---
id: 5900f3e71000cf542c50fefa
challengeType: 5
title: 'Problem 123: Prime square remainders'
---

## Description
<section id='description'>
Let pn be the nth prime: 2, 3, 5, 7, 11, ..., and let r be the remainder when (pn−1)n + (pn+1)n is divided by pn2.
For example, when n = 3, p3 = 5, and 43 + 63 = 280 ≡ 5 mod 25.
The least value of n for which the remainder first exceeds 109 is 7037.
Find the least value of n for which the remainder first exceeds 1010.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler123()</code> should return 21035.
    testString: assert.strictEqual(euler123(), 21035, '<code>euler123()</code> should return 21035.');

```

</section>

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

<div id='js-seed'>

```js
function euler123() {
  // Good luck!
  return true;
}

euler123();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>
