409

409 is a prime number.

409 is a centered triangular number.

409 has a representation as a sum of two squares: 409 = 3² + 20².

409 is the hypotenuse of a primitive Pythagorean triple: 409² = 120² + 391².

409 is the smallest prime that, along with both its prime neighbors, uses non-prime digits: 401, 409, 419.

409 is the number of primes less than 10,000 that form members of twin prime pairs.

Source: Prime Curios!