Take b = 2.

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

47 is prime.

b^((n-1)/47)-1 mod n = 10998, which is a unit, inverse 45808.

11 is prime.

b^((n-1)/11)-1 mod n = 13897, which is a unit, inverse 60906.

(11 * 47) divides n-1.

(11 * 47)^2 > n.

n is prime by Pocklington's theorem.