Primality proof for n = 1013266244677:

Take b = 2.

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

8053 is prime.
b^((n-1)/8053)-1 mod n = 979574053341, which is a unit, inverse 583849304123.

3911 is prime.
b^((n-1)/3911)-1 mod n = 718206703562, which is a unit, inverse 301643434691.

(3911 * 8053) divides n-1.

(3911 * 8053)^2 > n.

n is prime by Pocklington's theorem.