---
id: 5900f4421000cf542c50ff55
title: 'Problem 214: Totient Chains'
challengeType: 5
forumTopicId: 301856
dashedName: problem-214-totient-chains
---

# --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?

# --hints--

`euler214()` should return 1677366278943.

```js
assert.strictEqual(euler214(), 1677366278943);
```

# --seed--

## --seed-contents--

```js
function euler214() {

  return true;
}

euler214();
```

# --solutions--

```js
// solution required
```
