Primality proof for n = 46596523:

Take b = 2.

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

3023 is prime.
b^((n-1)/3023)-1 mod n = 19059231, which is a unit, inverse 35086028.

367 is prime.
b^((n-1)/367)-1 mod n = 45437254, which is a unit, inverse 22478148.

(367 * 3023) divides n-1.

(367 * 3023)^2 > n.

n is prime by Pocklington's theorem.