Primality proof for n = 430751:

Take b = 2.

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

1723 is prime.
b^((n-1)/1723)-1 mod n = 293175, which is a unit, inverse 198753.

(1723) divides n-1.

(1723)^2 > n.

n is prime by Pocklington's theorem.