Take b = 2.

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

137 is prime.

b^((n-1)/137)-1 mod n = 18560, which is a unit, inverse 479.

7 is prime.

b^((n-1)/7)-1 mod n = 13823, which is a unit, inverse 13094.

(7 * 137) divides n-1.

(7 * 137)^2 > n.

n is prime by Pocklington's theorem.