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.