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.