Factor any number by sieving every number around it.
The Lewis Sieve: Factorization by Default—A New Perspective on Primes and Composites For anyone who’s ever marveled at the elegance of the Sieve of Eratosthenes, there’s a new twist waiting to be discovered—a twist that not only finds the primes but also reveals the very building blocks of composite numbers. Welcome to the world of the Lewis Sieve . In this post, we’ll explore this innovative approach in depth. We’ll begin with a quick recap of the classical sieve, then introduce the concept behind the Lewis Sieve, and finally show how it unifies prime detection and factorization into one elegant process. Whether you’re a seasoned mathematician or simply passionate about number theory, prepare to see a familiar landscape with entirely new eyes. Revisiting a Classic: The Sieve of Eratosthenes Imagine you have a long chalkboard filled with numbers from 2 up to some large number N. The goal is to pick out the primes—the numbers that can only be divided evenly by 1 and themselves. The Siev...