Dynamical Sieve of Eratosthenes

TL;DR

This paper introduces a dynamic model of prime numbers over time, mimicking the Sieve of Eratosthenes, where numbers are represented as functions evolving along a timeline, offering a novel perspective on prime distribution.

Contribution

It presents a new dynamical framework for understanding prime numbers as functions over time, extending the classical sieve concept into a continuous, temporal domain.

Findings

Prime numbers can be modeled as zero-crossings of a time-dependent function.

The model replicates the sieve process dynamically over a timeline.

Provides a new perspective on prime distribution and properties.

Abstract

In this document, prime numbers are related as functions over time, mimicking the Sieve of Eratosthenes. For this purpose, the mathematical representation is a uni-dimentional time line depicting the number line for positive natural numbers N, where each number n represents a time t. In the same way as the Eratosthenes' sieve, which iteratively mark as composite the multiples of each prime, starting at each prime. This dynamical prime number function P(s) zero-cross all composite numbers departing from primes, following a linear progression over time.