A prime number is a natural number greater than 1 that can be divided evenly only by 1 and itself. Thus the first few prime numbers are

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...

You can see a longer
**list of prime numbers**
if you like, or you can play with
**the Sieve of Eratosthenes,**
which is an ancient method for identifying prime numbers.
The link points to a page with an interactive applet. Using
the applet requires that you have a
Java
compatible browser.

You can use another interactive applet to
**explore the Prime Number Theorem, the distribution of
prime twins, and the Goldbach conjecture.**

The reason why 1 is said not to be a prime number is merely
convenience. For example, if 1 was prime then the prime
factorization of 6 would not be unique since 2 times 3 = 1
times 2 times 3. A number that can be written as a product
of prime numbers is * composite.* Thus there are
three types of natural numbers: primes, composites, and 1.

A useful book on working with prime numbers computationally
is: Hans Riesel, * Prime Numbers and Computer Methods
for Factorization*, Birkauser Verlag, 1985.

A standard textbook of Number Theory, * intended for use
in a first course in Number Theory, at the upper
undergraduate or beginning graduate level* is: I.
Niven, H.S. Zuckerman, H.L. Montgomery, * An
Introduction to the Theory of Numbers,* 5th edition,
Wiley, 1991.

Another interesting text is: Paulo Ribenboim, * The Book
of Prime Number Records*, 2nd ed., Springer Verlag,
1989.

A major application of number theory and prime numbers is in
cryptography. An excellent introduction to this area is:
Kenneth H. Rosen, * Elementary Number Theory and its
applications,* 3rd ed., Addison Wesley, 1993, ISBN
0-201-57889-1.

Fine print, your comments, more links, Peter Alfeld, PA1UM

[11-Nov-1996]