Primality proof for n = 9049:
Take b = 2.
b^(n-1) mod n = 1.
29 is prime.
b^((n-1)/29)-1 mod n = 5938, which is a unit, inverse 4174.
13 is prime.
b^((n-1)/13)-1 mod n = 3978, which is a unit, inverse 8337.
(13 * 29) divides n-1.
(13 * 29)^2 > n.
n is prime by Pocklington's theorem.