Primality proof for n = 3251:
Take b = 3.
b^(n-1) mod n = 1.
13 is prime.
b^((n-1)/13)-1 mod n = 2941, which is a unit, inverse 2842.
5 is prime.
b^((n-1)/5)-1 mod n = 2013, which is a unit, inverse 2928.
(5^3 * 13) divides n-1.
(5^3 * 13)^2 > n.
n is prime by Pocklington's theorem.