Agoh-Giuga conjecture

In number theory the Agoh-Giuga conjecture on the Bernoulli numbers B_k postulates that p is a prime number if and only if

pB_p−1 is congruent to −1 mod p.

The conjecture as stated is due to Takashi Agoh ; an equivalent formulation is due to Giuseppe Giuga , from 1950, to the effect that p is prime if and only if