8 problems

Shapiro's conjecture. There is at least one prime at each height; equivalently, $pi_n\geq 1$ for every height $n$.

Martin's conjecture. The set

Erdős's average-order conjecture. The average order is

Inverse-growth conjecture. The logarithm of the asymptotic growth of any multi-partition is inversely related to the order of growth of its associated additive function.

Infinite-prime conjecture. There are infinitely many primes of this form.

Let $C$ be a smooth absolutely irreducible affine curve of degree $d$ defined over $\mathbb F_{p^k}$, and let $f:\mathbb F_{p^k}\rightarrow\mathbb F_{p^k}$ be an additive function…

Erdős–Kátai conjecture. For every fixed $c>1$,

Let $f$ be an additive function in the class $d4a0$, let $f(n;y)$ denote its truncation to prime factors at most $y$, and define … Write $\mu(f;y)$ and $\sigma(f;y)$ for the corres…