400 (number)
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Four hundred is the natural number following three hundred ninety-nine and preceding four hundred one.
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| Cardinal | Four hundred | ||
| Ordinal | 400th | ||
| Factorization | <math>2^4 \cdot 5^2<math> | ||
| 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.
See also: three hundred, five hundred
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, HTTP error code for Method not allowed
406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number, nontotient, untouchable number, also area code for Montana, HTTP error code for Not acceptable
407 = 11 × 37, sum of three consecutive primes (131 + 137 + 139), Mertens function returns 0, Harshad number, HTTP error code for Proxy authentication required
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
- HTTP error code for Request timeout
409 is a prime number, 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, 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
See also: 4-6-4, the year AD 464.
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
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), 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, pentatope number
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 numberko:400