Take b = 2.

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

47 is prime.

b^((n-1)/47)-1 mod n = 5824, which is a unit, inverse 1144.

7 is prime.

b^((n-1)/7)-1 mod n = 2450, which is a unit, inverse 11744.

(7 * 47) divides n-1.

(7 * 47)^2 > n.

n is prime by Pocklington's theorem.