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.