Agoh-Giuga conjecture

In 1950, Giuseppe Giuga conjectured that if and only if an integer $p$ is prime then it will satisfy the congruence

$$\sum _{i=1}^{p-1}{i}^{p-1}\equiv -1modp.$$

This is sometimes called the Giuga conjecture. Takashi Agoh rephrased the conjecture as $p{B}_{p-1}\equiv -1modp$, where $B$ is a Bernoulli number; this is called the Agoh-Giuga conjecture. In 2003 Simon Plouffe performed an exhaustive search for a counterexample below 50000 but came up empty.