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

By iterating $\varphi$, 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 $4$:

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

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 $25$?