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.