Primality proof for n = 855109789:
Take b = 2.
b^(n-1) mod n = 1.
5481473 is prime. b^((n-1)/5481473)-1 mod n = 487410094, which is a unit, inverse 809122865.
(5481473) divides n-1.
(5481473)^2 > n.
n is prime by Pocklington's theorem.