Primality proof for n = 25969:

Take b = 2.

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

541 is prime.
b^((n-1)/541)-1 mod n = 10392, which is a unit, inverse 22428.

(541) divides n-1.

(541)^2 > n.

n is prime by Pocklington's theorem.