Primality proof for n = 78607:

Take b = 2.

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

397 is prime.
b^((n-1)/397)-1 mod n = 28239, which is a unit, inverse 33334.

(397) divides n-1.

(397)^2 > n.

n is prime by Pocklington's theorem.