---
id: 5900f4421000cf542c50ff55
challengeType: 5
title: 'Problem 214: Totient Chains'
forumTopicId: 301856
---

## Description
<section id='description'>
Let φ be Euler's totient function, i.e. for a natural number n,
φ(n) is the number of k, 1 ≤ k ≤ n, for which gcd(k,n) = 1.

By iterating φ, each positive integer generates a decreasing chain of numbers ending in 1.
E.g. if we start with 5 the sequence 5,4,2,1 is generated.
Here is a listing of all chains with length 4:


5,4,2,1
7,6,2,1
8,4,2,1
9,6,2,1
10,4,2,1
12,4,2,1
14,6,2,1
18,6,2,1

Only two of these chains start with a prime, their sum is 12.

What is the sum of all primes less than 40000000 which generate a chain of length 25?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler214()</code> should return 1677366278943.
    testString: assert.strictEqual(euler214(), 1677366278943);

```

</section>

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

<div id='js-seed'>

```js
function euler214() {

  return true;
}

euler214();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>