Primality proof for n = 7229:

Take b = 2.

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

139 is prime.
b^((n-1)/139)-1 mod n = 2283, which is a unit, inverse 2416.

(139) divides n-1.

(139)^2 > n.

n is prime by Pocklington's theorem.