Primality proof for n = 20113:

Take b = 2.

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

419 is prime.
b^((n-1)/419)-1 mod n = 15068, which is a unit, inverse 17111.

(419) divides n-1.

(419)^2 > n.

n is prime by Pocklington's theorem.