204 is a
refactorable number. 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). Its square, 2042 = 41616, is the fourth
square triangular number. As a
figurate number, 204 is also a
nonagonal number and a truncated triangular pyramid number. 204 is a member of the
Mian-Chowla sequence. There are exactly 204
irreducible quintic polynomials over a four-element field, exactly 204 ways to place three non-attacking
chess queens on a 5 × 5 board, exactly 204 squares of an infinite chess move that are eight knight's moves from the center, exactly 204 strings of length 11 over a three-letter alphabet with no consecutively-repeated substring, and exactly 204 ways of
immersing an oriented circle into the oriented plane so that it has four double points. 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. ==In other fields==