

Math+CS guru? Prove this conjecture - assane101
http://www.texify.com/img/%5CLARGE%5C%21%5Cforall%20p%5Chspace%7B9pt%7D%20prime%2C%20%5Chspace%7B9pt%7D%20p%20%5Cnotin%20%5C%7B3%2C%205%2C%207%5C%7D%2C%20%5Chspace%7B9pt%7D%20%5Csum_%7Bk%20%5Cle%20p%20%7D%20prime%5E%7B%3F%7D%28p-k%29%20%2A%202%5E%7Bp-k%7D%20%5Cnotin%20P%2C%20%5Chspace%7B9pt%7D%20where%20%5Chspace%7B9pt%7D%20prime%5E%7B%3F%7D%28x%29%20%3D%20%20%5Cleft%5C%7B%20%20%20%7B%5Ctext%7B%201%20if%20x%20is%20prime%20%7D%20%5Catop%20%5Ctext%7B%200%20if%20not%20%7D%7D%20%20%20%5Cright..gif
P is the prime numbers set
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cpa
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?

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gems
What is the domain of $k$?

