Primality proof for n = 11534742073:
Take b = 2.
b^(n-1) mod n = 1.
6053 is prime.
b^((n-1)/6053)-1 mod n = 7116603997, which is a unit, inverse 5101419044.
199 is prime.
b^((n-1)/199)-1 mod n = 10971630218, which is a unit, inverse 79262084.
(199 * 6053) divides n-1.
(199 * 6053)^2 > n.
n is prime by Pocklington's theorem.