Primality proof for n = 3911:
Take b = 2.
b^(n-1) mod n = 1.
23 is prime.
b^((n-1)/23)-1 mod n = 990, which is a unit, inverse 3512.
17 is prime.
b^((n-1)/17)-1 mod n = 554, which is a unit, inverse 1659.
(17 * 23) divides n-1.
(17 * 23)^2 > n.
n is prime by Pocklington's theorem.