Take b = 2.

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

37 is prime.

b^((n-1)/37)-1 mod n = 979, which is a unit, inverse 152.

5 is prime.

b^((n-1)/5)-1 mod n = 329, which is a unit, inverse 2194.

(5 * 37) divides n-1.

(5 * 37)^2 > n.

n is prime by Pocklington's theorem.