Primality proof for n = 25396537147:

Take b = 2.

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

4232756191 is prime.
b^((n-1)/4232756191)-1 mod n = 63, which is a unit, inverse 23784058598.

(4232756191) divides n-1.

(4232756191)^2 > n.

n is prime by Pocklington's theorem.