400 (four hundred) is the natural number following 399 and preceding 401.
[3] 404 = 22 × 101, Mertens function returns 0,[3] nontotient, noncototient, number of integer partitions of 20 with an alternating permutation.
[27] A prime number, Sophie Germain prime,[31] Chen prime,[2] Eisenstein prime with no imaginary part, highly cototient number,[32] Mertens function returns 0[3] 422 = 2 × 211, Mertens function returns 0,[3] nontotient, since 422 = 202 + 20 + 2 it is the maximum number of regions into which 21 intersecting circles divide the plane.
[34] 423 = 32 × 47, Mertens function returns 0,[3] Harshad number, number of secondary structures of RNA molecules with 10 nucleotides[35] 424 = 23 × 53, sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Mertens function returns 0,[3] refactorable number,[36] self number[20] 425 = 52 × 17, pentagonal number,[37] centered tetrahedral number, sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0,[3] the second number that can be expressed as the sum of two squares in three different ways (425 = 202 + 52 = 192 + 82 = 162 + 132).
is the first factorial that is not a Harshad number in base 10.
432 is also three-dozen sets of a dozen, making it three gross.
An equilateral triangle whose area and perimeter are equal, has an area (and perimeter) equal to
[69] This number is the first of seven consecutive primes that are one less than a multiple of 4 (from 463 to 503).
470 = 2 × 5 × 47, sphenic number, nontotient, noncototient, cake number 471 = 3 × 157, sum of three consecutive primes (151 + 157 + 163), perfect totient number,[75] φ(471) = φ(σ(471)).
[76] 472 = 23 × 59, nontotient, untouchable number,[16] refactorable number,[36] number of distinct ways to cut a 5 × 5 square into squares with integer sides[77] 473 = 11 × 43, sum of five consecutive primes (83 + 89 + 97 + 101 + 103), Blum integer 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,[16] nonagonal number[78] 475 = 52 × 19, 49-gonal number, member of the Mian–Chowla sequence.
[20] A prime number, isolated prime, Sophie Germain prime,[31] Chen prime,[2] Eisenstein prime with no imaginary part, strictly non-palindromic number[48] 492 = 22 × 3 × 41, sum of six consecutive primes (71 + 73 + 79 + 83 + 89 + 97), refactorable number,[36] 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 492 under first definition, the 493d centered octagonal number is also a centered square number[89] 494 = 2 × 13 × 19 =