freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-214-totient-chains.md

id, title, challengeType, forumTopicId, dashedName

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

$$\begin{align} 5,4,2,1 & \\ 7,6,2,1 & \\ 8,4,2,1 & \\ 9,6,2,1 & \\ 10,4,2,1 & \\ 12,4,2,1 & \\ 14,6,2,1 & \\ 18,6,2,1 & \end{align}$$

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

What is the sum of all primes less than 40\\,000\\,000 which generate a chain of length 25?

--hints--

totientChains() should return 1677366278943.

assert.strictEqual(totientChains(), 1677366278943);

--seed--

--seed-contents--

function totientChains() {

  return true;
}

totientChains();

--solutions--

// solution required