2 problems

Multivariable Bateman–Horn conjecture. As $P\to+\infty$,

For $k\ge 2$ and $r\in\mathbb{Z}\setminus\\{0\\}$, let $C^k_{2r}$ denote the Bateman–Horn constant associated with the prime pair $(p,p^k+2r)$. Mean-value-one conjecture. The const…