Primality proof for n = 11483:

Take b = 2.

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

5741 is prime.
b^((n-1)/5741)-1 mod n = 3, which is a unit, inverse 3828.

(5741) divides n-1.

(5741)^2 > n.

n is prime by Pocklington's theorem.