On the moments of the gaps between consecutive primes

Marek Wolf

On the moments of the gaps between consecutive primes

Number Theory 2017-05-31 v1

Authors: Marek Wolf

Abstract

We derive heuristically formula for the $k$ --moments $M_k(x)$ of the gaps between consecutive primes $<x$ represented directly by $x$ $\pi(x)$ --- the number of primes up to: $M_k(x)= \Gamma(k+1)x^k/\pi^{k-1}(x)+\mathcal{O}(x)$ , We illustrate obtained results by computer data.

Keywords

prime gaps moments heuristic formula prime number theorem consecutive primes

Cite

@article{arxiv.1705.10766,
  title  = {On the moments of the gaps between consecutive primes},
  author = {Marek Wolf},
  journal= {arXiv preprint arXiv:1705.10766},
  year   = {2017}
}

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