Take b = 2.

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

521 is prime.

b^((n-1)/521)-1 mod n = 2846494, which is a unit, inverse 2767868.

23 is prime.

b^((n-1)/23)-1 mod n = 2187387, which is a unit, inverse 488146.

(23 * 521) divides n-1.

(23 * 521)^2 > n.

n is prime by Pocklington's theorem.