Primality proof for n = 11760675247:

Take b = 2.

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

653370847 is prime.
b^((n-1)/653370847)-1 mod n = 262143, which is a unit, inverse 9754285916.

(653370847) divides n-1.

(653370847)^2 > n.

n is prime by Pocklington's theorem.