617

617 is a prime number.

617 and 619 form a twin prime pair.

617 = 1!² + 2!² + 3!² + 4!².

617 is the largest multi-digit prime that is exactly half of a number formed with distinct consecutive digits: 1234.

617 has a representation as a sum of two squares: 617 = 16² + 19².

617 is the hypotenuse of a primitive Pythagorean triple: 617² = 105² + 608².

617 is a divisor of 31¹¹ - 1.

Source: Prime Curios!