Primality proof for n = 1454493979:

Take b = 2.

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

11543603 is prime.
b^((n-1)/11543603)-1 mod n = 50895301, which is a unit, inverse 127806526.

(11543603) divides n-1.

(11543603)^2 > n.

n is prime by Pocklington's theorem.