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'sconjecture would be a contradiction to Giuga's Conjecture, and vice versa.See also Bernoulli Number, Giuga's Conjecture
References
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 A046094in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.
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