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{{About|the numbers 400 to 499|the year 400 AD|400|other uses|400 (disambiguation)}}
{{Infobox number
| number = 400
| divisor = 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
| lang1 = [[Hebrew language|Hebrew]]
| lang1 symbol = <span style="font-size:150%;">ת</span>
|lang2=[[Armenian numerals|Armenian]]|lang2 symbol=Ն|lang3=[[Babylonian cuneiform numerals|Babylonian cuneiform]]|lang3 symbol=𒐚𒐏|lang4=[[Egyptian numerals|Egyptian hieroglyph]]|lang4 symbol=<span style="font-size:200%;">𓍥</span>}}
'''400''' ('''four hundred''') is the [[natural number]] following [[399 (number)|399]] and preceding [[#401|401]].
{{TOC limit|3}}

== Mathematical properties ==

A [[circle]] is divided into 400 [[grad (angle)|grads]].

==Integers from 401 to 499==

===400s===

====401====
401 is a [[prime number]], [[tetranacci number]],<ref>{{Cite OEIS|A000078|Tetranacci numbers}}</ref> [[Chen prime]],<ref name=A109611>{{Cite OEIS|A109611|Chen primes}}</ref> [[oeis:A006450|prime index prime]]
* [[Eisenstein prime]] 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]] returns 0,<ref name=A028442>{{Cite OEIS|A028442|Numbers n such that Mertens' function is zero}}</ref>
* Member of the [[Mian–Chowla sequence]].<ref name=A005282>{{Cite OEIS|A005282|Mian-Chowla sequence}}</ref>

====402====
402 = 2 &times; 3 &times; 67, [[sphenic number]], [[nontotient]], [[Harshad number]], number of graphs with 8 nodes and 9 edges<ref>{{cite OEIS|A008406|2=Triangle T(n,k) read by rows, giving number of graphs with n nodes (n >= 1) and k edges (0 <= k <= n(n-1)/2)}}</ref>
*[[HTTP 402|HTTP status code]] for "Payment Required".
*The [[Area code 402|area code]] for [[Nebraska]].

====403====
403 = 13 &times; 31, [[heptagonal number]], [[Mertens function]] returns 0.<ref name=A028442/>
* First number that is the product of an emirp pair.<ref>{{Cite OEIS|A083815|Semiprimes whose prime factors are distinct and the reversal of one factor is equal to the other}}</ref>
* [[HTTP 403]], the 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]].

====404====
404 = 2<sup>2</sup> &times; 101, Mertens function returns 0,<ref name=A028442/> nontotient, [[noncototient]], number of integer partitions of 20 with an alternating permutation.<ref>{{cite OEIS|A345170|Number of integer partitions of n with an alternating permutation}}</ref> 
* The [[HTTP 404]] 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.<ref>{{Cite magazine |last=Wiener |first=Anna |title=((Page Not Found: A Brief History of the 404 Error)) |url=https://www.wired.com/story/page-not-found-a-brief-history-of-the-404-error/ |access-date=2024-12-05 |magazine=Wired |language=en-US |issn=1059-1028}}</ref>
* One of the four area codes of the [[Area code 404|Atlanta calling area]].

====405====
405 = 3<sup>4</sup> &times; 5, Mertens function returns 0,<ref name=A028442/> [[Harshad number]], [[pentagonal pyramidal number]]; 
* [[HTTP 405|HTTP status code]] for "Method Not Allowed".
* [[Area code 405|Area code]] for central Oklahoma, including [[Oklahoma City]] and surrounding suburbs.
* [[Interstate 405 (California)|Interstate 405]] is a major, heavily traveled freeway in [[Southern California]], known to the local as "The 405".
* Sum of all numbers in a standard (3x3)x(3x3) [[Sudoku]].

====406====
406 = 2 &times; 7 &times; 29, [[sphenic number]], 28th [[triangular number]],<ref>{{Cite web |title=A000217 - OEIS |url=https://oeis.org/A000217 |access-date=2024-11-28 |website=oeis.org}}</ref> [[centered nonagonal number]],<ref>{{Cite OEIS|A060544|Centered 9-gonal (also known as nonagonal or enneagonal) numbers}}</ref> even nontotient, Narayana's cow number<ref>{{cite OEIS|A000930|Narayana's cows sequence}}</ref>
*[[HTTP 406|HTTP status code]] for "Not Acceptable".
{{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.
*[[Peugeot 406]] car.
*[[Area code 406|Area code]] for all of [[Montana]].

====407====
407 = 11 &times; 37,
*Sum of cubes of 4, 0 and 7 (4<sup>3</sup> + 0<sup>3</sup> + 7<sup>3</sup> = 407); [[narcissistic number]]<ref>{{Cite OEIS|A005188|Armstrong (or Plus Perfect, or narcissistic) numbers}}</ref>
*Sum of three consecutive primes (131 + 137 + 139)
*Mertens function returns 0<ref name=A028442/>
*Harshad number
*Lazy caterer number <ref name=A000124>{{cite OEIS|A000124|Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts}}</ref>
*[[HTTP 407|HTTP status code]] for "Proxy Authentication Required"
*Area code for [[Orlando, Florida|Orlando]], Florida
*Colloquial name for the Express Toll Route in Ontario

====408====
408 = 2<sup>3</sup> &times; 3 &times; 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]]<ref>{{Cite OEIS|A000129|Pell numbers}}</ref>
*[[Mertens function]] returns 0<ref name=A028442/>
*[[Octagonal number]]<ref name=A000567>{{Cite OEIS|A000567|Octagonal numbers}}</ref>
*[[Untouchable number]]<ref name=A005114>{{Cite OEIS|A005114|Untouchable numbers}}</ref>
*Harshad number
*[[HTTP 408|HTTP status code]] for "Request Timeout"
*Area code for the Silicon Valley

====409====
409 is a prime number, [[Chen prime]],<ref name=A109611/> [[centered triangular number]].<ref name=A005448>{{Cite OEIS|A005448|Centered triangular numbers}}</ref>

*A family of cleaning products, [[Formula 409]]
*An engine known as the [[Chevrolet Big-Block engine#409|Chevrolet 409]], a 409 cubic inch W-series [[V8 engine|V8]].
*The song "[[409 (song)|409]]" by [[The Beach Boys]], inspired by the above engine
*[[HTTP 409|HTTP status code]] for "Conflict"
*A [[Green Day]] song, "409 in Your Coffeemaker", included on their album ''[[1,039/Smoothed Out Slappy Hours]]''
*The [[Area code 409|area code]] for the corner of southeastern Texas
* [[Venice]] has 409 bridges.<ref>{{Cite web |title=Venice: The City Built on Water |url=https://www.google.com/maps/about/behind-the-scenes/streetview/treks/venice/ |access-date=2022-09-21 |website=Google Maps}}</ref>
*A [[Bullet For My Valentine]] song, "Room 409", from the album ''[[The Poison]]''
* [[Joe Paterno]] holds the record as the winningest head coach in [[NCAA Football Bowl Subdivision|NCAA FBS]] with 409 victories.

===410s===

====410====
410 = 2 &times; 5 &times; 41, [[sphenic number]], sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number, number of triangle-free graphs on 8 vertices<ref>{{cite OEIS|A006785|Number of triangle-free graphs on n vertices}}</ref>
*[[HTTP 410|HTTP status code]] for "Gone".
* [[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.

====411====
411 = 3 &times; 137, [[self number]],<ref name=A003052>{{Cite OEIS|A003052|Self numbers}}</ref> 
*[[HTTP 411|HTTP status code]] for "Length Required", slang for information (see [[4-1-1]])
*The number of possible [[FM broadcasting]] frequencies between 87.50 and 108.00 [[Hertz|MHz]] in 50&nbsp;kHz spacing countries{{importance inline|date=December 2020}}

====412====
412 = 2<sup>2</sup> &times; 103, nontotient, noncototient, sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), [[oeis:A006316|412<sup>64</sup> + 1 is prime]]
* [[HTTP 412|HTTP status code]] for "Precondition Failed"
* Area code for [[Pittsburgh]], [[Pennsylvania]].
* Fictitious Police Code for "Overacting" from "[http://www.wepsite.de/Freberg,Dragon.htm St. George and the Dragonet]" - [[Stan Freberg]]

====413====
413 = 7 &times; 59, [[Mertens function]] returns 0,<ref name=A028442/> self number,<ref name=A003052/> [[Blum integer]]
*[[HTTP 413|HTTP status code]] for "Request Entity Too Large"
* Area code for [[Western Massachusetts]].
*An important and recurring number in the [[webcomic]] [[Homestuck]] by [[Andrew Hussie]].

====414====
414 = 2 &times; 3<sup>2</sup> &times; 23, Mertens function returns 0,<ref name=A028442/> nontotient, Harshad number, number of balanced partitions of 31<ref>{{cite OEIS|A047993|Number of balanced partitions of n: the largest part equals the number of parts}}</ref>
:<math>\sum_{n=0}^{10}{414}^{n}</math> is prime<ref name=A162862>{{cite OEIS|A162862|Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime}}</ref>
* [[HTTP 414|HTTP status code]] for "Request-URI Too Long"
* [[Area code]] for [[Milwaukee, Wisconsin|Milwaukee]], Wisconsin.
* [[The 414s]], a group of hackers from Milwaukee, Wisconsin.

====415====
415 = 5 &times; 83, logarithmic number<ref>{{cite OEIS|A002104|Logarithmic numbers}}</ref>
*[[HTTP 415|HTTP status code]] for "Unsupported Media Type"
* [[415 Records]], a record label
* 415 refers to California [[Penal Code]], section 415, pertaining to public fighting, public disturbance, and public use of offensive words likely to provoke an immediate violent reaction.
*[[Area code 415]], a telephone area code for San Francisco, California

====416====
416 = 2<sup>5</sup> &times; 13, number of [https://mathworld.wolfram.com/IndependentVertexSet.html independent vertex sets] and [https://mathworld.wolfram.com/VertexCover.html vertex covers] in the 6-[https://mathworld.wolfram.com/SunletGraph.html sunlet graph]<ref>{{cite OEIS|A080040|2=a(n) = 2*a(n-1) + 2*a(n-2) for n > 1; a(0)=2, a(1)=2}}</ref>
*[[HTTP 416|HTTP status code]] for "Requested Range Not Satisfiable"
*416 is also [[Area codes 416, 647 and 437#416 in popular culture|a nickname]] for the city of [[Toronto]], based on [[Area codes 416, 647 and 437|the area code]] it used before [[overlay plan]]s added two more area codes.

====417====
417 = 3 &times; 139, [[Blum integer]]
*[[HTTP 417|HTTP status code]] for "Expectation Failed". Also the area code for southwestern Missouri, including [[Springfield, Missouri|Springfield]], and [[Joplin, Missouri|Joplin]].

====418====
418 = 2 &times; 11 &times; 19; [[sphenic number]],<ref>{{Cite OEIS|A007304|Sphenic numbers: products of 3 distinct primes}}</ref> balanced number.<ref>{{cite OEIS|A020492|Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203)}}</ref> It is also the fourth 71-[[Polygonal number|gonal]] number.<ref>{{Cite book |last1=Conway |first1=John H. |author-link=John Horton Conway  |last2=Guy |first2=Richard |author-link2=Richard K. Guy |title=The Book of Numbers |title-link=The Book of Numbers (math book) |date=2012 |publisher=[[Springer Science & Business Media|Springer]] |page=39 |doi=10.1007/978-1-4612-4072-3 |isbn=978-1-4612-4072-3 |oclc=39220031 |language=en }}</ref>
* The [[Addition|sum]] of the integers between [[13 (number)|13]] and [[31 (number)|31]], inclusive. 
* The [[Product (mathematics)|product]] of its digits as well as the sum of its [[prime factors]] are both 32. Also, [[131 (number)|131]], a strong concatenation of 13 and 31, is the 32nd prime number (while the 32nd composite number is [[48 (number)|48]]).
* The sum of the [[84 (number)|84]] [[Numerical digit|digits]] of the 22nd [[unique prime]] in [[Base ten|decimal]] (having a very distinct set of digits than all other known terms in the [[sequence]]).<ref>{{Cite OEIS|A040017|Unique period primes|access-date=2022-05-20}}
:That number is '''142,857,157,142,857,142,856,999,999,985,714,285,714,285,857,142,857,142,855,714,285,571,428,571,428,572,857,143'''.</ref>
* The number of [[Abrahadabra]]
* [[Hyper Text Coffee Pot Control Protocol]] status code for "Teapot" as an April Fools' joke.<ref>{{cite journal|url=https://tools.ietf.org/html/rfc2324#section-2.3.2|type=RFC|title=Hyper Text Coffee Pot Control Protocol (HTCPCP/1.0)|quote=Any attempt to brew coffee with a teapot should result in the error code "418 I'm a teapot". The resulting entity body MAY be short and stout.|access-date=13 Sep 2018|date=1 April 1998|author=L. Masinter|journal=Network Working Group|doi=10.17487/RFC2324 |url-access=subscription}}</ref><ref>{{cite journal|url=https://tools.ietf.org/html/rfc7168#section-2.3.3|title=The Hyper Text Coffee Pot Control Protocol for Tea Efflux Appliances (HTCPCP-TEA)|quote=TEA-capable pots that are not provisioned to brew coffee may return either a status code of 503, indicating temporary unavailability of coffee, or a code of 418 as defined in the base HTCPCP specification to denote a more permanent indication that the pot is a teapot.|type=RFC|access-date=13 Sep 2018|issn=2070-1721|date=1 April 2014|author=I. Nazar|journal=IETF Request for Comments (RFC) Pages - Test|doi=10.17487/RFC7168 |url-access=subscription}}</ref>

====419====
A prime number, [[Sophie Germain prime]],<ref name=A005384>{{Cite OEIS|A005384|Sophie Germain primes}}</ref> Chen prime,<ref name=A109611/> Eisenstein prime with no imaginary part, [[highly cototient number]],<ref>{{Cite OEIS|A100827|Highly cototient numbers}}</ref> Mertens function returns 0<ref name=A028442/>
*Refers to the Nigerian [[advance fee fraud]] scheme (after the section of the Nigerian Criminal Code it violates)
*The Area Code for [[Toledo, Ohio|Toledo, OH]] and other surrounding areas.

===420s===

====420====
{{Main|420 (number)}}

{{See also|420 (cannabis culture)}}

====421====
* A prime number, sum of five consecutive primes (73 + 79 + 83 + 89 + 97), [[centered square number]],<ref name=A001844>{{Cite OEIS|A001844|Centered square numbers}}</ref> also [[SMTP]] code meaning the transmission channel will be closing
* [[+421|Country calling code]] for [[Slovakia]]

====422====
422 = 2 &times; 211, Mertens function returns 0,<ref name=A028442/> nontotient, since 422 = 20<sup>2</sup> + 20 + 2 it is the maximum number of regions into which 21 [https://mathworld.wolfram.com/PlaneDivisionbyCircles.html intersecting circles divide the plane].<ref name=A014206>{{cite OEIS|A014206|2=a(n) = n^2 + n + 2}}</ref>

====423====
423 = 3<sup>2</sup> &times; 47, Mertens function returns 0,<ref name=A028442/> [[Harshad number]], number of secondary structures of RNA molecules with 10 nucleotides<ref>{{cite OEIS|A004148|Generalized Catalan numbers}}</ref>
* [[+423|Country calling code]] for [[Liechtenstein]]

====424====
424 = 2<sup>3</sup> &times; 53, sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Mertens function returns 0,<ref name=A028442/> [[refactorable number]],<ref name=A033950>{{Cite OEIS|A033950|Refactorable numbers}}</ref> self number<ref name=A003052/>

====425====
425 = 5<sup>2</sup> &times; 17, [[pentagonal number]],<ref name=A000326>{{Cite OEIS|A000326|Pentagonal numbers}}</ref> [[centered tetrahedral number]], sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0,<ref name=A028442/> the second number that can be expressed as the sum of two squares in three different ways (425 = 20<sup>2</sup> + 5<sup>2</sup> = 19<sup>2</sup> + 8<sup>2</sup> = 16<sup>2</sup> + 13<sup>2</sup>). 
* 425 is an area code in [[Washington (state)|Washington State.]]

====426====
426 = 2 &times; 3 &times; 71, sphenic number, nontotient, [[untouchable number]]

====427====
427 = 7 &times; 61, Mertens function returns 0.<ref name=A028442/> 427! + 1 is prime.

====428====
428 = 2<sup>2</sup> &times; 107, Mertens function returns 0, nontotient, 428<sup>32</sup> + 1 is prime<ref>{{cite OEIS|A006315|Numbers n such that n^32 + 1 is prime}}</ref>
*''[[428: Shibuya Scramble]]'', a video game

====429====
429 = 3 &times; 11 &times; 13, sphenic number, [[Catalan number]]<ref>{{Cite OEIS|A000108|Catalan numbers}}</ref>

===430s===

====430====
430 = 2 &times; 5 &times; 43, number of primes below 3000, sphenic number, untouchable number<ref name=A005114/>

====431====
A prime number, [[Sophie Germain prime]],<ref name=A005384/> sum of seven consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73), [[Chen prime]],<ref name=A109611/> [[oeis:A006450|prime index prime]],  [[Eisenstein prime]] with no imaginary part
*It is also the fourth [[Leyland number#Leyland number of the second kind|Leyland prime of the second kind]].
*[[Area code 431]] is a telephone area code for [[Manitoba]], Canada.

====432====
432 = 2<sup>4</sup> × 3<sup>3</sup> = 4<sup>2</sup> × 3<sup>3</sup>, the sum of four consecutive primes (103 + 107 + 109 + 113), a Harshad number, a [[highly totient number]],<ref name=A097942>{{Cite OEIS|A097942|Highly totient numbers}}</ref> an [[Achilles number]] and the 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. An equilateral triangle whose area and perimeter are equal, has an area (and perimeter) equal to <math>\sqrt{432}</math>.

====433====
A prime number, [[Markov number]],<ref>{{Cite OEIS|A002559|Markoff (or Markov) numbers}}</ref> [[star number]].<ref>{{Cite OEIS|A003154|Centered 12-gonal numbers. Also star numbers}}</ref>
* The perfect score in the game show ''[[Fifteen To One]]'', only ever achieved once in over 2000 shows. 
* 433 can refer to composer [[John Cage]]'s composition [[4′33″]] (pronounced "Four minutes, thirty-three seconds" or just "Four thirty-three").

====434====
434 = 2 &times; 7 &times; 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<ref name=A000096>{{cite OEIS|A000096|2=a(n) = n*(n+3)/2}}</ref>

====435====
435 = 3 &times; 5 &times; 29, sphenic number, 29th [[triangular number]],<ref>{{Cite web |title=A000217 - OEIS |url=https://oeis.org/A000217 |access-date=2024-11-28 |website=oeis.org}}</ref> [[hexagonal number]],<ref>{{Cite OEIS|A000384|Hexagonal numbers}}</ref> self number,<ref name=A003052/> number of compositions of 16 into distinct parts<ref>{{cite OEIS|A032020|Number of compositions (ordered partitions) of n into distinct parts}}</ref>
* The number of members in the [[US House of Representatives]].

====436====
436 = 2<sup>2</sup> &times; 109, nontotient, noncototient, lazy caterer number <ref name=A000124/>

====437====
437 = 19 &times; 23, [[Blum integer]]

====438====
438 = 2 &times; 3 &times; 73, sphenic number, [[Smith number]].<ref name=A006753>{{Cite OEIS|A006753|Smith numbers}}</ref> 
*The "438 match" or "438 game" has been used by cricket media to describe [[Fifth ODI, Australian cricket team in South Africa in 2005–06|the famous 2006 One Day International]] in which [[Australia national cricket team|Australia]] scored a world record 434 in their innings, only to see [[South Africa national cricket team|South Africa]] respond in their innings with 438.

====439====
A prime number, sum of three consecutive primes (139 + 149 + 151), sum of nine consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), strictly non-palindromic number<ref name=A016038>{{Cite OEIS|A016038|Strictly non-palindromic numbers}}</ref>

===440s===

====440====
{{Main|440 (number)}}

====441====
441 = 3<sup>2</sup> &times; 7<sup>2</sup> = 21<sup>2</sup>
* 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>).
* 441 is a [[centered octagonal number]],<ref>{{Cite OEIS|A016754|2=Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers}}</ref> a refactorable number,<ref name=A033950/> and a Harshad number.
* 441 is the number of squares on a [[Super Scrabble]] board.

====442====
442 = 2 &times; 13 &times; 17 = 21<sup>2</sup> + 1,<ref>{{cite OEIS|A002522|2=a(n) = n^2 + 1}}</ref> sphenic number, sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71)

====443====
A prime number, Sophie Germain prime,<ref name=A005384/> Chen prime,<ref name=A109611/> Eisenstein prime with no imaginary part, Mertens function sets new low of -9, which stands until 659.
*In computing, it is the default port for [[HTTP Secure|HTTPS]] connections.

====444====
444 = 2<sup>2</sup> &times; 3 &times; 37, refactorable number,<ref name=A033950/> [[Harshad number]], number of [[polyiamond|noniamonds]] without holes,<ref>{{Cite OEIS|A070765|Number of polyiamonds with n cells, without holes}}</ref> and a [[repdigit]].
* The title of the final track of [[Autechre]]'s 1993 debut album [[Incunabula (album)|''Incunabula'']].
*The 444th Fighter Squadron "Spare", a fictional air squadron in ''[[Ace Combat 7: Skies Unknown]]''.

====445====
445 = 5 &times; 89, number of series-reduced trees with 17 nodes<ref>{{cite OEIS|A000014|Number of series-reduced trees with n nodes}}</ref>

====446====
446 = 2 &times; 223, nontotient, self number<ref name=A003052/>

====447====
447 = 3 &times; 149, number of 1's in all partitions of 22 into odd parts<ref>{{cite OEIS|A036469|Partial sums of A000009 (partitions into distinct parts)}}</ref>
* The flight number of [[Air France Flight 447]]

====448====
448 = 2<sup>6</sup> &times; 7, untouchable number,<ref name=A005114/> refactorable number,<ref name=A033950/> Harshad number

====449====
A prime number, sum of five consecutive primes (79 + 83 + 89 + 97 + 101), Chen prime,<ref name=A109611/> Eisenstein prime with no imaginary part, [[Proth prime]].<ref>{{Cite OEIS|A080076|Proth primes}}</ref> Also the largest number whose [[factorial]] is less than 10<sup>1000</sup>

===450s===

====450====
450 = 2 &times; 3<sup>2</sup> &times; 5<sup>2</sup>, nontotient, sum of totient function for first 38 integers, refactorable number,<ref name=A033950/> Harshad number, 
*[[SMTP]] code meaning the requested mail action was not carried out.
*A perfect score in Canadian [[five-pin bowling]].
*An [[Area codes 450 and 579|area code]] in Southern Quebec.

====451====
451 = 11 &times; 41; 451 is a [[Wedderburn–Etherington number]]<ref>{{Cite OEIS|A001190|Wedderburn-Etherington numbers}}</ref> and a [[centered decagonal number]];<ref>{{Cite OEIS|A062786|Centered 10-gonal numbers}}</ref> its reciprocal has period 10; 451 is the smallest number with this period [[reciprocal length]].
*The novel ''[[Fahrenheit 451]]'' refers to the temperature in [[Fahrenheit]] that author [[Ray Bradbury]] understood to be the [[autoignition]] point of [[paper]].
**By extension, The numbers "451", and sometimes "0451", are often included as the first security code a player encounters in [[Immersive sim]] video games as a reference to the [[System Shock]] series of games which first included the code as their own reference to Bradbury's novel.<ref>{{cite web |last1=LeBlanc |first1=Marc |title=OG System Shock dev plays remake 1 |url=https://www.youtube.com/watch?v=3vL-Zt7Axes&t=20m38s |website=YouTube |date=June 2023 |access-date=18 August 2023}}</ref>
*[[HTTP status code]] for "[[HTTP 451|Unavailable For Legal Reasons]]" a HTTP response error when the user requests an illegal resource, such as a web page censored by a government.<ref>{{Cite web|title=451 Unavailable For Legal Reasons - HTTP {{!}} MDN|url=https://developer.mozilla.org/en-US/docs/Web/HTTP/Status/451|access-date=2021-04-23|website=developer.mozilla.org}}</ref>

====452====
452 = 2<sup>2</sup> &times; 113, number of surface-points of a tetrahedron with edge-length 15<ref>{{cite OEIS|A005893|Number of points on surface of tetrahedron}}</ref>
*SMTP code meaning that the requested mail action was not carried out because of insufficient system storage

====453====
453 = 3 &times; 151, [[Blum integer]]

====454====
454 = 2 &times; 227, nontotient, a [[Smith number]]<ref name=A006753/>

====455====
455 = 5 &times; 7 &times; 13, [[sphenic number]], [[tetrahedral number]]<ref>{{Cite OEIS|A000292|Tetrahedral numbers}}</ref>
*''455 Rocket'' is the title of a song by [[Kathy Mattea]]
*455&nbsp;kHz is a standard [[intermediate frequency]] for analog [[superheterodyne]] [[AM broadcast]] band receivers.
*The sum of the squares of the first 455 primes is divisible by 455.<ref>{{cite OEIS|A111441|Numbers k such that the sum of the squares of the first k primes is divisible by k}}</ref>

====456====
456 = 2<sup>3</sup> &times; 3 &times; 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), [[centered pentagonal number]],<ref>{{Cite OEIS|A005891|Centered pentagonal numbers}}</ref> [[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]], [[IPSOS]], the other being [[696 (number)|696]].<ref>{{cite book |author-link=Kenneth Grant (occultist) |last=Grant |first=Kenneth |year=1977 |title=Nightside of Eden |place=London |publisher=Frederick Muller Limited |isbn=0-584-10206-2 |page=119}}</ref>
* Number of contestants in the South Korean [[Netflix]] drama ''[[Squid Game]]''.

====457====
* A prime number, sum of three consecutive primes (149 + 151 + 157), self number.<ref name=A003052/>
* The international standard frequency for radio [[avalanche transceiver]]s (457&nbsp;kHz).

====458====
458 = 2 &times; 229, nontotient, number of partitions of 24 into divisors of 24<ref>{{cite OEIS|A018818|Number of partitions of n into divisors of n}}</ref>

====459====
459 = 3<sup>3</sup> &times; 17, triangular matchstick number<ref>{{cite OEIS|A045943|2=Triangular matchstick numbers: a(n) = 3*n*(n+1)/2}}</ref>
*[[459 West 18th Street]], a residential building at that address in [[Manhattan]]'s [[Chelsea, Manhattan|West Chelsea]] neighborhood, built in 2008.

===460s===

====460====
460 = 2<sup>2</sup> &times; 5 &times; 23, centered triangular number,<ref name=A005448/> dodecagonal number,<ref>{{Cite OEIS|A051624|12-gonal (or dodecagonal) numbers}}</ref> [[Harshad number]], sum of twelve consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61)

====461====
A prime number, Chen prime,<ref name=A109611/> [[sexy prime]] with 467, Eisenstein prime with no imaginary part, [[oeis:A006450|prime index prime]]

====462====
462 = 2 &times; 3 &times; 7 &times; 11, [[binomial coefficient]] <math> \tbinom {11}5 </math>, [[stirling number of the second kind]] <math>\left\{ {9 \atop 7} \right\}</math>, sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89), [[pronic number]],<ref>{{Cite OEIS|A002378|Oblong (or promic, pronic, or heteromecic) numbers}}</ref> [[sparsely totient number]],<ref>{{Cite OEIS|A036913|Sparsely totient numbers}}</ref> [[idoneal number]]

====463====
A prime number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79), [[centered heptagonal number]].<ref>{{Cite OEIS|A069099|Centered heptagonal numbers}}</ref> 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]] of [[Ceres (dwarf planet)|Ceres]]
*A common baseball [[double play]] (see [[baseball positions]])
*A single by [[Buck 65]], named after the baseball term

====464====
{{See also|4-6-4}}
464 = 2<sup>4</sup> &times; 29, [[primitive abundant number]],<ref>{{Cite OEIS|A091191|Primitive abundant numbers}}</ref> since 464 = 21<sup>2</sup> + 21 + 2 it is the maximum number of regions into which 22 [https://mathworld.wolfram.com/PlaneDivisionbyCircles.html intersecting circles divide the plane],<ref name=A014206/> maximal number of pieces that can be obtained by cutting an annulus with 29 cuts<ref name=A000096/>

* In [[chess]] it is the number of legal positions of the kings, not counting mirrored positions. Has some importance when constructing an [[endgame tablebase]].
* Model number of the home computer [[Amstrad CPC 464]].

====465====
465 = 3 &times; 5 &times; 31, [[sphenic number]], 30th [[triangular number]],<ref>{{Cite web |title=A000217 - OEIS |url=https://oeis.org/A000217 |access-date=2024-11-28 |website=oeis.org}}</ref> member of the [[Padovan sequence]],<ref>{{Cite OEIS|A000931|Padovan sequence}}</ref> Harshad number

====466====
466 = 2 &times; 233, noncototient, lazy caterer number.<ref name=A000124/>

====467====
A prime number, [[safe prime]],<ref name=A005385>{{Cite OEIS|A005385|Safe primes}}</ref> [[sexy prime]] with 461, Chen prime,<ref name=A109611/> Eisenstein prime with no imaginary part
:<math>\sum_{n=0}^{10}{467}^{n}</math> is prime<ref name=A162862/>

====468====
468 = 2<sup>2</sup> &times; 3<sup>2</sup> &times; 13, sum of ten consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), refactorable number,<ref name=A033950/> self number,<ref name=A003052/> Harshad number

====469====
469 = 7 &times; 67, [[centered hexagonal number]].<ref>{{Cite OEIS|A003215|Hex (or centered hexagonal) numbers}}</ref> 
469! - 1 is prime.

===470s===

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

====471====
471 = 3 &times; 157, sum of three consecutive primes (151 + 157 + 163), [[perfect totient number]],<ref>{{Cite OEIS|A082897|Perfect totient numbers}}</ref> φ(471) = φ(σ(471)).<ref name=A006872>{{cite OEIS|A006872|2=Numbers k such that phi(k) = phi(sigma(k))}}</ref>

====472====
472 = 2<sup>3</sup> &times; 59, nontotient, untouchable number,<ref name=A005114/> refactorable number,<ref name=A033950/> number of distinct ways to cut a 5 &times; 5 square into squares with integer sides<ref>{{cite OEIS|A045846|Number of distinct ways to cut an n X n square into squares with integer sides}}</ref>
*The [[Amstrad CPC472]] was a short-lived home computer for the Spanish market.

====473====
473 = 11 &times; 43, sum of five consecutive primes (83 + 89 + 97 + 101 + 103), [[Blum integer]]

====474====
474 = 2 &times; 3 &times; 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,<ref name=A005114/> [[nonagonal number]]<ref>{{Cite OEIS|A001106|9-gonal (or enneagonal or nonagonal) numbers}}</ref>

====475====
475 = 5<sup>2</sup> &times; 19, 49-[[polygonal number|gonal number]], member of the Mian–Chowla sequence.<ref name=A005282/>

====476====
476 = 2<sup>2</sup> &times; 7 &times; 17, [[Harshad number]], admirable number<ref>{{cite OEIS|A111592|Admirable numbers}}</ref>

====477====
477 = 3<sup>2</sup> &times; 53, [[pentagonal number]]<ref name=A000326/>

====478====
478 = 2 &times; 239, [[Pell number#Pell–Lucas numbers|Companion Pell number]], number of partitions of 26 that do not contain 1 as a part<ref>{{cite OEIS|A002865|Number of partitions of n that do not contain 1 as a part}}</ref>

====479====
A prime number, safe prime,<ref name=A005385/> sum of nine consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71), Chen prime,<ref name=A109611/> Eisenstein prime with no imaginary part, self number<ref name=A003052/>
* Also an area code in [[area code 479|the U.S. state of Arkansas]].

===480s===

====480====
480 = 2<sup>5</sup> &times; 3 &times; 5, sum of a twin prime (239 + 241), sum of four consecutive primes (109 + 113 + 127 + 131), highly totient number,<ref name=A097942/> refactorable number,<ref name=A033950/> Harshad number, [[largely composite number]]<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref>
:<math>\sum_{n=0}^{10}{480}^{n}</math> is prime<ref name=A162862/>

====481====
481 = 13 &times; 37, octagonal number,<ref name=A000567/> centered square number,<ref name=A001844/> Harshad number

====482====
482 = 2 &times; 241, nontotient, noncototient, number of series-reduced planted trees with 15 nodes<ref>{{cite OEIS|A001678|Number of series-reduced planted trees with n nodes}}</ref>

====483====
483 = 3 &times; 7 &times; 23, sphenic number, Smith number<ref name=A006753/>

====484====
484 = 2<sup>2</sup> &times; 11<sup>2</sup> = 22<sup>2</sup>, palindromic square, nontotient

====485====
485 = 5 &times; 97, number of triangles (of all sizes, including holes) in Sierpiński's triangle after 5 inscriptions<ref>{{cite OEIS|A048473|2=a(0)=1, a(n) = 3*a(n-1) + 2; a(n) = 2*3^n - 1}}</ref>
* [[RS-485]]

====486====
486 = 2 &times; 3<sup>5</sup>, Harshad number, [[Perrin number]]<ref>{{Cite OEIS|A001608|Perrin sequence}}</ref>
* Shorthand for the [[Intel 80486]] microprocessor chip.

====487====
A prime number, sum of three consecutive primes (157 + 163 + 167),  Chen prime,<ref name=A109611/>
* The only primes under 7.74 &times; 10<sup>13</sup> that divide their own [[Repeating decimal|decimal repetends]] are 3, 487, and 56598313.<ref>{{Cite OEIS|A045616|2=Primes p such that 10^(p-1) == 1 (mod p^2)}}</ref>
* Shorthand for the [[Intel 80487]] floating point processor chip.

====488====
488 = 2<sup>3</sup> &times; 61, nontotient, refactorable number,<ref name=A033950/> φ(488) = φ(σ(488)),<ref name=A006872/> number of surface points on a cube with edge-length 10.<ref>{{cite OEIS|A005897|2=a(n) = 6*n^2 + 2 for n > 0, a(0)=1}}</ref>

====489====
489 = 3 &times; 163, [[octahedral number]]<ref>{{Cite OEIS|A005900|Octahedral numbers}}</ref>

===490s===

====490====
490 = 2 &times; 5 &times; 7<sup>2</sup>, noncototient, sum of totient function for first 40 integers, number of [[integer partition]]s of 19,<ref>{{Cite OEIS|A000041|2=a(n) = number of partitions of n (the partition numbers)}}</ref> self number.<ref name=A003052/>
*A (possibly arbitrary) large number in the [[Christianity|Christian]] [[Gospel of Matthew]]. In [[Matthew 18|Matthew 18:21–35]], [[Jesus]] tells the [[Parable of the Unforgiving Servant]], instructing [[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].

====491====
A prime number, isolated prime, [[Sophie Germain prime]],<ref name=A005384/> Chen prime,<ref name=A109611/> Eisenstein prime with no imaginary part, strictly non-palindromic number<ref name="A016038">{{Cite OEIS|A016038|Strictly non-palindromic numbers}}</ref>

====492====
492 = 2<sup>2</sup> &times; 3 &times; 41, sum of six consecutive primes (71 + 73 + 79 + 83 + 89 + 97), refactorable number,<ref name=A033950/> member of a [[Ruth–Aaron pair]] with 493 under first definition

====493====
493 = 17 &times; 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<ref>{{cite OEIS|A011900|2=a(n) = 6*a(n-1) - a(n-2) - 2 with a(0) = 1, a(1) = 3}}</ref>

====494====
494 = 2 &times; 13 &times; 19 = [[eulerian number#Eulerian numbers of the second order|<math> \left\langle \!\! \left\langle {8 \atop 1} \right\rangle \!\! \right\rangle</math>]],<ref>{{cite OEIS|A008517|2=Second-order Eulerian triangle T(n, k), 1 <= k <= n}}</ref> sphenic number, nontotient

====495====
{{Main|495 (number)}}

====496====
{{Main|496 (number)}}

====497====
497 = 7 &times; 71, sum of five consecutive primes (89 + 97 + 101 + 103 + 107), lazy caterer number.<ref name=A000124/>

====498====
498 = 2 &times; 3 &times; 83, sphenic number, untouchable number,<ref name=A005114/> admirable number,<ref>{{Cite OEIS|A111592|Admirable numbers}}</ref> abundant number

====499====
A prime number, isolated prime, Chen prime,<ref name=A109611/> [[oeis:A059801|4<sup>499</sup> - 3<sup>499</sup> is prime]]

== References ==
{{Reflist}}

{{Integers|4}}
{{Authority control}}

[[Category:Integers]]