The Sieve of Eratosthenes - How Fast Can We Compute a Prime Number Table?

Abstract

A prime number is a natural number that is not divisible without remainder by any other natural number but 1 and itself. Primes are scattered irregularly among the set of natural numbers, and this fact has fascinated mathematicians throughout the centuries. Today, primes are not only a challenge for mathematicians, but are of very practical value – for instance, they play a central role in cryptography. In this chapter the authors explain a very old, but still practical algorithm for computing a table with all prime numbers up to a specified number.