400 (four hundred) is the natural number following 399 and preceding 401.
Mathematical properties
A circle is divided into 400 grads.
The number 400 equals 1111 in base 7.
Integers from 401 to 499
400s
401 401 is the 79th prime number. It is a Ramanujan prime, a Pythagorean prime, a Chen prime, a super-prime, and an Irregular prime. It is also a Tetranacci number, a zero of Mertens function, and a member of the Mian–Chowla sequence. There are 401 connected, planar, Eulerian graphs with a total of 9 vertices.
402 402 = 2 × 3 × 67. It is a sphenic number, a nontotient and a Harshad number. There are 402 graphs with 8 nodes and 9 edges.
403 403 = 13 × 31. It is a heptagonal number, a zero of Mertens function, and the smallest number that is the product of an emirp pair.
404 404 = 22 × 101, a zero of Mertens function, a nontotient and a noncototient. There are 404 integer partitions of 20 with an alternating permutation.
The HTTP 404 status code is usually sent from a web page if a user attempts to reach a broken or dead link. It has since become one of the most commonly reached, and thus most recognizable errors on the World Wide Web.
405
406 406 = 2 × 7 × 29. It is a sphenic number, the 28th triangular number, a centered nonagonal number, an even nontotient, and a Narayana's cow number.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.
407 407 = 11 × 37. It is a zero of Mertens function, a Harshad number, and a Lazy caterer number.It is the sum of the cubes of 4, 0 and 7 (43 + 03 + 73 = 407) and thus a narcissistic number. It is the sum of three consecutive primes (131 + 137 + 139).
408 408 = 23 × 3 × 17. It is a Pell number, a zero of Mertens function, an Octagonal number, an Untouchable number and a Harshad number. It is the sum of four consecutive primes (97 + 101 + 103 + 107) and the sum of eight consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).
409 409 is a prime number, a Chen prime, and a centered triangular number.
410s
410 410 = 2 × 5 × 41. It is a sphenic number, a nontotient, a Harshad number, and the sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79). There are 410 triangle-free graphs on 8 vertices.
411 411 = 3 × 137. It is a self number.
412 412 = 22 × 103. It is a nontotient, a noncototient, and the sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).
41264 + 1 is prime
413 413 = 7 × 59. It is a zero of Mertens function, a self number, and a Blum integer.
414 414 = 2 × 32 × 23. It is a zero of Mertens function, a nontotient, and a Harshad number. There are 414 balanced partitions of 31. is prime 415 415 = 5 × 83. It is a logarithmic number.
416 416 = 25 × 13. There are independent vertex sets and vertex covers in the 6-sunlet graph 417 417 = 3 × 139. It is a Blum integer. 418 418 = 2 × 11 × 19. It is a sphenic number, a balanced number. and the fourth 71-gonal number.
It is the sum of the integers between 13 and 31, inclusive.
The sum of the 84 digits of the 22nd unique prime in decimal (having a very distinct set of digits than all other known terms in the sequence).
419 419 is a prime number, a Sophie Germain prime, a Chen prime, an Eisenstein prime with no imaginary part, a highly cototient number, and a zero of Mertens function. 420s
420
421 421 is a prime number, a centered square number, and the sum of five consecutive primes (73 + 79 + 83 + 89 + 97).
422 422 = 2 × 211. It is a zero of Mertens function and a nontotient. Since 422 = 202 + 20 + 2, 422 is the maximum number of regions into which 21 intersecting circles divide the plane.
423 423 = 32 × 47. It is a zero of Mertens function and a Harshad number.
There are 423 secondary structures of RNA molecules with 10 nucleotides 424 424 = 23 × 53. It is a zero of Mertens function, a refactorable number, a self number and the sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).
425 425 = 52 × 17. It is a pentagonal number, a centered tetrahedral number, a zero of Mertens function, and the sum of three consecutive primes (137 + 139 + 149). It is the second number that can be expressed as the sum of two squares in three different ways (425 = 202 + 52 = 192 + 82 = 162 + 132).
426 426 = 2 × 3 × 71. It is a sphenic number, a nontotient, and an untouchable number.
427 427 = 7 × 61. It is a zero of Mertens function.
427! + 1 is prime.
428 428 = 22 × 107. It is a zero of Mertens function and a nontotient.
42832 + 1 is prime 429 429 = 3 × 11 × 13. It is a sphenic number and a Catalan number.
430s
430 430 = 2 × 5 × 43. It is a sphenic number and an untouchable number.
431 431 is a prime number, a Sophie Germain prime, a Chen prime, a prime index prime, an Eisenstein prime with no imaginary part, the fourth Leyland prime of the second kind and the sum of seven consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73).
432 432 = 24 × 33 = 42 × 33. It is a Harshad number, a highly totient number, an Achilles number and the sum of the totient function for first 37 integers. It is the sum of four consecutive primes (103 + 107 + 109 + 113). 432! is the first factorial that is not a Harshad number in base 10. An equilateral triangle whose area and perimeter are equal has an area (and perimeter) equal to .
433 433 is a prime number, a Markov number, and a star number. 434 434 = 2 × 7 × 31. It is a sphenic number, a nontotient and the sum of six consecutive primes (61 + 67 + 71 + 73 + 79 + 83). It is the maximal number of pieces that can be obtained by cutting an annulus with 28 cuts.
435 435 = 3 × 5 × 29. It is a sphenic number, a hexagonal number, a self number, and the 29th triangular number. There are 435 compositions of 16 into distinct parts. 436 436 = 22 × 109. It is a nontotient, a noncototient, and a lazy caterer number.
437 437 = 19 × 23. It is a Blum integer.
438 438 = 2 × 3 × 73. It is a sphenic number and a Smith number. 439 439 is a prime number and a strictly non-palindromic number. It is the sum of three consecutive primes (139 + 149 + 151) and the sum of nine consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).
440s
440 440 = 23 × 5 × 11. It is a Harshad number, an abundant number, a happy number, and the sum of the first 17 prime numbers.
A440 (pitch standard) is widely used for the musical note A4, the A above Middle C, when tuning instruments.
441 441 = 32 × 72 = 21. It is a centered octagonal number, a refactorable number, and a Harshad number.
441 is also the sum of the cubes of the first 6 natural numbers: 441 = 13 + 23 + 33 + 43 + 53 + 63.
442 442 = 2 × 13 × 17. It is a sphenic number and the sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
443 443 is a prime number, a Sophie Germain prime, a Chen prime, and an Eisenstein prime with no imaginary part.
Mertens function of 443 is -9, a new low which stands until 659. 444 444 is the largest known n for which there is a unique integer solution to a1+...+an=(a1)...(an) with a1≤a2≤...≤an.
445 445 = 5 × 89. There are 445 series-reduced trees with 17 nodes.
446 446 = 2 × 223. It is a nontotient and a self number.
447 447 = 3 × 149. There are 447 1's in all partitions of 22 into odd parts. 448 448 = 26 × 7. It is an untouchable number, a refactorable number, and a Harshad number.
449 449 is a prime number, a Chen prime, a Proth prime, an Eisenstein prime with no imaginary part, and the sum of five consecutive primes (79 + 83 + 89 + 97 + 101).
449! is the largest factorial less than 101000.
450s
450 450 = 2 × 32 × 52. It is a nontotient, a refactorable number, a Harshad number, and the sum of totient function for the first 38 integers.
451 451 = 11 × 41. It is a Wedderburn–Etherington number and a centered decagonal number. It is the smallest number whose reciprocal has period 10. 452 452 = 22 × 113. There are 452 surface-points of a tetrahedron with edge-length 15. 453 453 = 3 × 151. It is a Blum integer.
454 454 = 2 × 227. It is a nontotient and a Smith number.
455 455 = 5 × 7 × 13. It is a sphenic number and a tetrahedral number.
The sum of the squares of the first 455 primes is divisible by 455.
456 456 = 23 × 3 × 19. It is a centered pentagonal number, an icosahedral number, the sum of a pair of twin primes (227 + 229), and the sum of four consecutive primes (107 + 109 + 113 + 127).
It is one of the two values of the magical formula, IPSOS, the other being 696.
457 457 is a prime number, a self number, and the sum of three consecutive primes (149 + 151 + 157).
458 458 = 2 × 229. It is a nontotient. There are 458partitions of 24 into divisors of 24.
459 459 = 33 × 17. It is a triangular matchstick number. 460s
460 460 = 22 × 5 × 23. It is a centered triangular number, a dodecagonal number, a Harshad number, and the sum of twelve consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).
461 461 is a prime number, a Chen prime, a sexy prime with 467, an Eisenstein prime with no imaginary part, and a prime index prime.
462 462 = 2 × 3 × 7 × 11. Itis a pronic number, a sparsely totient number, an idoneal number, a stirling number of the second kind , the binomial coefficient , and the sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89).
463 463 is a prime number, a centered heptagonal number, sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79). It is the first of seven consecutive primes that are one less than a multiple of 4 (from 463 to 503).
It is a common baseball double play (see baseball positions).
There are 463 days in the synodic period of Ceres.
464
464 = 24 × 29. It is a primitive abundant number. and the maximal number of pieces that can be obtained by cutting an annulus with 29 cuts. Since 464 = 212 + 21 + 2, it is the maximum number of regions into which 22 intersecting circles divide the plane.
465 465 = 3 × 5 × 31. It is a sphenic number, a member of the Padovan sequence, a Harshad number, and the 30th triangular number.
466 466 = 2 × 233. It is a noncototient and a lazy caterer number.
467 467 is a prime number, a safe prime, a sexy prime with 461, a Chen prime, and an Eisenstein prime with no imaginary part. is prime
468 468 = 22 × 32 × 13. It is a refactorable number, a self number, a Harshad number and the sum of ten consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).
469 469 = 7 × 67. It is a centered hexagonal number.
469! - 1 is prime.
470s
470 470 = 2 × 5 × 47. It is a sphenic number, a nontotient, a noncototient, and a cake number. 471 471 = 3 × 157.It is the sum of three consecutive primes (151 + 157 + 163).
It is a perfect totient number, additionally, φ(471) = φ(σ(471)).
472 472 = 23 × 59. It is a nontotient, an untouchable number, and a refactorable number. There are 472 distinct ways to cut a 5 × 5 square into squares with integer sides. 473 473 = 11 × 43. It is a Blum integer and the sum of five consecutive primes (83 + 89 + 97 + 101 + 103).
474 474 = 2 × 3 × 79. It is a sphenic number, a nontotient, a noncototient, an untouchable number, a nonagonal number, the sum of the totient function for first 39 integers, and the sum of eight consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).
475 475 = 52 × 19. It is a 49-gonal number and a member of the Mian–Chowla sequence.
476 476 = 22 × 7 × 17. It is a Harshad number and an admirable number because it equals the sum of its proper divisors after subtracting one of them instead of adding it.
477 477 = 32 × 53. It is a pentagonal number.
478 478 = 2 × 239. It is a Companion Pell number. There are 478 partitions of 26 that do not contain 1 as a part.
479