# Local oscillations in moderately dense sequences of primes

## TL;DR

This paper investigates the distribution of differences between consecutive primes in moderately dense sequences, introducing a measure called curvature to quantify oscillations and providing sharp estimates for it.

## Contribution

It introduces a curvature-based measure to quantify oscillations in prime difference sequences and offers sharp estimates for this curvature in not-too-sparse sequences.

## Key findings

- Curvature effectively measures oscillations in prime difference sequences.
- Sharp estimates for curvature are derived for sequences that are not too sparse.
- The approach enhances understanding of prime distribution patterns.

## Abstract

The distribution of differences of consecutive members of sequences of primes is investigated. A quantitative measure for oscillations among these differences is the curvature of the sequence. If the sequence is not too sparse, then sharp estimates for its curvature are provided.