Primality proof for n = 673:
Take b = 5.
b^(n-1) mod n = 1.
7 is prime.
b^((n-1)/7)-1 mod n = 619, which is a unit, inverse 162.
3 is prime.
b^((n-1)/3)-1 mod n = 254, which is a unit, inverse 363.
2 is prime.
b^((n-1)/2)-1 mod n = 671, which is a unit, inverse 336.
(2^5 * 3 * 7) divides n-1.
(2^5 * 3 * 7)^2 > n.
n is prime by Pocklington's theorem.