Primality proof for n = 818488084109:

Take b = 2.

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

1269391 is prime.
b^((n-1)/1269391)-1 mod n = 521784089295, which is a unit, inverse 242313004962.

(1269391) divides n-1.

(1269391)^2 > n.

n is prime by Pocklington's theorem.