Primality proof for n = 943693:

Take b = 2.

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

4139 is prime.
b^((n-1)/4139)-1 mod n = 198186, which is a unit, inverse 239754.

(4139) divides n-1.

(4139)^2 > n.

n is prime by Pocklington's theorem.