Primality proof for n = 878766598991:

Take b = 2.

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

1814921 is prime.
b^((n-1)/1814921)-1 mod n = 300206661287, which is a unit, inverse 158983999210.

(1814921) divides n-1.

(1814921)^2 > n.

n is prime by Pocklington's theorem.