---
id: 5900f3e71000cf542c50fefa
challengeType: 5
title: 'Problem 123: Prime square remainders'
videoUrl: ''
localeTitle: 问题123：素数正方形余数
---

## Description
<section id="description">令pn为第n个素数：2,3,5,7,11 ......，并且当r（pn-1）n +（pn + 1）n除以pn2时，令r为余数。例如，当n = 3时，p3 = 5，并且43 + 63 =280≡5mod 25.余数首先超过109的n的最小值是7037.求出余数首次超过的n的最小值1010。 </section>

## Instructions
<section id="instructions">
</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler123()</code>应该返回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>