The Sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to a given limit. It was devised by the Greek mathematician Eratosthenes around 200 BCE, and it is still used today in various applications, such as cryptography and computer science. The basic idea of the Sieve of Eratosthenes is to eliminate all composite numbers (i.e., non-prime numbers) in a range of numbers from 2 to some upper limit. To do this, we start by marking all the numbers from 2 to the limit as potential primes. We then iterate through the list of numbers, starting with 2, and for each prime number we encounter, we mark all its multiples as composite. This process is repeated for each subsequent prime number until we reach the end of the list. At the end of this process, all the unmarked numbers that remain are primes. This is because any composite number in the list would have been marked as a multiple of some smaller prime number, and thus eliminated from the list. For example, if we sta