Primality proof for n = 6091:
Take b = 2.
b^(n-1) mod n = 1.
29 is prime.
b^((n-1)/29)-1 mod n = 3903, which is a unit, inverse 4095.
7 is prime.
b^((n-1)/7)-1 mod n = 1339, which is a unit, inverse 5254.
(7 * 29) divides n-1.
(7 * 29)^2 > n.
n is prime by Pocklington's theorem.