Primality proof for n = 10601:
Take b = 2.
b^(n-1) mod n = 1.
53 is prime.
b^((n-1)/53)-1 mod n = 8819, which is a unit, inverse 9203.
5 is prime.
b^((n-1)/5)-1 mod n = 402, which is a unit, inverse 6830.
(5^2 * 53) divides n-1.
(5^2 * 53)^2 > n.
n is prime by Pocklington's theorem.