Primality proof for n = 1335912079:
Take b = 2.
b^(n-1) mod n = 1.
6197 is prime.
b^((n-1)/6197)-1 mod n = 255522159, which is a unit, inverse 108130948.
61 is prime.
b^((n-1)/61)-1 mod n = 338666802, which is a unit, inverse 412790218.
(61 * 6197) divides n-1.
(61 * 6197)^2 > n.
n is prime by Pocklington's theorem.