city in the U.S. state of Wisconsin, the 28th most populous city in the United States and 39th most populous region in the United States. It is the county seat of Milwaukee County and is located on the southwestern shore of Lake Michigan. According to 2010 census data, the...

, Wisconsin.

The 414s
The 414s
The 414s gained notoriety in the early 1980s as a group of friends and computer hackers who broke into dozens of high-profile computer systems, including ones at Los Alamos National Laboratory, Sloan-Kettering Cancer Center, and Security Pacific Bank....

, a group of hackers from Milwakuee, Wisconsin.

----
415 = 5 × 83, HTTP error code for "unsupported media type"

415 Records
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, Romeo Void, and Wire Train...

, 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
Area code 415
North American Area code 415 is the Californian telephone area code for San Francisco and its northern suburbs .-History:415 was one of the original three area codes in California, established in 1947...

, a telephone area code for San Francisco, California
415 (group), a rap group from Oakland, California

----
416 = 2⁵ × 13, HTTP error code for "Requested Range not satisfiable"

416 is also a nickname for Toronto
Toronto
Toronto is the provincial capital of Ontario and the largest city in Canada. It is located in Southern Ontario on the northwestern shore of Lake Ontario. A relatively modern city, Toronto's history dates back to the late-18th century, when its land was first purchased by the British monarchy from...

, based on its area code

----
417 = 3 × 139, HTTP error code for "Expectation failed". Also the area code for southwestern Missouri, including Springfield

Springfield, Missouri

Springfield is the third largest city in the U.S. state of Missouri and the county seat of Greene County. According to the 2010 census data, the population was 159,498, an increase of 5.2% since the 2000 census. The Springfield Metropolitan Area, population 436,712, includes the counties of...

, and Joplin

Joplin, Missouri

Joplin is a city in southern Jasper County and northern Newton County in the southwestern corner of the US state of Missouri. Joplin is the largest city in Jasper County, though it is not the county seat. As of the 2010 census, the city population was 50,150...

.
----
418 = 2 × 11 × 19, sphenic number the number of Abrahadabra

Abrahadabra

Abrahadabra is a word that first publicly appeared in The Book of the Law, the central sacred text of Thelema. Its author, Aleister Crowley, described it as "the Word of the Aeon, which signifieth The Great Work accomplished." This is in reference to his belief that the writing of Liber Legis ...

, Hyper Text Coffee Pot Control Protocol

Hyper Text Coffee Pot Control Protocol

The Hyper Text Coffee Pot Control Protocol is a protocol for controlling, monitoring, and diagnosing coffee pots.HTCPCP is specified in the jocular RFC 2324, published on 1 April 1998. Although the RFC describing the protocol is an April Fools' Day joke, it specifies the protocol accurately enough...

error code for a teapot.
----
419 prime number, Sophie Germain prime

Sophie Germain prime

In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number...

, Chen prime, Eisenstein prime with no imaginary part, highly cototient number

Highly cototient number

In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above one and has more solutions to the equation...

, Mertens function returns 0, also refers to the Nigerian advance fee fraud

Advance fee fraud

An advance-fee fraud is a confidence trick in which the target is persuaded to advance sums of money in the hope of realizing a significantly larger gain...

scheme (after the section of the Nigerian Criminal Code it violates)

420s

420

420 (number)

420 is the natural number following 419 and preceding 421.420 is the sum of four consecutive primes . 420 is a zero of the Mertens function and is sparsely totient....

has its own article.
----
421 prime number, sum of five consecutive primes (73 + 79 + 83 + 89 + 97), centered square number

Centered square number

In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a...

, also SMTP code meaning the transmission channel will be closing
----
422 = 2 × 211, Mertens function returns 0, nontotient
----
423 = 3² × 47, Mertens function returns 0, Harshad number
----
424 = 2³ × 53, sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Mertens function returns 0, refactorable number

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. The first few refactorable numbers are listed in 1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96...

, self number
----
425 = 5² × 17, sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0
----
426 = 2 × 3 × 71, sphenic number, nontotient, untouchable number
----
427 = 7 × 61, Mertens function returns 0
----
428 = 2² × 107, Mertens function returns 0, nontotient

428: Fūsa Sareta Shibuya de, a video game

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

Catalan number

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involvingrecursively defined objects...

430s

430 = 2 × 5 × 43, sphenic number, untouchable number
----
431 prime number, Sophie Germain prime

Sophie Germain prime

, sum of seven consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73), Chen prime

Chen prime

A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes. The even number 2p + 2 therefore satisfies Chen's theorem....

, Eisenstein prime

Eisenstein prime

with no imaginary part
----
432 sum of four consecutive primes (103 + 107 + 109 + 113), a highly totient number

Highly totient number

A highly totient number k is an integer that has more solutions to the equation φ = k, where φ is Euler's totient function, than any integer below it. The first few highly totient numbers are...

, sum of totient function for first 37 integers and a Harshad number

Harshad number

.
4² x 3³= 3³ x 2⁴ =432. 432 is also three-dozen sets of a dozen, making it three gross.
----
433 prime number, Markov 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 equationx^2 + y^2 + z^2 = 3xyz,\,studied by .The first few Markov numbers are...

, star number

Star number

A star number is a centered figurate number that represents a centered hexagram, such as the one that Chinese checkers is played on.The nth star number is given by the formula 6n + 1...

. The perfect score in the game show Fifteen To One
Fifteen to One
Fifteen to One was a popular general knowledge quiz show broadcast on Channel 4 in the United Kingdom. It ran from 4 January 1988 to 19 December 2003, and had a reputation for being one of the toughest quizzes on TV. Throughout the show's run it was presented and produced by William G. Stewart...

, only ever achieved once in over 2000 shows.
----
434 = 2 × 7 × 31, sphenic number, sum of six consecutive primes (61 + 67 + 71 + 73 + 79 + 83)nontotient
----
435 = 3 × 5 × 29, sphenic number, triangular number, hexagonal number

Hexagonal number

A hexagonal number is a figurate number. The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side.The formula for the nth hexagonal number...

, self number
----
436 = 2² × 109, nontotient, noncototient
----
437 = 19 × 23
----
438 = 2 × 3 × 73, sphenic number, Smith number

Smith number

A Smith number is a composite number for which, in a given base , the sum of its digits is equal to the sum of the digits in its prime factorization. For example, 378 = 2 × 3 × 3 × 3 × 7 is a Smith number since 3 + 7 + 8 =...

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

Australia in South Africa, 5th ODI, 2006

The 5th One Day International cricket match between South Africa and Australia was played on 12 March 2006 at New Wanderers Stadium, Johannesburg. The match broke many cricket records, including both the first and the second team innings score of over 400 runs. Australia won the toss and elected to...

in which Australia scored a world record 434 in their innings, only to see South Africa respond in their innings with 438.
----
439 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 = 2³ × 5 × 11, the sum of the first seventeen prime numbers, Harshad number, also, in hertz

Hertz

The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

, the standard frequency

Concert pitch

Concert pitch refers to the pitch reference to which a group of musical instruments are tuned for a performance. Concert pitch may vary from ensemble to ensemble, and has varied widely over musical history...

to which most orchestra

Orchestra

An orchestra is a sizable instrumental ensemble that contains sections of string, brass, woodwind, and percussion instruments. The term orchestra derives from the Greek ορχήστρα, the name for the area in front of an ancient Greek stage reserved for the Greek chorus...

s tune the pitch A above middle C. A few orchestras tune slightly flatter or sharper than this.
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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
Centered octagonal number
A centered octagonal number is a 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...

, a refactorable number, and a Harshad number.
441 is the number of squares on a Super Scrabble
Super Scrabble
Super Scrabble, introduced in 2004, is a variant of the board game Scrabble. In North America Super Scrabble is manufactured by Winning Moves Games, but licensed by Hasbro. In the rest of the world it is manufactured by Tinderbox Games under license from Mattel. Super Scrabble is available in...

board.

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442 = 2 × 13 × 17, sphenic number, sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71)
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443 prime number, Sophie Germain prime, Chen prime,+ Eisenstein prime with no imaginary part, Mertens function sets new low of -9, which stands until 659
----
444 = 2² × 3 × 37, refactorable number, Harshad number
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445 = 5 × 89
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446 = 2 × 223, nontotient, self number
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447 = 3 × 149
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448 = 2⁶ × 7, untouchable number, refactorable number, Harshad number
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449 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

Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...

is less than 10¹⁰⁰⁰

450s

450 = 2 × 3² × 5², nontotient, sum of totient function for first 38 integers, refactorable number, Harshad number, also SMTP code meaning the requested mail action was not carried out, a perfect score in Canadian five-pin bowling

Five-pin bowling

Five-pin bowling is a bowling variant which is played only in Canada, where most 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 Club, in response to customers who complained that...

----
451 is a Wedderburn–Etherington number and a centered decagonal number

Centered decagonal number

A centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers...

; its reciprocal has period 10; 451 is the smallest number with this period reciprocal length

Reciprocal length

Reciprocal length or inverse length is a measurement used in several branches of science and mathematics. As the reciprocal of length, common units used for this measurement include the reciprocal metre or inverse metre , the reciprocal centimetre or inverse centimetre , and, in optics, the...

The number also has significance in the novel Fahrenheit 451
Fahrenheit 451
Fahrenheit 451 is a 1953 dystopian novel by Ray Bradbury. The novel presents a future American society where reading is outlawed and firemen start fires to burn books...

, as it is the temperature at which the paper in books ignites.

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452 = 2² × 113, also SMTP code meaning that the requested mail action was not carried out because of insufficient system storage
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453 = 3 × 151
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454 = 2 × 227, nontotient, a Smith number

Smith number

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455 = 5 × 7 × 13, sphenic number, tetrahedral number

Tetrahedral number

A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...

455 Rocket is the title of a song by Kathy Mattea
Kathy Mattea
Kathleen Alice "Kathy" Mattea is an American country music and bluegrass performer who often brings folk, Celtic and traditional country sounds to her music. Active since 1983 as a recording artist, she has recorded seventeen albums and has charted more than thirty singles on the Billboard Hot...

----
456 = 2³ × 3 × 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), centered pentagonal number

Centered pentagonal number

A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers...

----
457 prime number, sum of three consecutive primes (149 + 151 + 157), self number
----
458 = 2 × 229, nontotient
----
459 = 3³ × 17

460s

460 = 2² × 5 × 23, centered triangular number, Harshad number, sum of twelve consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61)
----
461 prime number, Chen prime, Eisenstein prime with no imaginary part
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462 = 2 × 3 × 7 × 11, sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89), pronic number

Pronic number

A pronic number, oblong number, rectangular number or heteromecic number, is a number which is the product of two consecutive integers, that is, n . The n-th pronic number is twice the n-th triangular number and n more than the n-th square number...

, sparsely totient number
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463 prime number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79), centered heptagonal number

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...

, number of days in the synodic period of Ceres

A common baseball double play
Double play
In baseball, a double play for a team or a fielder is the act of making two outs during the same continuous playing action. In baseball slang, making a double play is referred to as "turning two"....

(see baseball positions
Baseball positions
There are 9 fielding positions in baseball. Each position conventionally has an associated number which is used to score putouts...

)
A single by Buck 65
Buck 65
Richard Terfry , who uses the stage name Buck 65, is a Canadian experimental artist, MC and turntablist. Underpinned by an extensive background in abstract hip hop, his more recent music has extensively incorporated blues, country, rock, folk and avant garde influences.Terfry is also a radio host,...

, named after the baseball term

----
464 = 2⁴ × 29

In chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...

it is the number of legal positions of the kings, not counting mirrored positions. Has some importance when constructing an endgame tablebase
Endgame tablebase
An endgame tablebase is a computerized database that contains precalculated exhaustive analysis of a chess endgame position. It is typically used by a computer chess engine during play, or by a human or computer that is retrospectively analysing a game that has already been played.The tablebase...

.
See also: 4-6-4
4-6-4
Under the Whyte notation for the classification of steam locomotives, 4-6-4 represents the wheel arrangement of four leading wheels on two axles , six powered and coupled driving wheels on three axles, and four trailing wheels on two axles .Other equivalent classifications are:UIC classification:...

, the year AD 464.

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465 = 3 × 5 × 31, sphenic number

Sphenic number

, triangular number, member of the Padovan sequence

Padovan sequence

The Padovan sequence is the sequence of integers P defined by the initial valuesP=P=P=1,and the recurrence relationP=P+P.The first few values of P are...

, Harshad number
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466 = 2 × 233, noncototient
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467 prime number, safe prime

Safe prime

A safe prime is a prime number of the form 2p + 1, where p is also a prime. The first few safe primes are...

, Chen prime, Eisenstein prime with no imaginary part
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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 = 7 × 67, centered hexagonal number

Centered hexagonal number

A centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice....

470s

470 = 2 × 5 × 47, sphenic number, nontotient, noncototient

In golf
Golf
Golf is a precision club and ball sport, in which competing players use many types of clubs to hit balls into a series of holes on a golf course using the fewest number of strokes....

, 470 is the minimum length in yards from the tee to the hole on a Par 5.

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

Perfect totient number

In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers;...

----
472 = 2³ × 59, nontotient, untouchable number, refactorable number
----
473 = 11 × 43, sum of five consecutive primes (83 + 89 + 97 + 101 + 103)
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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 is a 49-gonal number

Polygonal number

In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots were thought of as alphas . These are one type of 2-dimensional figurate numbers.- Definition and examples :...

, member of the Mian–Chowla sequence.
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476 = 2² × 7 × 17, Harshad number
----
477 = 3² × 53
----
478 = 2 × 239
----
479 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

480s

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
----
481 = 13 × 37, octagonal number, centered square number, Harshad number
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482 = 2 × 241, nontotient, noncototient
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483 = 3 × 7 × 23, sphenic number, Smith number
----
484 = 2² × 11² = 22², nontotient
----
485 = 5 × 97
----
486 = 2 × 3⁵, Harshad number, also shorthand for the Intel 80486

Intel 80486

The Intel 80486 microprocessor was a higher performance follow up on the Intel 80386. Introduced in 1989, it was the first tightly pipelined x86 design as well as the first x86 chip to use more than a million transistors, due to a large on-chip cache and an integrated floating point unit...

microprocessor chip
----
487 prime number, sum of three consecutive primes (157 + 163 + 167), Chen prime, shorthand for the Intel 80487 floating point processor chip.
----
488 = 2³ × 61, nontotient, refactorable number
----
489 = 3 × 163, octahedral number

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...

490s

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

In Christianity
Christianity
Christianity is a monotheistic religion based on the life and teachings of Jesus as presented in canonical gospels and other New Testament writings...

, the Gospel of Matthew (Matthew 18:21-22
Gospel of Matthew
The Gospel According to Matthew is one of the four canonical gospels, one of the three synoptic gospels, and the first book of the New Testament. It tells of the life, ministry, death, and resurrection of Jesus of Nazareth...

) says that Jesus
Jesus
Jesus of Nazareth , commonly referred to as Jesus Christ or simply as Jesus or Christ, is the central figure of Christianity...

told Peter
Saint Peter
Saint Peter or Simon Peter was an early Christian leader, who is featured prominently in the New Testament Gospels and the Acts of the Apostles. The son of John or of Jonah and from the village of Bethsaida in the province of Galilee, his brother Andrew was also an apostle...

to forgive his brother "seventy times seven" times when his brother sins against him http://www.biblegateway.com/passage/?search=Matthew+18:21-35.

Also the number of Pokémon
Pokémon
is a media franchise published and owned by the video game company Nintendo and created by Satoshi Tajiri in 1996. Originally released as a pair of interlinkable Game Boy role-playing video games developed by Game Freak, Pokémon has since become the second most successful and lucrative video...

available as of the release of Pokémon Diamond and Pearl
Pokémon Diamond and Pearl
are role-playing games developed by Game Freak and published by Nintendo for the Nintendo DS. With the enhanced remake Pokémon Platinum, the games comprise the fifth installment and fourth generation of the Pokémon series of RPGs...

(excluding event Pokémon)

----
491 prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number
----
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 = 17 × 29, sum of seven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83), member of a Ruth–Aaron pair with 493 under first definition

As of August 2009, the number of Pokémon
Pokémon
is a media franchise published and owned by the video game company Nintendo and created by Satoshi Tajiri in 1996. Originally released as a pair of interlinkable Game Boy role-playing video games developed by Game Freak, Pokémon has since become the second most successful and lucrative video...

species, from the first set through the fourth generation (see List of Pokémon)
The number of bronze knuts equivalent to one gold galleon, in the monetary system of the world of Harry Potter
Harry Potter
Harry Potter is a series of seven fantasy novels written by the British author J. K. Rowling. The books chronicle the adventures of the adolescent wizard Harry Potter and his best friends Ron Weasley and Hermione Granger, all of whom are students at Hogwarts School of Witchcraft and Wizardry...

.

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494 = 2 × 13 × 19, sphenic number, nontotient
----
495

495 (number)

495 is the integer after 494 and before 496. It is a pentatope number.- Kaprekar transformation :The Kaprekar transformation is defined as follows for three-digit numbers:# Start with a three-digit number with at least two digits different....

has its own article.
----
496

496 (number)

Four hundred [and] ninety-six is the natural number following four hundred [and] ninety-five and preceding four hundred [and] ninety-seven.-In mathematics:...

has its own article.
----
497 = 7 × 71, sum of five consecutive primes (89 + 97 + 101 + 103 + 107)
----
498 = 2 × 3 × 83, sphenic number, untouchable number
----
499 prime number, Chen prime

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