257 is the natural number between 256 and 258. It is also a prime number.
257 is a prime number of the form 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 Proth prime. And since it is of the form 4n + 1, it is a Pythagorean prime.
It is also an irregular prime, and a long prime (in base 10) and a balanced prime. Since the next prime, 263, is 6 away, 257 is called a sexy prime.
Since 257 + 2 = 259, a semiprime, 257 is a Chen prime. It is also an Eisenstein prime with no imaginary part, and a Pierpont prime.
257 is the hypotenuse of a primitive Pythagorean triple:
In other fields
257 is the country calling code for Burundi. See List of country calling codes.