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

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler320()</code> should return 278157919195482660.
    testString: assert.strictEqual(euler320(), 278157919195482660);

```

</section>

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

<div id='js-seed'>

```js
function euler320() {

  return true;
}

euler320();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>