On the moments of the gaps between consecutive primes

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.

References in corpus (2)

• Nearest neighbor spacing distribution of prime numbers and quantum chaos
• Some heuristics on the gaps between consecutive primes