--description--

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 $p = 19,\ 8^3 + 8^2 × 19 = {12}^3$.

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

How many primes below one million have this remarkable property?

--hints--

primeCubePartnership() should return 173.

assert.strictEqual(primeCubePartnership(), 173);

--seed--

--seed-contents--

function primeCubePartnership() {

  return true;
}

primeCubePartnership();

--solutions--

// solution required