Primality proof for n = 8076987940436711:

Take b = 2.

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

13843970897 is prime.
b^((n-1)/13843970897)-1 mod n = 7993899921654333, which is a unit, inverse 7268912295528669.

(13843970897) divides n-1.

(13843970897)^2 > n.

n is prime by Pocklington's theorem.