Primality proof for n = 82373:

Take b = 2.

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

20593 is prime.
b^((n-1)/20593)-1 mod n = 15, which is a unit, inverse 71390.

(20593) divides n-1.

(20593)^2 > n.

n is prime by Pocklington's theorem.