freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-214-totient-chains.english.md

id, challengeType, title

id	challengeType	title
5900f4421000cf542c50ff55	5	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

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

Challenge Seed

function euler214() {
  // Good luck!
  return true;
}

euler214();

Solution

// solution required