10 problems

Let $A$ be a primitive set contained in $[x,\infty)$ for some $x\geq 2$, and define … where $\nu_0(a)=1/(a\log a)$. Erdős–Sárközy–Szemerédi conjecture. As $x\to\infty$, one should…

Let $U(z)$ and $d6d1_1(z)$ be the functions defined in the paper for $z\in(0,2)$. Equality conjecture. … This is one of the paper's open questions concerning the relationship betwe…

Let $\Omega(n)$ be the number of prime factors of $n$, counted with multiplicity, and let $\mathbb{N}_k=\{n:\Omega(n)=k\}$. For a set of odd primes $\mathcal Q$, write…

Let $A\subset \mathbb{Z}_{>1}$ be a primitive set, meaning that no member of $A$ divides another, and let … Let $\mathcal P$ denote the set of primes. Erdős's primitive set conject…

Erdős's primitive set conjecture. The maximum of $f(A)$, ranging over all primitive sets $A$ of positive integers, is attained by the set of primes $A=\mathbb{N}_1$.

Function-field Erdős conjecture. The sum $\mathcal{F}(A)$ is maximized, among primitive sets of polynomials, by the set of monic irreducible polynomials.

Erdős's conjecture. For every primitive set of positive integers $A\neq\{1\}$,

Let $q$ be a prime power, let $\mathcal{M}_q$ denote the monic polynomials in $\mathbb{F}_q[x]$, and let $\mathcal{I}_q$ denote the irreducible polynomials. For a nonzero polynomia…

Erdős's restricted-prime conjecture. Every set of primes $\mathscr P$ is Erdős-best among primitive subsets of ${\mathbb N}(\mathscr P)$. This generalizes the conjecture for all pr…

Let a nonempty set of natural numbers be primitive if no element of the set divides another, and let ${\mathbb P}$ denote the set of primes. Erdős's conjecture. For every primitive…