Primality proof for n = 13481018963:
Take b = 2.
b^(n-1) mod n = 1.
196993 is prime. b^((n-1)/196993)-1 mod n = 11454426697, which is a unit, inverse 13232075911.
(196993) divides n-1.
(196993)^2 > n.
n is prime by Pocklington's theorem.