The Ancient Algorithm: Sieve of Eratosthenes

In the realm of coding, we often find ourselves delving into the mysteries of mathematics to uncover solutions to age-old problems. One such classic problem is the quest to discover prime numbers. Dating back to the 3rd century BC, a brilliant algorithm was formulated by Eratosthenes that revolutionized the way we identify prime numbers. This ingenious algorithm, now known as the Sieve of Eratosthenes, provides a systematic approach to determining all primes up to a given number.

The essence of the algorithm lies in a series of steps that gradually weed out non-prime numbers, leaving behind the coveted set of prime numbers. While there are various methods to enhance this process, the modern interpretation of the sieve commences by acknowledging 2 as prime, filtering out all even numbers up to a specified value n, and identifying them as non-prime. Subsequently, the algorithm progresses to 3, repeating the same procedure for multiples of 3. This process iterates through all numbers up to n, excluding the ones already deemed non-prime.

Despite its ancient origins, the Sieve of Eratosthenes exemplifies the remarkable fusion of math and coding, enabling programmers to transform theoretical concepts into functional code effortlessly. Here is a concise JavaScript version of the algorithm sourced from Wikipedia:

// JavaScript implementation of the Sieve of Eratosthenes algorithm
const sieveOfEratosthenes = (n) => {
  let primes = [];
  let isPrime = new Array(n + 1).fill(true);

  for (let p = 2; p * p <= n; p++) {
    if (isPrime[p] === true) {
      for (let i = p * p; i <= n; i += p)
        isPrime[i] = false;
    }
  }

  for (let p = 2; p <= n; p++) {
    if (isPrime[p]) {
      primes.push(p);
    }
  }

  return primes;
};

// Example usage
const n = 20;
console.log(sieveOfEratosthenes(n));

Embark on this journey through time and numerical wonders as you explore the ancient marvel of the Sieve of Eratosthenes, a testament to the enduring fusion of mathematics and coding innovation.