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.