Primality proof for n = 46589:

Take b = 2.

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

613 is prime.
b^((n-1)/613)-1 mod n = 10605, which is a unit, inverse 30251.

(613) divides n-1.

(613)^2 > n.

n is prime by Pocklington's theorem.