Primality proof for n = 78364019:

Take b = 2.

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

19273 is prime.
b^((n-1)/19273)-1 mod n = 5524527, which is a unit, inverse 63176552.

(19273) divides n-1.

(19273)^2 > n.

n is prime by Pocklington's theorem.