9 problems

Let $p_n$ denote the $n$th prime, and define … Let $\mathcal{C}_{\mathcal{A}}$ denote the subring of algebraic elements of $\mathcal{A}$. Transcendence conjecture. … The paper prov…

Truncated asymptotic bounds conjecture. For every real $x\ge e$,

The $li_0$-$li_1$ bounds conjecture. For every real $x\ge e$,

Let $\pi(t)$ denote the number of primes at most $t$, and let $p,q>1$ satisfy … There exists a sufficiently large natural number $n_0$ such that, for all $x,y\geq n_0$, Young-type…

Minculete's conjecture.

Let $\pi(t)$ denote the number of primes at most $t$, and let $x,y\geq 2$. Second Hardy–Littlewood conjecture. … This is a classical subadditivity conjecture for the prime-counting…

The conjectures. (A) For every integer $k\ge0$, the set $\{n\ge1:a_n=k\}$ has a positive density $\delta_k$, and

Let $\beta(t)$ be the function defined in the paper, and let $\mu$ and $\alpha$ be the constants used there. Unimodality conjecture for $\beta$. There exists a constant…

Let $\mathcal{R}\subset \mathbb{R}_+$ be the Ramanujan set of values $x\in \mathbb{R}_+$ for which $\pi(x)$ is the nearest integer to … where $\pi(x)$ is the prime-counting functio…