Primality proof for n = 879331:
Take b = 2.
b^(n-1) mod n = 1.
29311 is prime. b^((n-1)/29311)-1 mod n = 78672, which is a unit, inverse 247921.
(29311) divides n-1.
(29311)^2 > n.
n is prime by Pocklington's theorem.