freeCodeCamp/curriculum/challenges/chinese/10-coding-interview-prep/project-euler/problem-216-investigating-the-primality-of-numbers-of-the-form-2n2-1.md

---
id: 5900f4451000cf542c50ff57
title: 'Problem 216: Investigating the primality of numbers of the form 2n2-1'
challengeType: 5
forumTopicId: 301858
dashedName: problem-216-investigating-the-primality-of-numbers-of-the-form-2n2-1
---

# --description--

Consider numbers t(n) of the form t(n) = 2n2-1 with n > 1.

The first such numbers are 7, 17, 31, 49, 71, 97, 127 and 161.

It turns out that only 49 = 7\*7 and 161 = 7\*23 are not prime.

For n ≤ 10000 there are 2202 numbers t(n) that are prime.

How many numbers t(n) are prime for n ≤ 50,000,000 ?

# --hints--

`euler216()` should return 5437849.

```js
assert.strictEqual(euler216(), 5437849);
```

# --seed--

## --seed-contents--

```js
function euler216() {

  return true;
}

euler216();
```

# --solutions--

```js
// solution required
```