204 (number)

204 is a refactorable number.^[1] 204 is a square pyramidal number: 204 balls may be stacked in a pyramid whose base is an 8 × 8 square, as it is a sum of all the perfect squares from 1 to 64 (i.e. 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² = 204).^[2] Its square, 204² = 41616, is the fourth square triangular number.^[3] As a figurate number, 204 is also a nonagonal number^[4] and a truncated triangular pyramid number.^[5] 204 is a member of the Mian-Chowla sequence.^[6]

There are exactly 204 irreducible quintic polynomials over a four-element field,^[7] exactly 204 ways to place three non-attacking chess queens on a 5 × 5 board,^[8] exactly 204 squares of an infinite chess move that are eight knight's moves from the center,^[9] exactly 204 strings of length 11 over a three-letter alphabet with no consecutively-repeated substring,^[10] and exactly 204 ways of immersing an oriented circle into the oriented plane so that it has four double points.^[11]

Both 204 and its square are sums of a pair of twin primes: 204 = 101 + 103 and 204² = 41616 = 20807 + 20809. The only smaller numbers with the same property are 12 and 84.^[12]

• 204 is the HTTP status code indicating the request was successfully fulfilled and that there is no additional content to send in the response payload body.^[13]