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.