Primality proof for n = 11351:

Take b = 2.

b^(n-1) mod n = 1.

227 is prime.
b^((n-1)/227)-1 mod n = 6858, which is a unit, inverse 4550.

(227) divides n-1.

(227)^2 > n.

n is prime by Pocklington's theorem.