Primality proof for n = 12545359681:

Take b = 2.

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

1866869 is prime.
b^((n-1)/1866869)-1 mod n = 6908199420, which is a unit, inverse 819548924.

(1866869) divides n-1.

(1866869)^2 > n.

n is prime by Pocklington's theorem.