Primality proof for n = 40024942543673:

Take b = 2.

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

25396537147 is prime.
b^((n-1)/25396537147)-1 mod n = 24760559515411, which is a unit, inverse 36222238642773.

(25396537147) divides n-1.

(25396537147)^2 > n.

n is prime by Pocklington's theorem.