Twin Primes

Date: 12/24/97 at 15:16:44
From: ALee256410
Subject: Twin primes

I'm a high school senior in Maryland. This year I am doing an 
independent research on twin primes. Do you know if there are any 
researches or studies being conducted on this topic? Thank you for 
your time.

Sincerely,

Austin Lee

Date: 01/10/98 at 11:00:01
From: Doctor Nick
Subject: Re: Twin primes

Hi Austin,

Twin primes are a very interesting area of investigation. A lot of 
research continues on them still. The big question, whether there are 
infinitely many of them, is still unsolved. If you have web access, 
try this page:

   http://www.astro.virginia.edu/~eww6n/math/TwinPrimes.html   

which has lots of neat information on twin primes.

You should also try your library (you might need to go to a university 
or college library) for the following books, which you should find 
quite helpful:

Ribenboim, P.; The Book of Prime Number Records, 2nd ed. New York: 
  Springer-Verlag, pp. 199-204, 1989.

Guy, R. K.; Unsolved Problems in Number Theory, 2nd ed. New York: 
  Springer-Verlag, pp. 19-23, 1994.

These are both great books that cover lots of interesting questions
about primes.  They are also both quite up to date. 

You also should look at

Dickson, L. E. History of the Theory of Numbers, vol. 1: Divisibility 
  and Primality. New York: Chelsea, 1952.

This book is part of a set of books covering all number theory up
to 1900.  It's a great place to start looking for the history
of any problem in number theory.

Don't get too discouraged by the difficult mathematics involved.
Research into twin primes is extremely complicated, at least on the 
graduate school level. For now, I'd suggest reading about what has 
been determined, the names of the people involved, and what the big 
open questions are.

Good luck, and have fun.

-Doctor Nick,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/