Primality proof for n = 5396885861:

Take b = 2.

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

7293089 is prime.
b^((n-1)/7293089)-1 mod n = 1317483561, which is a unit, inverse 3345450373.

(7293089) divides n-1.

(7293089)^2 > n.

n is prime by Pocklington's theorem.