Primality proof for n = 7691:

Take b = 2.

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

769 is prime.
b^((n-1)/769)-1 mod n = 1023, which is a unit, inverse 7067.

(769) divides n-1.

(769)^2 > n.

n is prime by Pocklington's theorem.