Primality proof for n = 8053:
Take b = 2.
b^(n-1) mod n = 1.
61 is prime.
b^((n-1)/61)-1 mod n = 6693, which is a unit, inverse 5193.
11 is prime.
b^((n-1)/11)-1 mod n = 2179, which is a unit, inverse 1992.
(11 * 61) divides n-1.
(11 * 61)^2 > n.
n is prime by Pocklington's theorem.