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.