Primality proof for n = 937:

Take b = 2.

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

13 is prime.
b^((n-1)/13)-1 mod n = 155, which is a unit, inverse 133.

3 is prime.
b^((n-1)/3)-1 mod n = 613, which is a unit, inverse 107.

(3^2 * 13) divides n-1.

(3^2 * 13)^2 > n.

n is prime by Pocklington's theorem.