Primality proof for n = 45827:

Take b = 2.

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

2083 is prime.
b^((n-1)/2083)-1 mod n = 24046, which is a unit, inverse 8174.

(2083) divides n-1.

(2083)^2 > n.

n is prime by Pocklington's theorem.