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.