---
id: 5900f3ef1000cf542c50ff02
title: 'Problem 131: Prime cube partnership'
challengeType: 5
forumTopicId: 301759
dashedName: problem-131-prime-cube-partnership
---

# --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`.

```js
assert.strictEqual(primeCubePartnership(), 173);
```

# --seed--

## --seed-contents--

```js
function primeCubePartnership() {

  return true;
}

primeCubePartnership();
```

# --solutions--

```js
// solution required
```