Primality proof for n = 6977:

Take b = 2.

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

109 is prime.
b^((n-1)/109)-1 mod n = 3282, which is a unit, inverse 4122.

(109) divides n-1.

(109)^2 > n.

n is prime by Pocklington's theorem.