The Sieve of Eratosthenes
(Eratosthenes of Cyrene, ca
Eratosthenes of Cyrene was one of the great
scientists of antiquity. He taught that the earth
is a ball and by ingenious application of the methods of elementary
geometry (at a time when most people thought that the earth is a flat
disk) he determined its circumference with an amazing precision to be
equal to 250000 "stadiums". This value corresponds roughly to 46000
kilometres. Today, as a more exact value the circumference of the
earth's equator is taken to be 40075 kilometres.
Furthermore, the name
of Eratosthenes is connected with the Sieve of Eratosthenes.
This procedure to generate prime numbers is
described as follows.
Sieve of Eratosthenes (general
is an interactive simulation (suitable for experiments) of the Sieve of
Some remarks on the
- The simulation can be started by input of the upper limit
the column number - followed by pressing the "Start" button.
Alternatively, with empty input fields, it can be started by pressing
the Start button - in
which case the default values for the upper limit and number of columns
will be applied. After pressing the Start button the initial
range of numbers is displayed in an array of
rows and columns.
- By choosing different colors and shapes for representing
the process of
out", various patterns appear in the course of the Sieve procedure.
These patterns can be varied by using different column numbers.
- Reaching or exceeding the root of the upper limit is
visually. This serves the purpose of showing that after reaching the
root of the upper limit no new numbers are crossed out.
- After finishing the Sieve procedure all the primes found
are printed out.