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.