I can't believe this hasen't been mention yet. But, RH is now 150 years old without being proven or disproven. Sadly, I have to wait two years intill I do the course on Analytical number theory so that I can understand it. But, when I do I will try and prove it.
Its strange but prime numbers and number theory was useless back in the old days, but now its one of the most improtant branches of mathematics.