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.