Primality proof for n = 674750394557:

Take b = 2.

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

24098228377 is prime.
b^((n-1)/24098228377)-1 mod n = 268435455, which is a unit, inverse 430257804336.

(24098228377) divides n-1.

(24098228377)^2 > n.

n is prime by Pocklington's theorem.