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.