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

# --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.

# --hints--

`euler381()` should return 139602943319822.

```js
assert.strictEqual(euler381(), 139602943319822);
```

# --seed--

## --seed-contents--

```js
function euler381() {

  return true;
}

euler381();
```

# --solutions--

```js
// solution required
```