257_(number)
257 (number)
Natural number
257 (two hundred [and] fifty-seven) is the natural number following 256 and preceding 258.
257 is a prime number of the form 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.[1]
Analogously, 257 is the third Sierpinski prime of the first kind, of the form ➜ .[2]
It is also a balanced prime,[3] an irregular prime,[4] a prime that is one more than a square,[5] and a Jacobsthal–Lucas number.[6]
Four-fold 257 is 1028, which is the prime index of the fifth Mersenne prime, 8191.[7][8]
There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (or polyhedral graphs with eight nodes).[9]