---
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 n3 + n2p is a perfect cube.

For example, when p = 19, 83 + 82×19 = 123.

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?

# --hints--

`euler131()` should return 173.

```js
assert.strictEqual(euler131(), 173);
```

# --seed--

## --seed-contents--

```js
function euler131() {

  return true;
}

euler131();
```

# --solutions--

```js
// solution required
```