Primality proof for n = 20719:

Take b = 2.

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

1151 is prime.
b^((n-1)/1151)-1 mod n = 13515, which is a unit, inverse 14849.

(1151) divides n-1.

(1151)^2 > n.

n is prime by Pocklington's theorem.