# Problem 214: Totient Chains
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?