257 is a prime number of the form $2^{2^{n}}+1,$ specifically with n = 3, and therefore a Fermat prime. Thus a regular polygon with 257 sides is constructible with compass and unmarked straightedge. It is currently the second largest known Fermat prime.

It is also a balanced prime, an irregular prime, a prime that is one more than a square, and a Jacobsthal–Lucas number.

There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (or polyhedral graphs with eight nodes).