Primality proof for n = 911:
Take b = 2.
b^(n-1) mod n = 1.
13 is prime.
b^((n-1)/13)-1 mod n = 576, which is a unit, inverse 533.
7 is prime.
b^((n-1)/7)-1 mod n = 567, which is a unit, inverse 527.
(7 * 13) divides n-1.
(7 * 13)^2 > n.
n is prime by Pocklington's theorem.