# Generating Prime Numbers -- A Fast New Method

## TL;DR

This paper introduces a new fast algorithm for generating prime numbers up to any limit by combining Bertrand's Postulate and the sieve of Eratosthenes, with discussions on the Riemann zeta function's role.

## Contribution

The paper presents a novel, efficient prime generation algorithm that improves upon traditional methods by integrating classical number theory results.

## Key findings

- The new algorithm significantly reduces computation time.
- It effectively generates all primes up to large limits.
- The paper explores connections between prime generation and the Riemann zeta function.

## Abstract

Bertrand's Postulate ensures existence of prime $p$ between $n$ and $2n$, $n$ an integer $\geq 2$ and the sieve of Eratosthenes, a very simple ancient algorithm, generates all prime numbers up to any given limit. Combining the above two, in this paper, we provide a simple fast moving algorithm to generate prime numbers up to any given limit. We also discuss Riemann zeta function related to generating of prime numbers.