Primality proof for n = 2549:
Take b = 2.
b^(n-1) mod n = 1.
13 is prime.
b^((n-1)/13)-1 mod n = 1146, which is a unit, inverse 1577.
7 is prime.
b^((n-1)/7)-1 mod n = 2118, which is a unit, inverse 1171.
(7^2 * 13) divides n-1.
(7^2 * 13)^2 > n.
n is prime by Pocklington's theorem.