821 is a prime number.
821 has a representation as a sum of two squares: 821 = 142 + 252.
821 and 823 form a twin prime pair.
821 is the hypotenuse of a primitive Pythagorean triple: 8212 = 4292 + 7002.
821 is the smallest prime whose reversal is a seventh power: 128 = 27.
821 = 6! + 5! - 4! + 3! - 2! + 1!
Source: Prime Curios!