Primality proof for n = 9032166434783:

Take b = 2.

b^(n-1) mod n = 1.

2103438853 is prime.
b^((n-1)/2103438853)-1 mod n = 3111728872073, which is a unit, inverse 1111915848724.

(2103438853) divides n-1.

(2103438853)^2 > n.

n is prime by Pocklington's theorem.