Primality proof for n = 25136521679249:

Take b = 2.

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

32061889897 is prime.
b^((n-1)/32061889897)-1 mod n = 23416939223832, which is a unit, inverse 18947801997842.

(32061889897) divides n-1.

(32061889897)^2 > n.

n is prime by Pocklington's theorem.