Problem 214: Totient Chains

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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?