5 problems

Let $M$ be a Seifert $3$-manifold with base orbifold $B$, and let $G=\pi_1(M)$. Suppose that the orbifold Euler characteristic satisfies $\chi(B)<0$. Negative-characteristic decida…

Let $n$ range over the positive integers, and consider the sequence of integers $n^2+1$. Infinitely many primes of the form $n^2+1$ conjecture. There exist infinitely many primes o…

Let $G$ be a group, and let $B(\Gamma)$ be a right-angled Baumslag–Solitar–Artin group whose underlying undirected graph is a star graph. Suppose that $G$ is virtually $B(\Gamma)$,…

Let $P^+(n)$ denote the greatest prime factor of $n$. Erdős–Pomerance conjecture. The inequality … holds for infinitely many integers $n$. The opposite increasing pattern is known…

An irreducible polynomial $f\in\mathbb{Z}[x]$ of degree at least one is said to represent a prime if $f(n)$ is prime for some integer $n$. Prime-values conjecture. Every irreducibl…