Which conjecture has remained unsolved the longest?

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This is not so much a question as a mathematical discussion.

Which conjecture/postulate/hypothesis in mathematics has remained unsolved for the longest?

Fermat's Last Theorem springs to mind but that was solved in the 90's by Andrew Wiles.

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The best method for tetrahedra packing dates back at least 2500 years. The packing density of .856347, discovered in 2010, hasn't been proven the best possible.