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.