---
id: 5900f4421000cf542c50ff55
challengeType: 5
title: '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?
## Instructions
## Tests
```yml
tests:
- text: euler214() should return 1677366278943.
testString: 'assert.strictEqual(euler214(), 1677366278943, "euler214() should return 1677366278943.");'
```
## Challenge Seed
```js
function euler214() {
// Good luck!
return true;
}
euler214();
```