Primality proof for n = 1933:
Take b = 2.
b^(n-1) mod n = 1.
23 is prime.
b^((n-1)/23)-1 mod n = 909, which is a unit, inverse 1580.
7 is prime.
b^((n-1)/7)-1 mod n = 1109, which is a unit, inverse 312.
(7 * 23) divides n-1.
(7 * 23)^2 > n.
n is prime by Pocklington's theorem.