Take b = 2.

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

83 is prime.

b^((n-1)/83)-1 mod n = 37315, which is a unit, inverse 47417.

61 is prime.

b^((n-1)/61)-1 mod n = 12714, which is a unit, inverse 41599.

(61 * 83) divides n-1.

(61 * 83)^2 > n.

n is prime by Pocklington's theorem.