# Generalization of Bertrand's Postulate for Gaussian Primes

## TL;DR

This paper extends Bertrand's Postulate to Gaussian primes, providing new insights into the distribution of primes in the complex plane, building on prior generalizations for real primes.

## Contribution

It formalizes the generalization of Bertrand's Postulate for Gaussian primes, a novel extension to complex primes.

## Key findings

- Gaussian primes are distributed according to the generalized postulate
- Provides bounds for the number of Gaussian primes in certain regions
- Enhances understanding of prime distribution in the complex plane

## Abstract

Bertrand's Postulate states about the prime distribution for the real numbers. The generalization of Bertrand's Postulate was proved by Das et al. [Arxiv 2018]. In this paper, we have formalized this idea for the Gaussian primes (or the primes on the complex plane). This result gives information about the prime distribution on the complex plane.