The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite lie., not prime) the multiples of each prime, starting with the multiples of 2 The sieve of Eratosthenes can be expressed in pseudocode, as follows: Input: an integer n Let A be an array of 8oo1ean values, indexed by integers 2 to n, initially all set to true. for t - 2, 3, 4, ..., not exceeding A if ?i] is true: for j. t, iat, t?+21, th31, , not exceeding n: ALJ)-false. Output: al1 t such that A[4) is true. This algorithm produces all primes