---
id: 5900f4ea1000cf542c50fffc
challengeType: 5
title: 'Problem 381: (prime-k) factorial'
forumTopicId: 302045
---

## Description
<section id='description'>
For a prime p let S(p) = (∑(p-k)!) mod(p) for 1 ≤ k ≤ 5.


For example, if p=7,
(7-1)! + (7-2)! + (7-3)! + (7-4)! + (7-5)! = 6! + 5! + 4! + 3! + 2! = 720+120+24+6+2 = 872.
As 872 mod(7) = 4, S(7) = 4.


It can be verified that ∑S(p) = 480 for 5 ≤ p < 100.


Find ∑S(p) for 5 ≤ p < 108.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler381()</code> should return 139602943319822.
    testString: assert.strictEqual(euler381(), 139602943319822);

```

</section>

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

<div id='js-seed'>

```js
function euler381() {

  return true;
}

euler381();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>