Sieve of Eratosthenes
The Sieve of Eratosthenes is an ancient and efficient algorithm for finding all prime numbers up to a specified integer limit. It works by iteratively marking the multiples of each prime number starting from 2, leaving the unmarked numbers as primes. This method is widely used in mathematics and computer science for its simplicity and optimal time complexity of O(n log log n) for generating primes.
Developers should learn this algorithm when working on problems involving prime numbers, such as cryptography, number theory, or competitive programming challenges. It is particularly useful for generating prime lists efficiently in applications like prime factorization, primality testing, or mathematical simulations, where performance is critical for large input ranges.