THE BEAL CONJECTURE: A banker from Dallas has offered to pay $1 million to anyone who can solve a particularly tricky maths problem. D Andrew Beal is a self-taught mathematician, and for the last 17 years he has offered a prize to anyone who can solve the "Beal Conjecture". The prize money started at £5,000, but now the rewards have risen dramatically. To win the money you have to solve/prove the following: If A^x + B^y = C^z, where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor. A deduction from fermat last theorem, a^x +b^x=c^x. The prize is awarded if the conjecture is proved or a counterexample is presented. The problem is aimed at discovering maths geeks around the world.
THE MILLENNIUM PROBLEMS: these are 7 maths problems, a total of $7 million prizes. Read more about the millennium problems at http://www.claymath.org/millennium-problems