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.
Created by Tormod Guldvog
Last updated September 14 2001
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.
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The Largest Known Primes
A page about big prime numbers and how they are found.¤
Review: Tormod | link detailsPrimesAmby's Math Resources: Prime Numbers
For beginners: this is a brief introduction to prime numbers, with a couple of exercises for you to solve.¤
Review: Tormod | link detailsPrimesAesthetics of the Prime Sequence
Turpel Armand runs a page which uses multimedia to show you the wonders of primes.¤
Review: Tormod | link detailsPrimesThe EFF Cooperative Computing Awards
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.¤
Review: Tormod | link detailsPrimesThe Prime Puzzles and Problems Connection
This is a wonderful page by Carlos Rivera. Lots of prime puzzles to waste your mind on!¤
Review: Tormod | link detailsPrimesMersenne Prime Search: Make Math History!!
Join the search for new Mersenne Primes. All you need is a computer (and quite a bit of patience).¤
Review: Tormod | link detailsPrimesAsk Dr. Math: Prime Number FAQ
This is a brief introduction to prime numbers, with an example of the Sieve of Eratosthenes technique for finding primes.¤
Review: Tormod | link detailsPrimesFinding primes & proving primality
A thorough guide to understanding how prime numbers are found, and how to prove that a given number is prime.¤number theory
Review: Tormod | link detailsPrimesPrime time
A New Scientist special feature on how scientists are working to solve the Riemann hypothesis.¤
Review: Tormod | link detailsPrimesFrequently Asked Questions about Primes
This is a FAQ about prime numbers, based on questions asked at the Prime Site.¤
Review: Tormod | link detailsPrimes