Take b = 2.

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

61 is prime.

b^((n-1)/61)-1 mod n = 4018, which is a unit, inverse 4014.

13 is prime.

b^((n-1)/13)-1 mod n = 51, which is a unit, inverse 3266.

(13 * 61) divides n-1.

(13 * 61)^2 > n.

n is prime by Pocklington's theorem.