Primality proof for n = 17543087:

Take b = 2.

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

887 is prime.
b^((n-1)/887)-1 mod n = 14737264, which is a unit, inverse 14758262.

31 is prime.
b^((n-1)/31)-1 mod n = 1070548, which is a unit, inverse 8990261.

(31 * 887) divides n-1.

(31 * 887)^2 > n.

n is prime by Pocklington's theorem.