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.