Primality proof for n = 78591707:
Take b = 2.
b^(n-1) mod n = 1.
39295853 is prime. b^((n-1)/39295853)-1 mod n = 3, which is a unit, inverse 26197236.
(39295853) divides n-1.
(39295853)^2 > n.
n is prime by Pocklington's theorem.