Part 1: 

Write a small autobiographical (first person) paper (about 1 - 2 minutes if read out loud) on Eratosthenes.  Be sure to answer at least):

• Who was Eratosthenes?
• What is the Sieve and what is it used for?
• What else is he known for?
   

                        The Sieve of Eratosthenes

   

   

   

  I was born in 276BC in Cyrene. I was not just an ordinary man. He was a mathematician, poet, astronomer, geographer, and athlete. Most importantly, I succeeded as the chief librarian of the Library of Alexandria. Most of my discoveries will contribute to most of the knowledge that that poeple will have in the future. For example, I devised a system for longitude and latitude, calculated the circumference of the Earth, created a map of the world, and devised a very famous algorithm known as the sieve of Eratosthenes, which as you can see, is named after me. 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.

  Hopefully, my works will inspire many people and help to build a better future. They will improve the knowledge that people have today and help people to come up with other methods and technology to help speed the process of several other tasks like how my sieve has helped in speeding up the task of having to find all primes from 1 to n.

   

                                                                      

                                                             After Eratosthenes' Death

   

  Eratosthenes was highly regarded by the people of his time, but unfortunately only fragments of his work 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.

   

   

   

   

   

Part 2:

Write a program implementing the Sieve of Eratosthenes to find all prime numbers less than 32768.

SieveOfEratosthenes.java 

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