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.