17 is a prime number
17 is the sum of four primes (2+3+5+7)
17 is the first number that can be written as the sum of a positive cube and a positive square in two different ways; that is, the smallest n such that x3 + y2 = n has two different solutions for x and y positive integers. The next such number is 65.(2cubed plus 3squared (8+9) or 1cubed plus 4squared (1+16))