On the moments of the gaps between consecutive primes

Marek Wolf

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arXiv · 1705.10766

On the moments of the gaps between consecutive primes

Marek Wolf

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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.

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Marek Wolf. 2017-05-30. On the moments of the gaps between consecutive primes. https://arxiv.org/abs/1705.10766

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