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.