Primality proof for n = 1667:
Take b = 2.
b^(n-1) mod n = 1.
17 is prime.
b^((n-1)/17)-1 mod n = 641, which is a unit, inverse 827.
7 is prime.
b^((n-1)/7)-1 mod n = 711, which is a unit, inverse 347.
(7^2 * 17) divides n-1.
(7^2 * 17)^2 > n.
n is prime by Pocklington's theorem.