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.