Primality proof for n = 3578453:

Take b = 2.

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

894613 is prime.
b^((n-1)/894613)-1 mod n = 15, which is a unit, inverse 3101326.

(894613) divides n-1.

(894613)^2 > n.

n is prime by Pocklington's theorem.