Argoh's Conjecture

Let be the th Bernoulli Number. Then does

Iff is Prime? For example, for , 2, ..., (mod ) is 0, , , 0, , 0, , 0, , 0, , ... (Sloane's A046094). There are no counterexamples less than . Any counterexample to Argoh's conjecture would be a contradiction to Giuga's Conjecture, and vice versa.

Borwein, D.; Borwein, J. M.; Borwein, P. B.; and Girgensohn, R. Giuga's Conjecture on Primality.'' Amer. Math. Monthly 103, 40-50, 1996.
Sloane, N. J. A. Sequence A046094 in The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.