Primality proof for n = 135694397:
Take b = 2.
b^(n-1) mod n = 1.
33923599 is prime. b^((n-1)/33923599)-1 mod n = 15, which is a unit, inverse 63324052.
(33923599) divides n-1.
(33923599)^2 > n.
n is prime by Pocklington's theorem.