Primality proof for n = 465104362351:

Take b = 2.

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

3100695749 is prime.
b^((n-1)/3100695749)-1 mod n = 157164017366, which is a unit, inverse 400635322390.

(3100695749) divides n-1.

(3100695749)^2 > n.

n is prime by Pocklington's theorem.