Primes are equidistributed in arithmetic progressions on average up to modulus \(q^{1−ε}\) for EVERY ε — twice the reach of the Bombieri–Vinogradov theorem. Half the modern theory of primes leans on this doubling.
The Problems
Not schoolwork — the questions that resisted Erdős, Hilbert, and everyone since. The club keeps three shelves: what is still open, what AI recently settled, and what took humanity centuries.
Tagged prime-distribution — 2 entries. Clear
All non-trivial zeros of the Riemann zeta function lie exactly on the critical line Re(s) = 1/2. The single most consequential open statement in pure mathematics.