397 is a prime number.
397 is conjectured to be the largest prime that can be represented uniquely as the sum of three positive squares (32 + 82 + 182).
397 is a Cuban prime. Cuban primes, named after differences between successive cubic numbers, have the form n3 - (n - 13).
397 has a representation as a sum of two squares: 397 = 62 + 192.
397 is the hypotenuse of a primitive Pythagorean triple: 3972 = 2282 + 3252.
Source: Prime Curios!