400 (number)

400 Cardinal four hundred Ordinal 400th
(four hundredth)Factorization Divisors 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 Roman numeral CD Binary 110010000_{2} Octal 620_{8} Duodecimal 294_{12} Hexadecimal 190_{16} Hebrew ת (Tav) 400 (four hundred) is the natural number following 399 and preceding 401. (For the year 400 AD, see 400)
Contents
Mathematical properties
A circle is divided into 400 grads, which is equal to 360 degrees and 2π radians. (Degrees and radians are the SI accepted units).
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.
Other fields
Four hundred is also
 The Four Hundred (oligarchy) of ancient Athens.
 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), leading to the generation of such lists as the Forbes 400
 The Atari 400 home computer.
 A former limited stop bus route which operated from Bolton to Stockport and Manchester Airport from 1970 to 2004, known as the TransLancs Express.
 in the title of the film Les Quatre Cent Coups (The 400 Blows), a French film directed by François Truffaut.
 A Lebanese card game. 400 (card game)
 the designation for a class of Ontario highways called 400Series Highways.
 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.
 The yard number of the RMS Olympic, the RMS Titanic's sister ship.
 .400 (2 hits out of 5 atbats) 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 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, 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. Also HTTP status code for an unauthorized request, 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 [1].
402 = 2 × 3 × 67, sphenic number, nontotient, Harshad number, also HTTP status code for payment required, area code for Nebraska
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 for southern Alberta.
404 = 2^{2} × 101, Mertens function returns 0, nontotient, noncototient. 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.
405 = 3^{4} × 5, Mertens function returns 0, Harshad number; HTTP error code for "Method not allowed". Area code for central Oklahoma, including Oklahoma City and surrounding suburbs.
406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number, nontotient, and HTTP error code for "Not acceptable".
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 mystical significance to him, as intimated in the poem.
See also the Peugeot 406 car.
407 = 11 × 37,
 sum of cubes of 4, 0 and 7 (4^{3} + 0^{3} + 7^{3} = 407); narcissistic number
 sum of three consecutive primes (131 + 137 + 139)
 Mertens function returns 0
 Harshad number
 HTTP error code for Proxy authentication required
 Area code for Orlando, Florida
408 = 2^{3} × 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
 Mertens function returns 0
 Octagonal number
 Untouchable number
 Harshad number
 HTTP error code for Request timeout
 Area code for the Silicon Valley
409 is a prime number, Chen prime, centered triangular number.
 A family of cleaning products, Formula 409
 An engine known as the Chevrolet 409, a 409 cubic inch Wseries V8.
 The song 409 by The Beach Boys, which was inspired by the above engine.
 HTTP error code for Conflict
 Green Day have made a song, 409 in Your Coffeemaker, included on their album 1,039/Smoothed Out Slappy Hours.
 The area code for a part of eastern Texas.
 Bullet For My Valentine has released a song, "Room 409", from the album The Poison
410s
410 = 2 × 5 × 41, 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 metropolitan area and the Eastern Shore.
411 = 3 × 137, self number, HTTP error code for "Length required", slang for information (see 411)
412 = 2^{2} × 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.
413 = 7 × 59, Mertens function returns 0, self number, HTTP error code for "Request entity too large", area code for Western Massachusetts.
414 = 2 × 3^{2} × 23, Mertens function returns 0, nontotient, Harshad number, HTTP error code for "Request URI too long", Area code for Milwaukee, Wisconsin.
 The 414s, a group of hackers from Milwakuee, Wisconsin.
415 = 5 × 83, HTTP error 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
 415 (group), a rap group from Oakland, California
416 = 2^{5} × 13, HTTP error code for "Requested Range not satisfiable"
 416 is also a nickname for Toronto, based on its area code
417 = 3 × 139, HTTP error code for "Expectation failed". Also the area code for southwestern Missouri, including Springfield, and Joplin.
418 = 2 × 11 × 19, sphenic number the number of Abrahadabra, Hyper Text Coffee Pot Control Protocol error code for a teapot.
419 prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, highly cototient number, Mertens function returns 0, also refers to the Nigerian advance fee fraud scheme (after the section of the Nigerian Criminal Code it violates)
420s
420 has its own article.
421 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
422 = 2 × 211, Mertens function returns 0, nontotient
423 = 3^{2} × 47, Mertens function returns 0, Harshad number
424 = 2^{3} × 53, sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Mertens function returns 0, refactorable number, self number
425 = 5^{2} × 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 = 2^{2} × 107, Mertens function returns 0, nontotient
 428: Fūsa Sareta Shibuya de, a video game
429 = 3 × 11 × 13, sphenic number, Catalan number
430s
430 = 2 × 5 × 43, sphenic number, untouchable number
431 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
432 sum of four consecutive primes (103 + 107 + 109 + 113), a highly totient number, sum of totient function for first 37 integers and a Harshad number. 4^{2} x 3^{3}= 3^{3} x 2^{4} =432. 432 is also threedozen sets of a dozen, making it three gross.
433 prime number, Markov number, star number. The perfect score in the game show Fifteen To One, 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, self number
436 = 2^{2} × 109, nontotient, noncototient
437 = 19 × 23
438 = 2 × 3 × 73, sphenic number, Smith number. The "438 match" or "438 game" has been used by cricket media to describe the famous 2006 One Day International 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 nonpalindromic number
440s
440 = 2^{3} × 5 × 11, the sum of the first seventeen prime numbers, Harshad number, also, in hertz, the standard frequency to which most orchestras tune the pitch A above middle C. A few orchestras tune slightly flatter or sharper than this.
441 = 3^{2} × 7^{2} = 21^{2}
 441 is the sum of the cubes of the first 6 natural numbers (441 = 1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} + 6^{3}).
 441 is a centered octagonal number, a refactorable number, and a Harshad number.
 441 is the number of squares on a Super Scrabble board.
442 = 2 × 13 × 17, sphenic number, sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71)
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 = 2^{2} × 3 × 37, refactorable number, Harshad number
445 = 5 × 89
446 = 2 × 223, nontotient, self number
447 = 3 × 149
448 = 2^{6} × 7, untouchable number, refactorable number, Harshad number
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 is less than 10^{1000}
450s
450 = 2 × 3^{2} × 5^{2}, 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 fivepin bowling
451 is a Wedderburn–Etherington number and a centered decagonal number; its reciprocal has period 10; 451 is the smallest number with this period reciprocal length.
 The number also has significance in the novel Fahrenheit 451, as it is the temperature at which the paper in books ignites.
452 = 2^{2} × 113, also SMTP code meaning that the requested mail action was not carried out because of insufficient system storage
453 = 3 × 151
454 = 2 × 227, nontotient, a Smith number
455 = 5 × 7 × 13, sphenic number, tetrahedral number
 455 Rocket is the title of a song by Kathy Mattea
456 = 2^{3} × 3 × 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), centered pentagonal number
457 prime number, sum of three consecutive primes (149 + 151 + 157), self number
458 = 2 × 229, nontotient
459 = 3^{3} × 17
460s
460 = 2^{2} × 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
462 = 2 × 3 × 7 × 11, sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89), pronic number, sparsely totient number
463 prime number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79), centered heptagonal number, number of days in the synodic period of Ceres
 A common baseball double play (see baseball positions)
 A single by Buck 65, named after the baseball term
464 = 2^{4} × 29
 In chess it is the number of legal positions of the kings, not counting mirrored positions. Has some importance when constructing an endgame tablebase.
 See also: 464, the year AD 464.
465 = 3 × 5 × 31, sphenic number, triangular number, member of the Padovan sequence, Harshad number
466 = 2 × 233, noncototient
467 prime number, safe prime, Chen prime, Eisenstein prime with no imaginary part
468 = 2^{2} × 3^{2} × 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
470s
470 = 2 × 5 × 47, sphenic number, nontotient, noncototient
 In golf, 470 is the minimum length in yards from the tee to the hole on a Par 5.
471 = 3 × 157, sum of three consecutive primes (151 + 157 + 163), perfect totient number
472 = 2^{3} × 59, nontotient, untouchable number, refactorable number
473 = 11 × 43, sum of five consecutive primes (83 + 89 + 97 + 101 + 103)
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 49gonal number, member of the Mian–Chowla sequence.
476 = 2^{2} × 7 × 17, Harshad number
477 = 3^{2} × 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 = 2^{5} × 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
482 = 2 × 241, nontotient, noncototient
483 = 3 × 7 × 23, sphenic number, Smith number
484 = 2^{2} × 11^{2} = 22^{2}, nontotient
485 = 5 × 97
486 = 2 × 3^{5}, Harshad number, also shorthand for the Intel 80486 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 = 2^{3} × 61, nontotient, refactorable number
489 = 3 × 163, octahedral number
490s
490 = 2 × 5 × 7^{2}, noncototient, sum of totient function for first 40 integers, self number.
 In Christianity, the Gospel of Matthew (Matthew 18:2122) says that Jesus told Peter to forgive his brother "seventy times seven" times when his brother sins against him [2].
 Also the number of Pokémon available as of the release of Pokémon Diamond and Pearl (excluding event Pokémon)^{[1]}
491 prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, strictly nonpalindromic number
492 = 2^{2} × 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 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.
494 = 2 × 13 × 19, sphenic number, nontotient
495 has its own article.
496 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
References
Categories: Integers
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