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Searching for Primes

Did you know that there are prime numbers with billions of digits? This week we take a look at how number theorists search for these monsters.

Posted by Tormod Guldvog
13 September, 2001 04:09:17

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For beginners, the world of prime numbers may seem to be a mixture of chaos and strict order.

If you start at 1 and count all the integers until, say, 1 million, there is a finite number of primes. The problem is that it is very difficult to find out exactly how many primes there are, and how they are spaced out over the endless list of integers.

But over the years, new theories have emerged which predict where and how often primes will emerge.

Using these theories, modern prime hunters have located primes which are so large that they defy the imagination. And the only thing we can say for sure about prime numbers, is that there are many more to come.

Some of the links below point to sites where you can actively take part in the search for primes. You can also test your skills to see how good you are at determining whether a given number is prime.

Related Links

The Largest Known Primes
http://www.utm.edu/research/primes/largest.html
A page about big prime numbers and how they are found.

Amby's Math Resources: Prime Numbers
http://amby.com/educate/math/2-1_prim.html
For beginners: this is a brief introduction to prime numbers, with a couple of exercises for you to solve.

Aesthetics of the Prime Sequence
http://www2.vo.lu/homepages/armand/index.html
Turpel Armand runs a page which uses multimedia to show you the wonders of primes.

The EFF Cooperative Computing Awards
http://www.eff.org/awards/coop.html
The Electronic Frontier Foundation offers huge prizes to those who can find the first primes with more than 10,000,000 digits - and even more money for larger primes.

The Prime Puzzles and Problems Connection
http://www.primepuzzles.net/
This is a wonderful page by Carlos Rivera. Lots of prime puzzles to waste your mind on!

Mersenne Prime Search: Make Math History!!
http://www.mersenne.org/prime.htm
Join the search for new Mersenne Primes. All you need is a computer (and quite a bit of patience).

Ask Dr. Math: Prime Number FAQ
http://www.forum.swarthmore.edu/dr.math/faq/faq.prime.num.html
This is a brief introduction to prime numbers, with an example of the Sieve of Eratosthenes technique for finding primes.

Finding primes & proving primality
http://www.utm.edu/research/primes/prove/proving.html
A thorough guide to understanding how prime numbers are found, and how to prove that a given number is prime.¤number theor

Prime time
http://www.newscientist.com/nlh/1111/prime.html
A New Scientist special feature on how scientists are working to solve the Riemann hypothesis.

Frequently Asked Questions about Primes
http://www.utm.edu/research/primes/notes/faq.html
This is a FAQ about prime numbers, based on questions asked at the Prime Site.