Primality proof for n = 5659:

Take b = 2.

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

41 is prime.
b^((n-1)/41)-1 mod n = 4481, which is a unit, inverse 5414.

23 is prime.
b^((n-1)/23)-1 mod n = 3007, which is a unit, inverse 271.

(23 * 41) divides n-1.

(23 * 41)^2 > n.

n is prime by Pocklington's theorem.