A heuristic formula for the prime counting function

  1. Al-Mouid Mohammed Hasibul Haque
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Abstract

Using heuristic methods we create a simple but exact formula for the prime counting function. Then we make an asymptotic approximation of this new formula for the prime counting function using two distributions \(H(z)\) and \(h(z)\), which are defined in the paper, that act in a similar manner to the Dirac distribution though they are not the same. By doing so we derive a relatively simple asymptotic formula for the prime counting function without using analytic number theory.

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  1. Version published to 10.31219/osf.io/48dpc_v2 on OSF Preprints
  2. Version published to 10.31219/osf.io/48dpc on OSF Preprints