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.