5 problems

Chowla–Todd's conjecture.

Let the preceding Ova-Ova-Prime-Ova construction be given, and let $N$ denote the number of primes it produces. The Ova-Ova-Prime-Ova counting conjecture. Although the preceding th…

Let $\mathbb{P}$ be the set of rational primes, let $\mathbb{P}_2\subset\mathbb{P}$ be the set of twin primes, and let $\mathbb{P}_4\subset\mathbb{P}$ be the set of prime quadruple…

Let $a,b\in\mathbb Z$ satisfy $a\ne 0$, $b>0$, and $(a,b)=1$, and let $c,r$ be as in the preceding conjecture, with $(r-1)!<c\leq r!$. Factorial-unit conjecture. If $n\geq r$, ther…

Let $a,b\in\mathbb Z$ satisfy $a\ne 0$, $b>0$, and $(a,b)=1$. Let $c$ be the least positive integer such that for every integer $m\geq c$ there is a positive integer $x$ with…