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# Riemann H. proved true, if settled by 2100

### Question

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The Riemann hypothesis is a conjecture stating that the nontrivial zeroes of the Riemann zeta function $\zeta(s)$ all have real part equal to $1/2$. The Riemann zeta function also has zeroes at the strictly negative even integers $-2, -4, -6, \ldots$, which are by definition its trivial zeroes. The hypothesis would therefore be correct if all zeroes of the Riemann zeta function other than these trivial zeroes had real part equal to $1/2$.

The conjecture is significant because it implies the tightest possible error bounds on a wide range of estimates in analytic number theory, starting from the tight asymptotic $\pi(x) = \textrm{Li}(x) + O(\sqrt{x} \log x)$ for the prime counting function $\pi(x)$. It has now become standard practice to prove theorems of analytic number theory conditional on the Riemann hypothesis or some of its closely related generalizations.

Will the Riemann Hypothesis be proved true by 2100?

This question will resolve positively if the Millennium Prize for the proof of the Riemann hypothesis is awarded before the resolve date of this question. It will resolve negatively if the Millennium Prize is awarded, according to rule 5.c of the Millennium Prize Rules, for the disproof of the Riemann hypothesis. It will resolve ambiguously if the Prize is not awarded for either achievement until the resolve date of the question, or if the Prize is awarded for a proof that the Riemann hypothesis is undecidable in ZFC set theory.

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