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.