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.