Take b = 2.

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

61 is prime.

b^((n-1)/61)-1 mod n = 5233, which is a unit, inverse 6129.

31 is prime.

b^((n-1)/31)-1 mod n = 18552, which is a unit, inverse 15487.

(31 * 61) divides n-1.

(31 * 61)^2 > n.

n is prime by Pocklington's theorem.