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.