Primality proof for n = 32371:
Take b = 2.
b^(n-1) mod n = 1.
83 is prime.
b^((n-1)/83)-1 mod n = 18904, which is a unit, inverse 16379.
13 is prime.
b^((n-1)/13)-1 mod n = 24780, which is a unit, inverse 30371.
(13 * 83) divides n-1.
(13 * 83)^2 > n.
n is prime by Pocklington's theorem.