Primality proof for n = 25339:
Take b = 2.
b^(n-1) mod n = 1.
103 is prime.
b^((n-1)/103)-1 mod n = 21399, which is a unit, inverse 13885.
41 is prime.
b^((n-1)/41)-1 mod n = 1860, which is a unit, inverse 22628.
(41 * 103) divides n-1.
(41 * 103)^2 > n.
n is prime by Pocklington's theorem.