**Prime and Rare**

Just as bird-watchers might travel to the ends of the Earth to

glimpse the tundra swan or the yellow-eared parrot, some mathematicians

pursue equally exotic quarry. The search for large prime numbers -- after

this on Earth and Sky.

**Date
**

JB: This is Earth and Sky, on the subject of a rare species of…numbers. These numbers are known as "primes," and they can be evenly divided only by themselves and one. For example, five and seven are primes. The search for larger and larger prime numbers is something of a

competitive sport amongst mathematicians. Dr. Hendrik Lenstra of the

University of California at Berkeley spoke with us about the thrill of the

chase:

(Tape 0:02:49-0:03:01) There is no largest prime number and people always find it an interesting game to find a larger prime number than the previous guy did because there is no formula for generating arbitrarily large prime numbers. (Tape 0:03:19-0:03:29) If I write down a large number -- and that is certainly true for a number of two million digits -- then it is not all that easy to decide whether or not it is a prime number. (Tape 0:03:35-0:04:01) You really need to know theorems and properties of prime numbers and then you can see whether the number you have actually enjoys those properties and if it doesn't, well then you can forget about it -- it won't be a prime number. And if it does, well then you can perhaps start from that information and build up an actual proof that it is a prime number and that is what makes the game interesting. It is difficult and therefore you want to do it -- it is just like climbing mountains.

JB: There's a practical side to the ‘game,' too -- large prime numbers are involved in testing computer chips for flaws. Thanks to Dr. Hendrik Lenstra for speaking with us. And with thanks to the National Science Foundation, I'm Joel Block, for Deborah Byrd, for Earth and Sky.

Author: Beverly Wachtel

Thanks to the following individual for aiding in the preparation of this

script:

Dr. Hendrik W. Lenstra

Department of Mathematics

University of California

Berkeley, Ca

hwl@math.berkeley.edu

MORE INFO

As of June 1999, the largest known prime number is 2 to the power 6,972,593, and then you subtract 1 -- it's about 2,000,000 digits long!

If you enjoyed this program, you may be interested in the following websites:

The Prime Pages:

http://www.utm.edu/research/primes/largest.html#intro

Mathematical Sciences Research Institute:

http://www.msri.org