Primality proof for n = 1325514287:

Take b = 2.

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

5683 is prime.
b^((n-1)/5683)-1 mod n = 1209125572, which is a unit, inverse 961061061.

839 is prime.
b^((n-1)/839)-1 mod n = 264920365, which is a unit, inverse 753758760.

(839 * 5683) divides n-1.

(839 * 5683)^2 > n.

n is prime by Pocklington's theorem.