Primality proof for n = 613:
Take b = 2.
b^(n-1) mod n = 1.
17 is prime.
b^((n-1)/17)-1 mod n = 585, which is a unit, inverse 197.
3 is prime.
b^((n-1)/3)-1 mod n = 64, which is a unit, inverse 182.
(3^2 * 17) divides n-1.
(3^2 * 17)^2 > n.
n is prime by Pocklington's theorem.