Primality proof for n = 991:
Take b = 2.
b^(n-1) mod n = 1.
11 is prime.
b^((n-1)/11)-1 mod n = 49, which is a unit, inverse 809.
5 is prime.
b^((n-1)/5)-1 mod n = 798, which is a unit, inverse 267.
(5 * 11) divides n-1.
(5 * 11)^2 > n.
n is prime by Pocklington's theorem.