Primality proof for n = 859:
Take b = 2.
b^(n-1) mod n = 1.
13 is prime.
b^((n-1)/13)-1 mod n = 772, which is a unit, inverse 780.
11 is prime.
b^((n-1)/11)-1 mod n = 792, which is a unit, inverse 500.
(11 * 13) divides n-1.
(11 * 13)^2 > n.
n is prime by Pocklington's theorem.