## Giuga Sequence

A finite, increasing sequence of Integers such that

A sequence is a Giuga sequence Iff it satisfies

for , ..., . There are no Giuga sequences of length 2, one of length 3 (), two of length 4 ( and ), 3 of length 5 ( , , and ), 17 of length 6, 27 of length 7, and hundreds of length 8. There are infinitely many Giuga sequences. It is possible to generate longer Giuga sequences from shorter ones satisfying certain properties.

Borwein, D.; Borwein, J. M.; Borwein, P. B.; and Girgensohn, R. Giuga's Conjecture on Primality.'' Amer. Math. Monthly 103, 40-50, 1996.