---
id: 5900f3e71000cf542c50fefa
challengeType: 5
title: 'Problem 123: Prime square remainders'
forumTopicId: 301750
---
## 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.
## Instructions
## Tests
```yml
tests:
- text: euler123() should return 21035.
testString: assert.strictEqual(euler123(), 21035);
```
## Challenge Seed
```js
function euler123() {
// Good luck!
return true;
}
euler123();
```