Primality proof for n = 43936391:

Take b = 2.

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

118747 is prime.
b^((n-1)/118747)-1 mod n = 10165600, which is a unit, inverse 13352110.

(118747) divides n-1.

(118747)^2 > n.

n is prime by Pocklington's theorem.