Here is a list of problems I challenged my teacher to solve, and myself, too, included: 1) Find an explicit formula for primes
This, has been proved to not exist, but might it exist as a step function or as an unevaluated/impossible integral? Or both? Since, the change in adjacent prime results in some regular pattern, couldn't we solve for the change in the change of prime, etc., and write the integral sign for it?
2) Find an explicit formula for Fibonacci sequence
Same as above, but without the analyzing the change of this function, since it only repeats the main sequence, only that we can write f'=f+constant. The method I think I am doing is by approximating, adding terms to the approximate Fibonacci explicit formula.
3) Prove twin prime conjecture
No way out of that...
4) Prove Riemann Hypothesis
It just looks good on a list of problems.
Anyways, you can't bet on me getting these cause I'm only in 10th grade of high school.