Primality proof for n = 7287076501559:
Take b = 2.
b^(n-1) mod n = 1.
28597 is prime.
b^((n-1)/28597)-1 mod n = 1778141898950, which is a unit, inverse 2976823924432.
28307 is prime.
b^((n-1)/28307)-1 mod n = 492222539746, which is a unit, inverse 1985604159647.
(28307 * 28597) divides n-1.
(28307 * 28597)^2 > n.
n is prime by Pocklington's theorem.