---
id: 5900f3c51000cf542c50fed8
challengeType: 5
title: 'Problem 87: Prime power triples'
forumTopicId: 302201
---

## Description
<section id='description'>

The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is 28. In fact, there are exactly four numbers below fifty that can be expressed in such a way:

<div style='margin-left: 4em;'>
  28 = 2<sup>2</sup> + 2<sup>3</sup> + 2<sup>4</sup><br>
  33 = 3<sup>2</sup> + 2<sup>3</sup> + 2<sup>4</sup><br>
  49 = 5<sup>2</sup> + 2<sup>3</sup> + 2<sup>4</sup><br>
  47 = 2<sup>2</sup> + 3<sup>3</sup> + 2<sup>4</sup>
</div>

How many numbers below fifty million can be expressed as the sum of a prime square, prime cube, and prime fourth power?

</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>primePowerTriples()</code> should return a number.
    testString: assert(typeof primePowerTriples() === 'number');
  - text: <code>primePowerTriples()</code> should return 1097343.
    testString: assert.strictEqual(primePowerTriples(), 1097343);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function primePowerTriples() {

  return true;
}

primePowerTriples();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>