Primality proof for n = 6720124867:

Take b = 2.

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

7537 is prime.
b^((n-1)/7537)-1 mod n = 2154371083, which is a unit, inverse 2314953447.

71 is prime.
b^((n-1)/71)-1 mod n = 800144366, which is a unit, inverse 489940597.

(71 * 7537) divides n-1.

(71 * 7537)^2 > n.

n is prime by Pocklington's theorem.