Crazy Polynomial
Let there be a polynomial representing the zeros of the prime counting function . Examining small intervals, the average difference of two zeros can be represented as , where and are integers. Find .
The answer is 6.
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1 solution
For ideas take a look at the problem calculus madness under my profile. The result from this integral can be generalized into a polynomial form by turning the integral into a sum and then solving for a certain coefficient a. After using a, one can come up with a relationship that will give a certain polynomial function that we are looking for. We can integrate around the function, and we get the answer 4 π 2 . 4 + 2 = 6 .