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.