4 problems

Negative-jump conjecture. Negative jumps of $\eta_N(x)$ occur at every point $x+1\in\mathcal P$, where $\mathcal P$ is the set of primes, and

Normalized Chebyshev-prime criterion. A Chebyshev prime of index $l$ is a prime $p_m$ satisfying the displayed inequality. This criterion is the formulation used to relate generali…

Prime-power midpoint conjecture. The jump satisfies

Midpoint jump conjecture. The jump at the prime $p_n$ satisfies