---
id: 5900f3e71000cf542c50fefa
title: 'Problem 123: Prime square remainders'
challengeType: 5
forumTopicId: 301750
dashedName: problem-123-prime-square-remainders
---

# --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.

# --hints--

`euler123()` should return 21035.

```js
assert.strictEqual(euler123(), 21035);
```

# --seed--

## --seed-contents--

```js
function euler123() {

  return true;
}

euler123();
```

# --solutions--

```js
// solution required
```