There are some prime values, $p$, for which there exists a positive integer, $n$, such that the expression $n^3+n^{2}p$ is a perfect cube.

For example, when $p=19$, $8^3+8^2\times 19={12}^3$.

What is perhaps most surprising is that for each prime with this property the value of $n$ is unique, and there are only four such primes below one-hundred.

How many primes below one million have this remarkable property?