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. 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.

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