Primality proof for n = 12672138976649:
Take b = 2.
b^(n-1) mod n = 1.
1584017372081 is prime.
b^((n-1)/1584017372081)-1 mod n = 255, which is a unit, inverse 9740153880091.
(1584017372081) divides n-1.
(1584017372081)^2 > n.
n is prime by Pocklington's theorem.