Take b = 2.

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

43 is prime.

b^((n-1)/43)-1 mod n = 1467, which is a unit, inverse 7471.

37 is prime.

b^((n-1)/37)-1 mod n = 3056, which is a unit, inverse 1990.

(37 * 43) divides n-1.

(37 * 43)^2 > n.

n is prime by Pocklington's theorem.