Sieve of Eratosthenes

Topic

Prime and Composite Numbers

Definition

The Sieve of Eratosthenes is an ancient algorithm used to find all prime numbers up to a specified integer.

Description

The Sieve of Eratosthenes is a fundamental algorithm in number theory, particularly useful for identifying prime numbers. It works by iteratively marking the multiples of each prime number starting from 2. The numbers which remain unmarked after all multiples of each prime are marked are the prime numbers.

The relevance of the Sieve of Eratosthenes in the study of prime and composite numbers cannot be overstated. It provides a simple yet effective method for generating primes, which are the building blocks of number theory. Understanding primes is crucial for various fields, including cryptography, computer science, and pure mathematics. By systematically eliminating the multiples of each prime, the sieve efficiently filters out composite numbers, leaving a clear list of primes up to a given limit. This method is not only historically significant but also serves as an educational tool to illustrate the properties and distribution of prime numbers.

For a complete collection of terms related to primes and composites click on this link: Prime and Composites Collection.