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.