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.