Primality proof for n = 4133:
Take b = 2.
b^(n-1) mod n = 1.
1033 is prime. b^((n-1)/1033)-1 mod n = 15, which is a unit, inverse 3582.
(1033) divides n-1.
(1033)^2 > n.
n is prime by Pocklington's theorem.