Primality proof for n = 1618781663:

Take b = 2.

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

22679 is prime.
b^((n-1)/22679)-1 mod n = 256029465, which is a unit, inverse 1269146842.

401 is prime.
b^((n-1)/401)-1 mod n = 660993085, which is a unit, inverse 107698225.

(401 * 22679) divides n-1.

(401 * 22679)^2 > n.

n is prime by Pocklington's theorem.