# 400 (number)

400 (number)
400
Cardinal four hundred
Ordinal 400th
(four hundredth)
Factorization $2^4 \cdot 5^2$
Divisors 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Roman numeral CD
Binary 1100100002
Octal 6208
Duodecimal 29412
Hebrew ת (Tav)

400 (four hundred) is the natural number following 399 and preceding 401. (For the year 400 AD, see 400)

## Mathematical properties

400 is the square of 20.

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 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.

## 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 = 22 × 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 = 34 × 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.

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
• HTTP error code for Proxy authentication required
• Area code for Orlando, Florida

408 = 23 × 3 × 17

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

### 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 4-1-1)

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

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

414 = 2 × 32 × 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 = 25 × 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 = 32 × 47, Mertens function returns 0, Harshad number

424 = 23 × 53, sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Mertens function returns 0, refactorable number, self number

425 = 52 × 17, sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0

426 = 2 × 3 × 71, sphenic number, nontotient, untouchable number

427 = 7 × 61, Mertens function returns 0

428 = 22 × 107, Mertens function returns 0, nontotient

• 428: Fūsa Sareta Shibuya de, a video game

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

### 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. 42 x 33= 33 x 24 =432. 432 is also three-dozen sets of a dozen, making it three gross.

433 prime number, Markov number, 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 = 22 × 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 non-palindromic number

### 440s

440 = 23 × 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 = 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 = 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 = 22 × 3 × 37, refactorable number, Harshad number

445 = 5 × 89

446 = 2 × 223, nontotient, self number

447 = 3 × 149

448 = 26 × 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 101000

### 450s

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

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 = 22 × 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

456 = 23 × 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 = 33 × 17

### 460s

460 = 22 × 5 × 23, centered triangular number, Harshad number, sum of twelve consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61)

461 prime number, Chen prime, Eisenstein prime with no imaginary part

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

464 = 24 × 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.

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 = 22 × 32 × 13, sum of ten consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), refactorable number, self number, Harshad number

469 = 7 × 67, centered hexagonal number

### 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 = 23 × 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 49-gonal number, member of the Mian–Chowla sequence.

476 = 22 × 7 × 17, Harshad number

477 = 32 × 53

478 = 2 × 239

479 prime number, safe prime, sum of nine consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71), Chen prime, Eisenstein prime with no imaginary part, self number

### 480s

480 = 25 × 3 × 5, sum of a twin prime (239 + 241), sum of four consecutive primes (109 + 113 + 127 + 131), highly totient number, refactorable number, Harshad number

481 = 13 × 37, octagonal number, centered square number, Harshad number

482 = 2 × 241, nontotient, noncototient

483 = 3 × 7 × 23, sphenic number, Smith number

484 = 22 × 112 = 222, nontotient

485 = 5 × 97

486 = 2 × 35, Harshad number, also shorthand for the Intel 80486 microprocessor chip

487 prime number, sum of three consecutive primes (157 + 163 + 167), Chen prime, shorthand for the Intel 80487 floating point processor chip.

488 = 23 × 61, nontotient, refactorable number

489 = 3 × 163, octahedral number

### 490s

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

491 prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number

492 = 22 × 3 × 41, sum of six consecutive primes (71 + 73 + 79 + 83 + 89 + 97), refactorable number, member of a Ruth–Aaron pair with 493 under first definition

493 = 17 × 29, sum of seven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83), member of a Ruth–Aaron pair with 493 under first definition

• As of August 2009, the number of Pokémon 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

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