← 399 401 → 400
← 400 410 420 430 440 450 460 470 480 490 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
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	1100100002
Octal	6208
Duodecimal	29412
Hexadecimal	19016
Hebrew ת (Tav)

400 (four hundred) is the natural number following three hundred [and] ninety-nine and preceding four hundred [and] one.

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.
• 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.
• For the year 400 AD, see 400.
• The classic novel Fahrenheit 451.
• The yard number of the RMS Olympic, the RMS Titanic's sister ship.

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, 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".

Wikisource has original text related to this article:

406

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 (4³ + 0³ + 7³ = 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 = 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 error code for Request timeout

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 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".

411 = 3 × 137, self number, HTTP error code for "Length required", slang for information (see 4-1-1)

412 = 2² × 103, nontotient, noncototient, HTTP error code for "Precondition failed".

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

414 = 2 × 3² × 23, Mertens function returns 0, nontotient, Harshad number, HTTP error code for "Request URI too long", Area code for Milwaukee, 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.

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

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

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, Zuckerman 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

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, sum of the cubes of the first natural numbers, centered octagonal number, refactorable number, Harshad number

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 Wedderburn-Etherington number; 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 fictional 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, Smith number

455 = 5 × 7 × 13, sphenic number, tetrahedral number

• 455 Rocket is the title of a song by Kathy Mattea

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

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 = 2⁴ × 29

See also: 4-6-4, 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 = 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. In Christianity, the Matthew 18:21-22 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 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

• Currently the number of Pokémon species, from the first set through the fourth generation (see List of Pokémon)

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