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.