Primality proof for n = 108654662777:

Take b = 2.

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

853291 is prime.
b^((n-1)/853291)-1 mod n = 11514690233, which is a unit, inverse 51817184719.

(853291) divides n-1.

(853291)^2 > n.

n is prime by Pocklington's theorem.