Primality proof for n = 78751358483857:

Take b = 2.

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

1640653301747 is prime.
b^((n-1)/1640653301747)-1 mod n = 45220901259084, which is a unit, inverse 55112987644395.

(1640653301747) divides n-1.

(1640653301747)^2 > n.

n is prime by Pocklington's theorem.