---
id: 5900f4ae1000cf542c50ffbf
title: 'Problem 320: Factorials divisible by a huge integer'
challengeType: 5
forumTopicId: 301977
dashedName: problem-320-factorials-divisible-by-a-huge-integer
---

# --description--

Let N(i) be the smallest integer n such that n! is divisible by (i!)1234567890

Let S(u)=∑N(i) for 10 ≤ i ≤ u.

S(1000)=614538266565663.

Find S(1 000 000) mod 1018.

# --hints--

`euler320()` should return 278157919195482660.

```js
assert.strictEqual(euler320(), 278157919195482660);
```

# --seed--

## --seed-contents--

```js
function euler320() {

  return true;
}

euler320();
```

# --solutions--

```js
// solution required
```