Primality proof for n = 46723:

Take b = 2.

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

599 is prime.
b^((n-1)/599)-1 mod n = 9944, which is a unit, inverse 28779.

(599) divides n-1.

(599)^2 > n.

n is prime by Pocklington's theorem.