# Density of set of distinctions of dices and also tops

Consider the set $A$ of all-natural numbers which are of the kind $k^3-p$, for $k$ a favorable integer and also $p$ a favorable prime. Does $A$ have a thickness (of any one of the common kinds for collections of all-natural numbers) and also if so, what is it?

$A$ has a great deal of numbers, and also it appears rather hard to me to confirm that a certain number is not in $A$, other than that most dices are not in $A$.

An ignorant strategy would certainly be to claim that the opportunity $n$ amounts to $k^3-p$ for an offered $k$ has to do with $\frac{1}{\ln(k^3-n)}$. After that the opportunity $n$ is not equivalent to $k^3-p$ for any kind of $k$ is $$\prod_{k=\sqrt[3]{n}}^\infty {1-\frac{1}{\ln(k^3-n)}}$$ as this mosts likely to absolutely no, "all" numbers need to remain in A.