$1 Million Millennium Problem #6
The Birch and Swinnerton-Dyer Conjecture
~ A problem that has perplexed mathematicians for at 1,000 years ~
This problem is related to Fermat's Last Theorem, the Riemann Hypothesis, and our overall understanding of the prime numbers. Millennium #6 may turn out to be "pure mathematics." However, Andrew Wiles' proof of the Last Theorem created new excitement irregardless of whether it was "pure" or "applied."
See Keith Devlin's "The Millennium Problems: The Seven Greatest Unsolved Puzzles of Our Time, Basic Books, 2002.