Primality proof for n = 647:
Take b = 2.
b^(n-1) mod n = 1.
19 is prime.
b^((n-1)/19)-1 mod n = 543, which is a unit, inverse 591.
17 is prime.
b^((n-1)/17)-1 mod n = 292, which is a unit, inverse 534.
(17 * 19) divides n-1.
(17 * 19)^2 > n.
n is prime by Pocklington's theorem.