The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is $28$. In fact, there are exactly four numbers below fifty that can be expressed in such a way:

$$\begin{array}{rl}28& =2^2+2^3+2^4\\ 33& =3^2+2^3+2^4\\ 49& =5^2+2^3+2^4\\ 47& =2^2+3^3+2^4\end{array}$$

How many numbers below fifty million can be expressed as the sum of a prime square, prime cube, and prime fourth power?