Primality proof for n = 4691:
Take b = 2.
b^(n-1) mod n = 1.
67 is prime.
b^((n-1)/67)-1 mod n = 2920, which is a unit, inverse 2617.
7 is prime.
b^((n-1)/7)-1 mod n = 1825, which is a unit, inverse 3249.
(7 * 67) divides n-1.
(7 * 67)^2 > n.
n is prime by Pocklington's theorem.