The Sieve of Eratosthenes

 

 

 

While researching Eratosthenes (born in 276BC in Cyrene, which is modern day Libya) and several works based on him and his discoveries, I became fascinated with his brilliance. He was not just an ordinary man. He was a mathematician, poet, astronomer, geographer, and athlete. Most importantly, he succeeded as the chief librarian of the Library of Alexandria. Most of his discoveries contribute to most of the knowledge that we have today. For example, he devised a system for longitude and latitude, calculated the circumference of the Earth, created a map of the world based on the geographical knowledge of the European people of that time, and devised a very famous algorithm known as the sieve of Eratosthenes. Throughout this paper I will be discussing the sieve of Eratosthenes and how it is used.

The sieve of Eratosthenes is an algorithm used to locate all prime numbers from one to a specified maximum number, n. It involves a chart from one to n with x rows and y columns. In order to go through all prime numbers within that range (1 to n, where n is the maximum number) the user must locate and remove from the chart all of the multiples of the numbers in the first row. As a result, the chart will contain only prime numbers from one to n.

Eratosthenes was highly regarded in the ancient world, but unfortunately only fragments of his writing have survived. For example, as written by Quesada, “several improvements have been made to the Sieve by reducing the size of the initial set and by avoiding some duplication in the removal process.” However, if it was not for Eratosthenes, there probably would never have been a table of primes, or any quicker algorithm for locating prime numbers within a range of numbers.

            In 195BC, Eratosthenes died at a very old age by voluntarily starving himself, due to despair at his blindness.

 

 

 

 

                                                                                 Works Cited

 

 

 

 

 

Antonio R. Quesada, “On the K-th extension of the Sieve of eratosthenes,” International Journal of Mathematics and Mathematical Sciences, vol. 18, no. 3, pp. 539-544, 1995. doi:10.1155/S0161171295000688

 

 

 

Moulton, J. Paul. "Sieve of Eratosthenes." The Gale Encyclopedia of Science. Ed. K. Lee Lerner and Brenda Wilmoth Lerner. Vol. 5. 3^rd ed. Detroit: Gale, 2004. 3632-3633. Gale Virtual Reference Library. Gale. Nassau Community College Library - SUNY. 17 Apr. 2008 http://go.galegroup.com/ps/start.do?p=GVRL&u=sunynassau.

 

 

 

Baldwin, Doug, and Greg Scragg. Algorithms and Data Structures: The Science of Computing. Charles River Media, 2004.

 

 Create your own educational wiki!HelpPublic, not yet premium Privacy Policy RSS