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# 400 (number)

Four hundred is the natural number following three hundred ninety-nine and preceding four hundred one.

 Cardinal Four hundred Ordinal 400th Factorization $2^4 \cdot 5^2$ Roman numeral CD Binary 110010000 Hexadecimal 190 Hebrew ת (Tav)

## Mathematical Properties

400 is the square of 20.

A circle is divided into 400 gradians, which is equal to 360 degrees and 2π radians. (Degrees and radians are the preferred 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

• a common ISO-standard film speed for photographic films.
• an HTTP status code for a bad request.
• a phrase meaning the wealthiest, most famous, or most powerful social group, leading to the generation of such lists as the Forbes 400
• in the title of the film Les Quatre Cent Coups (The 400 Blows), a French film directed by François Truffaut.

For the year 400 AD, see 400.

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), 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

405 = 34 × 5, Mertens function returns 0, Harshad number

406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number, nontotient, untouchable number, also area code for Montana

407 = 11 × 37, sum of three consecutive primes (131 + 137 + 139), Mertens function returns 0, Harshad number

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), Mertens function returns 0, octagonal number, untouchable number, Harshad number

409 prime number, centered triangular number, also name of a detergent

410 = 2 × 5 × 41, sphenic number, sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number

411 = 3 × 137, self number

412 = 22 × 103, nontotient, noncototient

413 = 7 × 59, Mertens function returns 0, self number

414 = 2 × 32 × 23, Mertens function returns 0, nontotient, Harshad number

415 = 5 × 83, it is also the area code for San Francisco, California

416 = 25 × 13

417 = 3 × 139

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

419 prime number, Sophie Germain prime, highly cototient number, Mertens function returns 0

420 has its own page

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, 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)

432 sum of four consecutive primes (103 + 107 + 109 + 113), a highly totient number, and a Harshad number.

433 prime 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, 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, Mertens function sets new low of -9, which stands until 659

444 = 22 × 3 × 37, Harshad number

445 = 5 × 89

446 = 2 × 223, nontotient, self number

447 = 3 × 149

448 = 26 × 7, untouchable number, Harshad number

449 prime number, sum of five consecutive primes (79 + 83 + 89 + 97 + 101)

450 = 2 × 32 × 52, nontotient, 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.

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

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

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

465 = 3 × 5 × 31, sphenic number, triangular number, Harshad number

466 = 2 × 233, noncototient

467 prime number, safe prime

468 = 22 × 32 × 13, sum of ten consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), 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

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, untouchable number, nonagonal number

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), 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, 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)

488 = 23 × 61, nontotient

489 = 3 × 163, octahedral number

490 = 2 × 5 × 72, noncototient, self number

491 prime number, Sophie Germain prime, strictly non-palindromic number

492 = 22 × 3 × 41, sum of six consecutive primes (71 + 73 + 79 + 83 + 89 + 97)

493 = 17 × 29, sum of seven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83)

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

495 = 32 × 5 × 11

496 now 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

03-10-2013 05:06:04