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:

~~~
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
~~~

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