400 (number)

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

Template:Numbers 0-1000
Cardinal	400 four hundred
Ordinal	400th four hundredth
Factorization	$2^{4}\cdot 5^{2}$
Roman numeral	CD
Roman numeral (Unicode)	CD, cd
Binary	110010000
Octal	620
Duodecimal	294
Hexadecimal	190
Hebrew	ת (Tav)

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 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.

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. Also, area code for Rhode Island, also HTTP status code for an unauthorized request, also in the name of a retirement plan, 401(k)

402 = 2 × 3 × 67, sphenic number, nontotient, Harshad number, also HTTP status code for payment required

403 = 13 × 31, Mertens function returns 0. Also, HTTP status code for forbidden, also in the name of a retirement plan, 403(b)

404 = 2² × 101, Mertens function returns 0, nontotient, noncototient. Also, HTTP status code for "file not found", perhaps the most famous HTTP status code of all time, Secton 404 of the Sarbanes-Oxley Act. .

405 = 3⁴ × 5, Mertens function returns 0, Harshad number; HTTP error code for "Method not allowed"; see also Interstate 405

406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number, nontotient, untouchable number, also area code for Montana, 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 three consecutive primes (131 + 137 + 139)
Mertens function returns 0
Harshad number
HTTP error code for Proxy authentication required
The number of species in the anime series Pokèmon

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 cleaning product 409®, see butoxyethanol
There is also an automobile called the 409
For the song about that car, see the group The Beach Boys.
The year 409 or 409 BC
HTTP error code for Conflict

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

412 = 2² × 103, nontotient, noncototient, HTTP error code for recondition 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

415 = 5 × 83, it is also the area code for San Francisco, California, HTTP error code for Unsupported media type

416 = 2⁵ × 13, HTTP error code for Requested Range not satisfiable

417 = 3 × 139, HTTP error code for Expectation failed

418 = 2 × 11 × 19, sphenic number, also area code for Quebec

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)

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

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. 432 is also the area code for parts of West Texas.

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

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. Also the largest number whose factorial is less than 10¹⁰⁰⁰

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

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 burns.

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

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

463 prime number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79), centered heptagonal number

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

470 = 2 × 5 × 47, sphenic number, nontotient, noncototient

471 = 3 × 157, sum of three consecutive primes (151 + 157 + 163)

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; see also, Interstate 475

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

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

488 = 2³ × 61, nontotient, refactorable number

489 = 3 × 163, octahedral number

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

494 = 2 × 13 × 19, sphenic number, nontotient

495 = 3² × 5 × 11, pentatope number, 51-gonal number, 166-gonal number. In base 10, 495 has the property that if you start with a three digit number, arrange the digits in ascending order, then in descending order, subtracting the smaller number from the larger number and repeating the process eventually yields 495.

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