Primality proof for n = 105465631:

Take b = 2.

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

13367 is prime.
b^((n-1)/13367)-1 mod n = 78944065, which is a unit, inverse 60399229.

(13367) divides n-1.

(13367)^2 > n.

n is prime by Pocklington's theorem.