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|---|---|---|---|---|
| Cardinal | four hundred | |||
| Ordinal | 400th (four hundredth) |
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| Factorization | 24× 52 | |||
| Divisors | 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 | |||
| Roman numeral | CD | |||
| Binary | 1100100002 | |||
| Ternary | 1122113 | |||
| Quaternary | 121004 | |||
| Quinary | 31005 | |||
| Senary | 15046 | |||
| Octal | 6208 | |||
| Duodecimal | 29412 | |||
| Hexadecimal | 19016 | |||
| Vigesimal | 10020 | |||
| Base 36 | B436 | |||
| Hebrew | ת (Tav) | |||
400 (four hundred) is the natural number following 399 and preceding 401.
Mathematical properties[edit]
400 is the square of 20. 400 is the sum of the powers of 7 from 0 to 3, thus making it a repdigit in base 7 (1111).
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[edit]
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 Trans-Lancs 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 400-Series 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 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 year changes according to a cycle of exactly 400 years, of which 97 are leap years and 303 are common.
- 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
- 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.
- In gematria 400 is the largest single number that can be represented without using the Sophit forms (see Kaph, Mem, Nun, Pe, and Tzade).
Integers from 401 to 499[edit]
400s[edit]
401[edit]
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.
- 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 [1].
402[edit]
402 = 2 × 3 × 67, sphenic number, nontotient, Harshad number,
- HTTP status code for "Payment Required", area code for Nebraska
403[edit]
403 = 13 × 31, Mertens function returns 0.
- 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[edit]
404 = 22 × 101, Mertens function returns 0, nontotient, noncototient.
- 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[edit]
405 = 34 × 5, Mertens function returns 0, Harshad number;
- HTTP status code for "Method Not Allowed".
- Area code for central Oklahoma, including Oklahoma City and surrounding suburbs.
406[edit]
406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number, nontotient
- HTTP status 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[edit]
407 = 11 × 37,
- sum of cubes of 4, 0 and 7 (43 + 03 + 73 = 407); narcissistic number
- sum of three consecutive primes (131 + 137 + 139)
- Mertens function returns 0
- Harshad number
- HTTP status code for "Proxy Authentication Required"
- Area code for Orlando, Florida
- Colloquial name for the Express Toll Route in Ontario
408[edit]
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
- Mertens function returns 0
- Octagonal number
- Untouchable number
- Harshad number
- HTTP status code for "Request Timeout"
- Area code for the Silicon Valley
409[edit]
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 W-series V8.
- The song "409" by The Beach Boys, which was inspired by the above engine.
- HTTP status 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[edit]
410[edit]
410 = 2 × 5 × 41, sphenic number, sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number
- HTTP status 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[edit]
411 = 3 × 137, self number,
- HTTP status code for "Length Required", slang for information (see 4-1-1)
412[edit]
412 = 22 × 103, nontotient, noncototient, sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59)
- HTTP status code for "Precondition Failed"
- Area code for Pittsburgh, Pennsylvania.
- Fictitious Police Code for "Overacting" from "St. George and the Dragonet" - Stan Freeberg
413[edit]
413 = 7 × 59, Mertens function returns 0, self number
- HTTP status code for "Request Entity Too Large", area code for Western Massachusetts.
- A very prominent and recurring number in the webcomic Homestuck.
414[edit]
414 = 2 × 32 × 23, Mertens function returns 0, nontotient, Harshad number
- HTTP status code for "Request-URI Too Long", Area code for Milwaukee, Wisconsin.
- The 414s, a group of hackers from Milwaukee, Wisconsin.
415[edit]
415 = 5 × 83,
- 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
- 415 (group), a rap group from Oakland, California
416[edit]
416 = 25 × 13
- HTTP status code for "Requested Range Not Satisfiable"
- 416 is also a nickname for the city of Toronto, based on the area code it used before overlay plans added two more area codes.
417[edit]
417 = 3 × 139
- HTTP status code for "Expectation Failed". Also the area code for southwestern Missouri, including Springfield, and Joplin.
418[edit]
418 = 2 × 11 × 19, sphenic number,
- the number of Abrahadabra, Hyper Text Coffee Pot Control Protocol status code for "Teapot" as an April Fools' joke.
419[edit]
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)
420s[edit]
420[edit]
421[edit]
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
422[edit]
422 = 2 × 211, Mertens function returns 0, nontotient
423[edit]
423 = 32 × 47, Mertens function returns 0, Harshad number
424[edit]
424 = 23 × 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[edit]
425 = 52 × 17, pentagonal number, sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0
426[edit]
426 = 2 × 3 × 71, sphenic number, nontotient,
427[edit]
427 = 7 × 61, Mertens function returns 0
428[edit]
428 = 22 × 107, Mertens function returns 0, nontotient
- 428: Fūsa Sareta Shibuya de, a video game
429[edit]
429 = 3 × 11 × 13, sphenic number, Catalan number
430s[edit]
430[edit]
430 = 2 × 5 × 43, sphenic number, untouchable number
431[edit]
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
- The distance between Earth and the star Polaris in light years
432[edit]
432 = 24 x 33 = 42 x 33, 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.
433[edit]
A prime number, Markov number, star number.
- 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[edit]
434 = 2 × 7 × 31, sphenic number, sum of six consecutive primes (61 + 67 + 71 + 73 + 79 + 83), nontotient
435[edit]
435 = 3 × 5 × 29, sphenic number, triangular number, hexagonal number, self number
436[edit]
436 = 22 × 109, nontotient, noncototient
437[edit]
437 = 19 × 23
438[edit]
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[edit]
A prime number, sum of three consecutive primes (139 + 149 + 151), sum of nine consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), strictly non-palindromic number
440s[edit]
440[edit]
440 = 23 × 5 × 11, the sum of the first seventeen prime numbers, Harshad number,
- 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[edit]
441 = 32 × 72 = 212
- 441 is the sum of the cubes of the first 6 natural numbers (441 = 13 + 23 + 33 + 43 + 53 + 63).
- 441 is a centered octagonal number, a refactorable number, and a Harshad number.
- 441 is the number of squares on a Super Scrabble board.
442[edit]
442 = 2 × 13 × 17, sphenic number, sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71)
443[edit]
A prime number, Sophie Germain prime, Chen prime,+ Eisenstein prime with no imaginary part, Mertens function sets new low of -9, which stands until 659.
- In computing, it is the default port for HTTPS connections.
444[edit]
444 = 22 × 3 × 37, refactorable number, Harshad number.
445[edit]
445 = 5 × 89
446[edit]
446 = 2 × 223, nontotient, self number
447[edit]
447 = 3 × 149
448[edit]
448 = 26 × 7, untouchable number, refactorable number, Harshad number
449[edit]
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 101000
450s[edit]
450[edit]
450 = 2 × 32 × 52, nontotient, sum of totient function for first 38 integers, refactorable number, Harshad number,
- SMTP code meaning the requested mail action was not carried out, a perfect score in Canadian five-pin bowling and an area code in Southern Quebec.
451[edit]
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.
- The novel Fahrenheit 451 refers to the temperature in Fahrenheit that author Ray Bradbury understood to be the autoignition point of paper.
452[edit]
452 = 22 × 113
- SMTP code meaning that the requested mail action was not carried out because of insufficient system storage
453[edit]
453 = 3 × 151
454[edit]
454 = 2 × 227, nontotient, a Smith number
455[edit]
455 = 5 × 7 × 13, sphenic number, tetrahedral number
- 455 Rocket is the title of a song by Kathy Mattea
- 455 kHz is a standard intermediate frequency for analog superheterodyne AM broadcast band receivers.
456[edit]
456 = 23 × 3 × 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), centered pentagonal number
457[edit]
- A prime number, sum of three consecutive primes (149 + 151 + 157), self number.
- The international standard frequency for radio avalanche transceivers (457 kHz).
458[edit]
458 = 2 × 229, nontotient
459[edit]
459 = 33 × 17
460s[edit]
460[edit]
460 = 22 × 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)
461[edit]
A prime number, Chen prime, sexy prime with 467, Eisenstein prime with no imaginary part
462[edit]
462 = 2 × 3 × 7 × 11, binomial coefficient 
, sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89), pronic number, sparsely totient number
463[edit]
A 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[edit]
464 = 24 × 29, primitive abundant number
- 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: 4-6-4, the year AD 464.
465[edit]
465 = 3 × 5 × 31, sphenic number, triangular number, member of the Padovan sequence, Harshad number
466[edit]
466 = 2 × 233, noncototient
467[edit]
A prime number, safe prime, sexy prime with 461, Chen prime, Eisenstein prime with no imaginary part
468[edit]
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[edit]
469 = 7 × 67, centered hexagonal number
470s[edit]
470[edit]
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.
- 470 is an Olympic class of sailing dinghy
471[edit]
471 = 3 × 157, sum of three consecutive primes (151 + 157 + 163), perfect totient number
472[edit]
472 = 23 × 59, nontotient, untouchable number, refactorable number
473[edit]
473 = 11 × 43, sum of five consecutive primes (83 + 89 + 97 + 101 + 103)
474[edit]
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[edit]
475 = 52 × 19, 49-gonal number, member of the Mian–Chowla sequence.
476[edit]
476 = 22 × 7 × 17, Harshad number
477[edit]
477 = 32 × 53, pentagonal number
478[edit]
478 = 2 × 239
479[edit]
A prime number, safe prime, sum of nine consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71), Chen prime, Eisenstein prime with no imaginary part, self number
- Also an area code in the U.S. state of Arkansas.
480s[edit]
480[edit]
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[edit]
481 = 13 × 37, octagonal number, centered square number, Harshad number
482[edit]
482 = 2 × 241, nontotient, noncototient
483[edit]
483 = 3 × 7 × 23, sphenic number, Smith number
484[edit]
484 = 22 × 112 = 222, nontotient
485[edit]
485 = 5 × 97
486[edit]
486 = 2 × 35, Harshad number, Perrin number
- shorthand for the Intel 80486 microprocessor chip
487[edit]
A prime number, sum of three consecutive primes (157 + 163 + 167), Chen prime,
- The only primes under 200,000,000 that divide their own decimal periods are 3, 487, and 56598313.
- Shorthand for the Intel 80487 floating point processor chip.
488[edit]
488 = 23 × 61, nontotient, refactorable number
489[edit]
489 = 3 × 163, octahedral number
490s[edit]
490[edit]
490 = 2 × 5 × 72, noncototient, sum of totient function for first 40 integers, partition number (integer partitions of 19), self number.
- In Christianity, the Gospel of Matthew (Matthew 18:21-22) says that Jesus told Peter to forgive his brother "seventy times seven" times when his brother sins against him [2].
491[edit]
A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number
492[edit]
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[edit]
493 = 17 × 29, sum of seven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83), member of a Ruth–Aaron pair with 492 under first definition
494[edit]
494 = 2 × 13 × 19, sphenic number, nontotient
495[edit]
496[edit]
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)
497[edit]
497 = 7 × 71, sum of five consecutive primes (89 + 97 + 101 + 103 + 107)
498[edit]
498 = 2 × 3 × 83, sphenic number, untouchable number, admirable number, abundant number
499[edit]
A prime number, Chen prime
References[edit]
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