Take b = 3.

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

47 is prime.

b^((n-1)/47)-1 mod n = 627, which is a unit, inverse 15.

5 is prime.

b^((n-1)/5)-1 mod n = 1770, which is a unit, inverse 2177.

(5^2 * 47) divides n-1.

(5^2 * 47)^2 > n.

n is prime by Pocklington's theorem.