313 is a prime number, as is 10313 + 313.
313 has a representation as a sum of two squares: 313 = 122 + 132.
If 313 people are chosen at random, then the probability that at least five of them will share the same birthday is greater than 50%.
313 is 100111001 in base 2 (binary).
311 and 313 form a twin prime pair.
313 is the hypotenuse of a primitive Pythagorean triple: 3132 = 252 + 3122.
Source: Prime Curios!