Primality proof for n = 13037:

Take b = 2.

b^(n-1) mod n = 1.

3259 is prime.
b^((n-1)/3259)-1 mod n = 15, which is a unit, inverse 6084.

(3259) divides n-1.

(3259)^2 > n.

n is prime by Pocklington's theorem.