Primality proof for n = 23371:
Take b = 2.
b^(n-1) mod n = 1.
41 is prime.
b^((n-1)/41)-1 mod n = 423, which is a unit, inverse 23150.
19 is prime.
b^((n-1)/19)-1 mod n = 7813, which is a unit, inverse 13404.
(19 * 41) divides n-1.
(19 * 41)^2 > n.
n is prime by Pocklington's theorem.