Primality proof for n = 617:
Take b = 2.
b^(n-1) mod n = 1.
11 is prime.
b^((n-1)/11)-1 mod n = 417, which is a unit, inverse 472.
7 is prime.
b^((n-1)/7)-1 mod n = 419, which is a unit, inverse 483.
(7 * 11) divides n-1.
(7 * 11)^2 > n.
n is prime by Pocklington's theorem.