Primality proof for n = 3398045597:

Take b = 2.

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

323131 is prime.
b^((n-1)/323131)-1 mod n = 1985494282, which is a unit, inverse 1724205324.

(323131) divides n-1.

(323131)^2 > n.

n is prime by Pocklington's theorem.