freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-128-hexagonal-tile-differences.md

---
id: 5900f3ec1000cf542c50feff
challengeType: 5
title: 'Problem 128: Hexagonal tile differences'
forumTopicId: 301755
---

## Description
<section id='description'>
A hexagonal tile with number 1 is surrounded by a ring of six hexagonal tiles, starting at "12 o'clock" and numbering the tiles 2 to 7 in an anti-clockwise direction.
New rings are added in the same fashion, with the next rings being numbered 8 to 19, 20 to 37, 38 to 61, and so on. The diagram below shows the first three rings.


By finding the difference between tile n and each of its six neighbours we shall define PD(n) to be the number of those differences which are prime.
For example, working clockwise around tile 8 the differences are 12, 29, 11, 6, 1, and 13. So PD(8) = 3.
In the same way, the differences around tile 17 are 1, 17, 16, 1, 11, and 10, hence PD(17) = 2.
It can be shown that the maximum value of PD(n) is 3.
If all of the tiles for which PD(n) = 3 are listed in ascending order to form a sequence, the 10th tile would be 271.
Find the 2000th tile in this sequence.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler128()</code> should return 14516824220.
    testString: assert.strictEqual(euler128(), 14516824220);

```

</section>

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

<div id='js-seed'>

```js
function euler128() {

  return true;
}

euler128();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>