Primality proof for n = 74551:
Take b = 2.
b^(n-1) mod n = 1.
71 is prime.
b^((n-1)/71)-1 mod n = 13961, which is a unit, inverse 4037.
7 is prime.
b^((n-1)/7)-1 mod n = 36461, which is a unit, inverse 59952.
(7 * 71) divides n-1.
(7 * 71)^2 > n.
n is prime by Pocklington's theorem.