How exactly can you rigorously prove that though. You can't test every number, and unless you could the possibility remains that there is a number with an infinite stopping time.
Yeah, no-one yet knows how to prove or disprove it. This is why it is an unsolved problem.
And the Riemann Hypothesis one is that all the non-trivial zeros of this special function called the
Riemann-Zeta function have real part ½. (The input values of the Riemann Hypothesis are complex numbers (something known to HSC 4U Maths students), which are numbers with a
real part and an
imaginary part, so the hypothesis is that any input value (apart from some trivial ones, which are the negative even integers, which can easily be shown to all be zeros) such that the Riemann-Zeta function equals 0 has a real part of ½.)
(Link to Riemann-Zeta function for anyone curious:
https://en.wikipedia.org/wiki/Riemann_zeta_function .)