Math+CS guru? Prove this conjecture Posted by assane101 on Monday July 22, 2013 @11:55AM from the texify.com dept. 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 ( 2 comments | 2 points | on HN )
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?