Open mathematical problems

Open problemEditorial · Analytic number theory

Riemann Hypothesis

Every nontrivial zero $\rho$ of the Riemann zeta function satisfies $\operatorname{Re}(\rho)=\tfrac12$ .

Source checked Jul 24, 20262 pinned Lean statementsInspect problem

Open problemEditorial · Additive number theory

Every even integer $n>2$ can be written as $n=p+q$ with $p$ and $q$ prime.

Source checked Jul 24, 20261 pinned Lean statementInspect problem

Open problemEditorial · Number theory

There are infinitely many primes $p$ for which $p+2$ is also prime.

Source checked Jul 24, 20261 pinned Lean statementInspect problem

Open problemEditorial · Number theory

For every positive integer $n$ , there is a prime $p$ satisfying $n^2<p<(n+1)^2$ .

Source checked Jul 24, 20261 pinned Lean statementInspect problem