---
id: 5900f50d1000cf542c51001f
challengeType: 5
title: 'Problem 417: Reciprocal cycles II'
forumTopicId: 302086
---

## Description
<section id='description'>
A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

1/2= 0.5
1/3= 0.(3)
1/4= 0.25
1/5= 0.2
1/6= 0.1(6)
1/7= 0.(142857)
1/8= 0.125
1/9= 0.(1)
1/10= 0.1

Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Unit fractions whose denominator has no other prime factors than 2 and/or 5 are not considered to have a recurring cycle.
We define the length of the recurring cycle of those unit fractions as 0.


Let L(n) denote the length of the recurring cycle of 1/n.
You are given that ∑L(n) for 3 ≤ n ≤ 1 000 000 equals 55535191115.


Find ∑L(n) for 3 ≤ n ≤ 100 000 000
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler417()</code> should return 446572970925740.
    testString: assert.strictEqual(euler417(), 446572970925740);

```

</section>

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

<div id='js-seed'>

```js
function euler417() {
  // Good luck!
  return true;
}

euler417();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>