Agoh's Bernoulli-number characterization of primes

Let $B_k$ denote the $k$-th Bernoulli number, and let $n$ be a positive integer.

Agoh's conjecture. The integer $n$ is prime if and only if

$$nB_{n-1}\equiv -1\pmod n.$$

The source states that this conjecture is equivalent to Giuga's conjecture. Its resolution status is not supplied here.