Primality proof for n = 7537:

Take b = 2.

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

157 is prime.
b^((n-1)/157)-1 mod n = 6241, which is a unit, inverse 2239.

(157) divides n-1.

(157)^2 > n.

n is prime by Pocklington's theorem.