Statistics of small prime quadratic non-residues

TL;DR

This paper investigates the distribution of small prime quadratic non-residues and shows that their average behavior closely relates to the distribution of prime numbers, specifically approximating the 2k-th prime.

Contribution

It establishes a new approximation connecting the averages of small prime quadratic non-residues to prime number distribution, providing insight into their statistical properties.

Findings

Average of the k-th smallest prime quadratic non-residue approximates the 2k-th prime.

Provides a new statistical relationship between quadratic non-residues and primes.

Enhances understanding of the distribution of quadratic non-residues modulo primes.

Abstract

We prove that the average of the $k$-th smallest prime quadratic non-residue modulo a prime approximates the $2k$-th smallest prime.