Eccoci.

Let $\phi$ be Euler's totient function, i.e. for a natural number $n$, $\phi(n)$ is the number of $k$, $1 \le k \le n$, for which $\gcd(k, n) = 1$.

By iterating $\phi$, 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 $40000000$ which generate a chain of length $25$?