Primality proof for n = 9613:
Take b = 2.
b^(n-1) mod n = 1.
89 is prime.
b^((n-1)/89)-1 mod n = 5873, which is a unit, inverse 7292.
3 is prime.
b^((n-1)/3)-1 mod n = 3085, which is a unit, inverse 2175.
(3^3 * 89) divides n-1.
(3^3 * 89)^2 > n.
n is prime by Pocklington's theorem.