section_path: Computational methods/Sieves
section_name: Sieves
paragraph_text: Sieves
  
  Before computers, mathematical tables listing all of the primes or prime factorizations up to a given limit were commonly printed. The oldest known method for generating a list of primes is called the sieve of Eratosthenes. The animation shows an optimized variant of this method. Another more asymptotically efficient sieving method for the same problem is the sieve of Atkin. In advanced mathematics, sieve theory applies similar methods to other problems.