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| {{about|the numbers 400 to 499|the year 400 AD|400}}
| | To your abode the clash of clans hack ([http://circuspartypanama.com visit website]) tool; there are unquestionably also hack tools for the other games. Americans can check out those hacks and obtain dozens of which they need. It is sure these people will have lost with regards to fun once they have the hack tool that they can.<br><br> |
| {{Infobox number
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| | number = 400
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| | divisor = 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
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| | lang1 = [[Hebrew language|Hebrew]]
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| | lang1 symbol = <span style="font-size:150%;">ת</span> (Tav)
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| }}
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| '''400''' ('''four hundred''') is the [[natural number]] following 399 and preceding 401.
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| {{TOC limit|3}}
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| == Mathematical properties ==
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| 400 is the [[square number|square]] of [[20 (number)|20]]. 400 is the sum of the powers of 7 from 0 to 3, thus making it a repdigit in base 7 (1111).
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| A [[circle]] is divided into 400 [[grad (angle)|grads]], which is equal to 360 [[degree (angle)|degree]]s and 2π [[radian]]s. (Degrees and radians are the [[International System of Units|SI]] accepted units).
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| 400 is a [[self number]] 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]].
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| == Other fields ==
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| '''Four hundred''' is also
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| * [[The Four Hundred (oligarchy)]] of ancient [[Athens]].
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| * an [[HTTP status code#400|HTTP status code]] for a [[HTTP_status_code#4xx_Client_Error|bad client request]].
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| * 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]]), leading to the generation of such lists as the [[Forbes 400]]
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| * The [[Atari 8-bit family|Atari 400]] home computer.
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| * A former limited stop bus route which operated from [[Bolton]] to [[Stockport]] and [[Manchester Airport]] from 1970 to 2004, known as the Trans-Lancs Express.
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| * in the title of the film ''Les Quatre Cent Coups'' (''[[The 400 Blows]]''), a French film directed by [[François Truffaut]].
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| * A Lebanese card game. [[400 (card game)]]
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| * the designation for a class of [[Ontario]] highways called [[400-series highways (Ontario)|400-Series Highways]].
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| * [[Twin Cities 400|The 400]], later the Twin Cities 400, a [[Chicago and North Western Railway]] passenger train that traveled 400 miles between [[Minneapolis/St. Paul]] and [[Chicago, Illinois]] in 400 minutes.
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| * The yard number of the [[RMS Olympic]], the [[RMS Titanic]]'s sister ship.
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| * .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|Ted Williams of the Boston Red Sox]] in 1941.
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| * The number of days in a [[Gregorian calendar]] year changes according to a cycle of exactly 400 years, of which 97 are leap years and 303 are common.
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| * The [[Intertestamental period]] or period of time between the writings of the Hebrew Bible and the Christian New Testament texts is traditionally considered to be a roughly four hundred year period
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| * The Sun is approximately 400 times the size of the Moon but also is approximately 400 times further away, creating the temporary illusion in which the Sun and Moon in Earth's sky appear as if of similar size.
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| * In [[gematria]] 400 is the largest single number that can be represented without using the [[Sophit]] forms (see [[Kaph]], [[Mem]], [[Nun]], [[Pe_(letter)|Pe]], and [[Tzade]]).
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| ==Integers from 401 to 499==
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| ===400s===
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| ====401====
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| A [[prime number]], [[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]], [[Eisenstein prime]] with no imaginary part, [[Mertens function]] returns 0, member of the [[Mian–Chowla sequence]].
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| *[[HTTP 401|HTTP status code]] for "Unauthorized", area code for [[Rhode Island]], also in the name of a retirement plan, [[401(k)]]. [[Stephen Colbert]]'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].
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| ====402==== | |
| 402 = 2 × 3 × 67, [[sphenic number]], [[nontotient]], [[Harshad number]],
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| *[[HTTP 402|HTTP status code]] for "Payment Required", [[Area code 402|area code]] for [[Nebraska]]
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| ====403====
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| 403 = 13 × 31, [[Mertens function]] returns 0.
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| *[[HTTP 403|HTTP status code]] for "Forbidden"; also in the name of a retirement plan in the United States, 403(b). The [[Area code 403|area code]] for southern Alberta.
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| ====404====
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| 404 = 2<sup>2</sup> × 101, Mertens function returns 0, nontotient, [[noncototient]].
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| *[[HTTP 404|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 [[Area code 404|Atlanta calling area]].
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| ====405====
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| 405 = 3<sup>4</sup> × 5, Mertens function returns 0, Harshad number;
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| *[[HTTP 405|HTTP status code]] for "Method Not Allowed". [[Area code 405|Area code]] for central Oklahoma, including [[Oklahoma City]] and surrounding suburbs.
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| ====406====
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| {{wikisourcepar|406}}
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| 406 = 2 × 7 × 29, [[sphenic number]], [[triangular number]], [[centered nonagonal number]], nontotient
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| *[[HTTP 406|HTTP status code]] for "Not Acceptable".
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| *''[[wikisource:406|406]]'' is a poem by [[John Boyle O'Reilly]]. 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 [[mysticism|mystical]] significance to him, as intimated in the poem.
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| *See also the [[Peugeot 406]] car.
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| ====407====
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| 407 = 11 × 37,
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| *sum of cubes of 4, 0 and 7 (4<sup>3</sup> + 0<sup>3</sup> + 7<sup>3</sup> = 407); [[narcissistic number]]
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| *sum of three consecutive primes (131 + 137 + 139)
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| *Mertens function returns 0
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| *[[Harshad number]]
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| *[[HTTP 407|HTTP status code]] for "Proxy Authentication Required"
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| *Area code for [[Orlando, Florida|Orlando]], Florida
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| ====408====
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| 408 = 2<sup>3</sup> × 3 × 17
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| *Sum of four consecutive primes (97 + 101 + 103 + 107)
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| *Sum of eight consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67)
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| *[[Pell number]]
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| *[[Mertens function]] returns 0
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| *[[Octagonal number]]
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| *[[Untouchable number]]
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| *Harshad number
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| *[[HTTP 408|HTTP status code]] for "Request Timeout"
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| *Area code for the Silicon Valley
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| ====409====
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| 409 is a prime number, Chen prime, [[centered triangular number]].
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| *A family of cleaning products, [[Formula 409]]
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| *An engine known as the [[Chevrolet Big-Block engine#409|Chevrolet 409]], a 409 cubic inch W-series [[V8 engine|V8]].
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| *The song "[[409 (song)|409]]" by [[The Beach Boys]], which was inspired by the above engine.
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| *[[HTTP 409|HTTP status code]] for "Conflict"
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| *''[[Green Day]]'' have made a song, ''409 in Your Coffeemaker'', included on their album [[1,039/Smoothed Out Slappy Hours]].
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| *The [[Area code 409|area code]] for a part of eastern Texas.
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| *''[[Bullet For My Valentine]]'' has released a song, "Room 409", from the album [[The Poison]]
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| ===410s===
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| ====410====
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| 410 = 2 × 5 × 41, [[sphenic number]], sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number
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| *[[HTTP 410|HTTP status code]] for "Gone".
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| * [[Area codes 410 and 443|Area Code 410]], a telephone area code for the US State of Maryland, representing portions of the state including the [[Baltimore metropolitan area]] and the Eastern Shore.
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| ====411====
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| 411 = 3 × 137, [[self number]],
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| *[[HTTP 411|HTTP status code]] for "Length Required", slang for information (see [[4-1-1]])
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| ====412====
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| 412 = 2<sup>2</sup> × 103, nontotient, noncototient, sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59)
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| * [[HTTP 412|HTTP status code]] for "Precondition Failed"
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| * Area code for [[Pittsburgh]], [[Pennsylvania]].
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| * Fictitious Police Code for "Overacting" from "[http://www.wepsite.de/Freberg,Dragon.htm St. George and the Dragonet]" - [[Stan Freeberg]]
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| ====413====
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| 413 = 7 × 59, [[Mertens function]] returns 0, self number
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| *[[HTTP 413|HTTP status code]] for "Request Entity Too Large", area code for [[Western Massachusetts]].
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| ====414====
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| 414 = 2 × 3<sup>2</sup> × 23, Mertens function returns 0, nontotient, [[Harshad number]]
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| *[[HTTP 414|HTTP status code]] for "Request-URI Too Long", [[Area code]] for [[Milwaukee, Wisconsin|Milwaukee]], Wisconsin.
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| * [[The 414s]], a group of hackers from Milwaukee, Wisconsin.
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| ====415====
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| 415 = 5 × 83,
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| *[[HTTP 415|HTTP status code]] for "Unsupported Media Type"
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| * [[415 Records]], a record label
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| * 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.
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| *[[Area code 415]], a telephone area code for San Francisco, California
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| *[[415 (group)]], a rap group from Oakland, California
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| ====416====
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| 416 = 2<sup>5</sup> × 13
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| *[[HTTP 416|HTTP status code]] for "Requested Range Not Satisfiable"
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| *416 is also [[Area codes 416, 647 and 437#416 in popular culture|a nickname]] for the city of [[Toronto]], based on [[Area codes 416, 647 and 437|the area code]] it used before [[overlay plan]]s added two more area codes.
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| ====417====
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| 417 = 3 × 139
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| *[[HTTP 417|HTTP status code]] for "Expectation Failed". Also the area code for southwestern Missouri, including [[Springfield, Missouri|Springfield]], and [[Joplin, Missouri|Joplin]].
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| ====418====
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| 418 = 2 × 11 × 19, sphenic number,
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| * the number of [[Abrahadabra]], [[Hyper Text Coffee Pot Control Protocol]] status code for "Teapot" as an April Fools' joke.
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| ====419====
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| A prime number, [[Sophie Germain prime]], Chen prime, Eisenstein prime with no imaginary part, [[highly cototient number]], Mertens function returns 0 | |
| *refers to the Nigerian [[advance fee fraud]] scheme (after the section of the Nigerian Criminal Code it violates)
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| ===420s===
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| ====420====
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| {{Main|420 (number)}}
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| {{seealso|420 (cannabis culture)}}
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| ====421====
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| A prime number, sum of five consecutive primes (73 + 79 + 83 + 89 + 97), [[centered square number]], also [[SMTP]] code meaning the transmission channel will be closing
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| ====422====
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| 422 = 2 × 211, Mertens function returns 0, nontotient
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| ====423====
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| 423 = 3<sup>2</sup> × 47, Mertens function returns 0, Harshad number
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| ====424====
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| 424 = 2<sup>3</sup> × 53, sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Mertens function returns 0, [[refactorable number]], self number
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| ====425====
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| 425 = 5<sup>2</sup> × 17, [[pentagonal number]], sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0
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| ====426====
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| 426 = 2 × 3 × 71, sphenic number, nontotient,
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| ====427====
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| 427 = 7 × 61, Mertens function returns 0
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| ====428====
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| 428 = 2<sup>2</sup> × 107, Mertens function returns 0, nontotient
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| *''[[428: Fūsa Sareta Shibuya de]]'', a video game
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| ====429====
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| 429 = 3 × 11 × 13, sphenic number, [[Catalan number]]
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| ===430s===
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| ====430====
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| 430 = 2 × 5 × 43, sphenic number, untouchable number
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| ====431====
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| A prime number, [[Sophie Germain prime]], sum of seven consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73), [[Chen prime]], [[Eisenstein prime]] with no imaginary part
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| *The distance between Earth and the star Polaris in light years
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| ====432====
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| 432 = 2<sup>4</sup> x 3<sup>3</sup> = 4<sup>2</sup> x 3<sup>3</sup>, The sum of four consecutive primes (103 + 107 + 109 + 113), a [[highly totient number]], sum of totient function for first 37 integers. 432! is the first factorial that is not a [[Harshad number]] in base 10. 432 is also three-dozen sets of a dozen, making it three gross.
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| ====433====
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| A prime number, [[Markov number]], [[star number]].
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| * The perfect score in the game show ''[[Fifteen To One]]'', only ever achieved once in over 2000 shows.
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| ====434====
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| 434 = 2 × 7 × 31, sphenic number, sum of six consecutive primes (61 + 67 + 71 + 73 + 79 + 83), nontotient
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| ====435====
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| 435 = 3 × 5 × 29, sphenic number, triangular number, [[hexagonal number]], self number
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| ====436====
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| 436 = 2<sup>2</sup> × 109, nontotient, noncototient
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| ====437====
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| 437 = 19 × 23
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| ====438====
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| 438 = 2 × 3 × 73, sphenic number, [[Smith number]].
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| *The "438 match" or "438 game" has been used by cricket media to describe [[Australia in South Africa, 5th ODI, 2006|the famous 2006 One Day International]] in which [[Australia national cricket team|Australia]] scored a world record 434 in their innings, only to see [[South Africa national cricket team|South Africa]] respond in their innings with 438.
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| ====439====
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| 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
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| ===440s===
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| ====440====
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| 440 = 2<sup>3</sup> × 5 × 11, the sum of the first seventeen prime numbers, Harshad number,
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| *in [[hertz]], the [[Concert pitch|standard frequency]] to which most [[orchestra]]s tune the pitch A above middle C. A few orchestras tune slightly flatter or sharper than this.
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| ====441====
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| 441 = 3<sup>2</sup> × 7<sup>2</sup> = 21<sup>2</sup>
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| * 441 is the sum of the cubes of the first 6 natural numbers (441 = 1<sup>3</sup> + 2<sup>3</sup> + 3<sup>3</sup> + 4<sup>3</sup> + 5<sup>3</sup> + 6<sup>3</sup>).
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| * 441 is a [[centered octagonal number]], a refactorable number, and a Harshad number.
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| * 441 is the number of squares on a [[Super Scrabble]] board.
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| ====442====
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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====
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| 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
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| ====444====
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| 444 = 2<sup>2</sup> × 3 × 37, refactorable number, Harshad number
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| ====445====
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| 445 = 5 × 89
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| ====446====
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| 446 = 2 × 223, nontotient, self number
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| ====447====
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| 447 = 3 × 149
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| ====448====
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| 448 = 2<sup>6</sup> × 7, untouchable number, refactorable number, Harshad number
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| ====449====
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| A prime number, sum of five consecutive primes (79 + 83 + 89 + 97 + 101), Chen prime, Eisenstein prime with no imaginary part, [[Proth prime]]. Also the largest number whose [[factorial]] is less than 10<sup>1000</sup>
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| ===450s===
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| ====450====
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| 450 = 2 × 3<sup>2</sup> × 5<sup>2</sup>, nontotient, sum of totient function for first 38 integers, refactorable number, Harshad number,
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| *SMTP code meaning the requested mail action was not carried out, a perfect score in Canadian [[five-pin bowling]] and an [[Area codes 450 and 579|area code]] in Southern Quebec.
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| ====451====
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| 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]].
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| *The novel ''[[Fahrenheit 451]]'' refers to the temperature that author [[Ray Bradbury]] understood to be the autoignition point of paper.
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| ====452====
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| 452 = 2<sup>2</sup> × 113
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| *SMTP code meaning that the requested mail action was not carried out because of insufficient system storage
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| ====453====
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| 453 = 3 × 151
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| ====454====
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| 454 = 2 × 227, nontotient, a [[Smith number]]
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| ====455====
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| 455 = 5 × 7 × 13, [[sphenic number]], [[tetrahedral number]]
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| *''455 Rocket'' is the title of a song by [[Kathy Mattea]]
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| *455 kHz is a standard [[intermediate frequency]] for analog [[superheterodyne]] [[AM broadcast]] band receivers.
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| ====456====
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| 456 = 2<sup>3</sup> × 3 × 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), [[centered pentagonal number]]
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| ====457====
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| A prime number, sum of three consecutive primes (149 + 151 + 157), self number
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| ====458====
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| 458 = 2 × 229, nontotient
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| ====459====
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| 459 = 3<sup>3</sup> × 17
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| ===460s===
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| ====460====
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| 460 = 2<sup>2</sup> × 5 × 23, centered triangular number, dodecagonal number, Harshad number, sum of twelve consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61)
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| ====461====
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| A prime number, Chen prime, [[sexy prime]] with 467, Eisenstein prime with no imaginary part
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| ====462====
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| 462 = 2 × 3 × 7 × 11, [[binomial coefficient]] <math> \tbinom {11}5 </math>, sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89), [[pronic number]], [[sparsely totient number]]
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| ====463====
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| A prime number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79), [[centered heptagonal number]],
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| *Number of days in the [[synodic period]] of [[Ceres (dwarf planet)|Ceres]]
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| *A common baseball [[double play]] (see [[baseball positions]])
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| *A single by [[Buck 65]], named after the baseball term
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| ====464====
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| 464 = 2<sup>4</sup> × 29, [[primitive abundant number]]
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| * In [[chess]] it is the number of legal positions of the kings, not counting mirrored positions. Has some importance when constructing an [[endgame tablebase]].
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| * ''See also:'' [[4-6-4]], the year AD 464.
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| ====465====
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| 465 = 3 × 5 × 31, [[sphenic number]], triangular number, member of the [[Padovan sequence]], Harshad number
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| ====466====
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| 466 = 2 × 233, noncototient
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| ====467====
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| A prime number, [[safe prime]], [[sexy prime]] with 461, Chen prime, Eisenstein prime with no imaginary part
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| ====468====
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| 468 = 2<sup>2</sup> × 3<sup>2</sup> × 13, sum of ten consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), refactorable number, self number, Harshad number
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| ====469====
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| 469 = 7 × 67, [[centered hexagonal number]]
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| ===470s===
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| ====470====
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| 470 = 2 × 5 × 47, sphenic number, nontotient, noncototient
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| * In [[golf]], 470 is the minimum length in [[yards]] from the tee to the hole on a Par 5.
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| * [[470 (dinghy)|470]] is an Olympic class of sailing [[dinghy]]
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| ====471====
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| 471 = 3 × 157, sum of three consecutive primes (151 + 157 + 163), [[perfect totient number]]
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| ====472====
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| 472 = 2<sup>3</sup> × 59, nontotient, untouchable number, refactorable number
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| ====473====
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| 473 = 11 × 43, sum of five consecutive primes (83 + 89 + 97 + 101 + 103)
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| ====474====
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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]]
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| ====475====
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| 475 = 5<sup>2</sup> × 19, 49-[[polygonal number|gonal number]], member of the Mian–Chowla sequence.
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| ====476====
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| 476 = 2<sup>2</sup> × 7 × 17, Harshad number
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| ====477====
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| 477 = 3<sup>2</sup> × 53, [[pentagonal number]]
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| ====478====
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| 478 = 2 × 239
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| ====479====
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| 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
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| * Also an area code in [[area code 479|the U.S. state of Arkansas]].
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| ===480s===
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| ====480====
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| 480 = 2<sup>5</sup> × 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
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| ====481====
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| 481 = 13 × 37, octagonal number, centered square number, Harshad number
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| ====482====
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| 482 = 2 × 241, nontotient, noncototient
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| ====483====
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| 483 = 3 × 7 × 23, sphenic number, Smith number
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| ====484====
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| 484 = 2<sup>2</sup> × 11<sup>2</sup> = 22<sup>2</sup>, nontotient
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| ====485====
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| 485 = 5 × 97
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| ====486====
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| 486 = 2 × 3<sup>5</sup>, Harshad number, [[perrin sequence|Perrin number]]
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| *shorthand for the [[Intel 80486]] microprocessor chip
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| ====487====
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| A prime number, sum of three consecutive primes (157 + 163 + 167), Chen prime,
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| * The only primes under 200,000,000 that divide their own decimal periods are 3, 487, and 56598313.
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| * Shorthand for the [[Intel 80487]] floating point processor chip.
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| ====488====
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| 488 = 2<sup>3</sup> × 61, nontotient, refactorable number
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| ====489====
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| 489 = 3 × 163, [[octahedral number]]
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| ===490s===
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| ====490====
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| 490 = 2 × 5 × 7<sup>2</sup>, noncototient, sum of totient function for first 40 integers, [[partition (number theory)| partition number]] (integer partitions of 19), self number.
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| *In [[Christianity]], the Gospel of Matthew ([[Gospel of Matthew|Matthew 18:21-22]]) says that [[Jesus]] told [[Saint Peter|Peter]] to forgive his brother "seventy times seven" times when his brother sins against him [http://www.biblegateway.com/passage/?search=Matthew+18:21-35].
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| ====491====
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| A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number
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| ====492====
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| 492 = 2<sup>2</sup> × 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
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| ====493====
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| 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
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| ====494====
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| 494 = 2 × 13 × 19, sphenic number, nontotient
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| ====495====
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| {{Main|495 (number)}}
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| ====496====
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| {{Main|496 (number)}} is the third perfect number, a number whose divisors add up to the actual number (1+2+4+8+16+31+62+124+248=496)
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| ====497====
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| 497 = 7 × 71, sum of five consecutive primes (89 + 97 + 101 + 103 + 107)
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| ====498====
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| 498 = 2 × 3 × 83, sphenic number, untouchable number, admirable number, abundant number
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| ====499====
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| A prime number, Chen prime
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| == References ==
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| {{Reflist}}
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| {{Integers|4}}
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| {{DEFAULTSORT:400 (Number)}}
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| [[Category:Integers|49e02 400]]
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