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.