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.