Primality proof for n = 135049:
Take b = 2.
b^(n-1) mod n = 1.
331 is prime.
b^((n-1)/331)-1 mod n = 43427, which is a unit, inverse 87323.
17 is prime.
b^((n-1)/17)-1 mod n = 122808, which is a unit, inverse 40379.
(17 * 331) divides n-1.
(17 * 331)^2 > n.
n is prime by Pocklington's theorem.