ABSTRACT
Division is a little trickier. It's natural to ask if the list of primes ever terminates. It turns out that it does not; that is, there are infinitely many primes. This fact is one of the most basic results in number theory. The first written record we have of it is in Euclid's Elements, which was written. The Euclidean Algorithm is one of the oldest and most useful algorithms in all of number theory. When Euclid proved that there are infinitely many primes, he did so by showing that there cannot be a largest prime number. Nevertheless, there is a long history, the Sieve of Eratosthenes, of finding primes, especially large ones. Eratosthenes was born in Cyrene and lived in Alexandria, Egypt. He made important contributions to many subjects, especially geography. In number theory, he is famous for a method of producing a list of prime numbers up to a given bound without using division.
