Primality proof for n = 4657:

Take b = 2.

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

97 is prime.
b^((n-1)/97)-1 mod n = 3284, which is a unit, inverse 2744.

(97) divides n-1.

(97)^2 > n.

n is prime by Pocklington's theorem.