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.