Primality proof for n = 1288531:
Take b = 2.
b^(n-1) mod n = 1.
139 is prime.
b^((n-1)/139)-1 mod n = 974056, which is a unit, inverse 578537.
103 is prime.
b^((n-1)/103)-1 mod n = 685617, which is a unit, inverse 338714.
(103 * 139) divides n-1.
(103 * 139)^2 > n.
n is prime by Pocklington's theorem.