It is a sum of even numbers, because they almost all all are powers of 2.
The only element of the sum that can be odd is when p = k. This element is prime(0), which is 0 because 0 is not prime.
Thus, the overall sum is necessarily even.
It is easy to check that this sum is strictly larger than 2. Thus, it cannot be a prime number.
What is this conjecture for?
