Agoh–Giuga conjecture on Bernoulli numbers

Let $n$ be a positive integer and let $B_{n-1}$ denote the $(n-1)$-st Bernoulli number. Agoh–Giuga conjecture. The integer $n$ is prime if and only if

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

This conjecture characterizes the prime numbers through a congruence involving Bernoulli numbers; the source gives no resolution status.