# On the minimal number of small elements generating prime field

## TL;DR

This paper establishes an upper bound on the number of small elements needed to generate a finite prime field, specifically within a certain interval related to the prime p.

## Contribution

It provides a new upper bound for the minimal number of small elements required to generate the finite field _p, improving understanding of field generation with limited element sizes.

## Key findings

- Derived an explicit upper bound for generating elements
- Identified the interval size related to prime p for field generation
- Enhanced bounds for minimal generating sets in prime fields

## Abstract

In this note, we give an upper bound for the number of elements from the interval $[1,p^{1/4e^{1/2}+\epsilon}]$ necessary to generate the finite field $\mathbb{F}_{p}$ with $p$ an odd prime.