Prime Numbers

The Mahalo Top 7

Wikipedia: Prime Numbers
Wolfram Mathworld: Prime Number
University of St. Andrews: Prime Numbers
University of Tennessee at Martin: The Prime Pages
Camosun College: Sieve of Eratosthenes
The Beauty of Mathematics: The Prime Number Theorem
YouTube Video: The Language of Mathematics: Prime Numbers (Time: 3:42)

Prime Numbers News and Articles

Google News: Prime Numbers
Burlington Free Press: How Math Protects People from Information Theft (March 28, 2008)
Physorg.com: A Mighty Number Falls (May 21, 2007)
Seed: Prime Numbers Get Hitched (April 27, 2006)
Plus: The Prime Number Lottery (November 2003)
BBC News: Prime Number Breakthrough (April 4, 2003)
The Guardian: German Discovers Longest Prime Number (March 2, 2005)
New Scientist: 7-Million Digit Prime Number Discovered (June 1, 2004)
CNN.com: Student Finds Largest Known Prime Number (December 11, 2003)
Science News Online: Prime Pursuit (October 26, 2002)

Prime Numbers History

University of Aarhus: History of Prime Numbers
PlanetMath: History of Prime Numbers
Canada Wide 2008 Virtual Science Fair: History of Prime Numbers
University of Tennessee at Martin: Mersenne Primes: History, Theorems and Lists

Notable Figures in Prime Numbers

Euclid

Mahalo's Guide to Euclid
Wikipedia: Euclid
University of St. Andrews: Euclid of Alexandria
Clark University: Eudlid's Elements

Eratosthenes

Wikipedia: Eratosthenes | Sieve of Eratosthenes
University of St. Andrews: Eratosthenes of Cyrene
Wolfram Mathworld: Sieve of Eratosthenes

Pierre de Fermat

Wikipedia: Pierre de Fermat
University of St. Andrews: Pierre de Fermat
Wolfram Mathworld: Fermat Primes

Marin Mersenne

Wikipedia: Marin Mersenne
University of St. Andrews: Marin Mersenne
Wolfram Mathworld: Mersenne Prime

Charles Jean de la Valle Poussin

Wikipedia: Charles Jean de la Valle Poussin
University of St. Andrews: Charles Jean Gustave Nicolas Baron de la Vallée Poussin
SpringerLink: De la Vallée-Poussin Theorem

Jacques Hadamard

Wikipedia: Jacques Hadamard
University of St. Andrews: Jacques Salomon Hadamard
Planet Math: Jacques Hadamard

Derrick Norman Lehmer

Wikipedia: Derrick Norman Lehmer
University of St. Andrews: Derrick Norman Lehmer
Smart Computing: Derrick Norman Lehmer

Sophie Germain

Wikipedia: Sophie Germain
University of St. Andrews: Marie-Sophie Germain
Wolfram Mathworld: Sophie Germain Prime

Prime Numbers Fun Stuff

The Prime Puzzles & Problems Connection
Arizona State University: The Prime Number Maze
Murderous Maths: Prime Numbers
FunTrivia.com: Prime Numbers Quiz
XP Math: King Kongs Prime Numbers

Prime Numbers Research

Science News: Creeping Up on Reimann (April 4, 2008)
University of Tennessee at Martin: Prime Conjectures and Open Questions
Petrospec Technologies: Goldbach Conjecture Research

Prime Numbers Education Resources

Wolfram Demonstrations Project: Why a Number Is Prime
University of Zimbabwe: Prime Numbers
Fact Monster: Prime Numbers
University of Illinois at Urbana-Champaign: Prime Number Tutorial
Bay Mills Community College Math Tutorials: Numbers -Prime Numbers
The Math Forum: Prime Numbers

Prime Numbers Photos and Videos

Google Images: Prime Numbers Photos
Yahoo! Images: Prime Numbers Photos
Google Videos: [http://video.google.com/videosearch?q=prime+numbers
YouTube Videos: Prime Numbers
YouTube Video: Prime Numbers Proof (Time: 2:07)
YouTube Video: The Language of Mathematics 10: Finding Prime Factors (Time: 9:44)

Prime Numbers Blogs and Forums

BetterExplained: Another Look at Prime Numbers (September 7, 2007)
Math Help Forum: Prime Numbers (January 5, 2007)
Teacher Magazine: On The Reservation: Prime Numbers (October 24, 2006)
Math Forum: FAQ: Prime Numbers

Prime Numbers Books and Publications

Google Books: Prime Numbers Books Search
eBay: Prime Numbers Books Search
Amazon.com: Prime Numbers Books Search
Google Books: Prime Numbers and Computer Methods for Factorization
Google Books: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem

Prime Numbers Theories

Wolfram Mathworld: Prime Number Theorem | Fibonacci Prime | Legendre's Conjecture | Mersenne Prime
Wikipedia: Cramer's Conjecture | Schinzel's hypothesis H | Fermat Prime

Related Searches

Number Theory | Algebra | Geometry | Mathematics | Cryptography | Calculus | Statistics | Graph Theory | Euclid | Hans Riesel

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Guide Note

A prime number is a number greater than one whose only two factors are one and itself.

Fast Facts:

The only even prime number is 2
Earliest Contributor: Euclid
Other Prominent Contributors: Eratosthenes, Marin Mersenne, Pierre de Fermat, Jacques Hadamard, Charles de la Vallee Poussin, Derrick Norman Lehmer
Major Property: base 10 prime numbers except 2 and 5 end in 1, 3, 7 or 9
Special Primes: Wieferich Prime, Mersenne Prime, Fermat Primes, Sophie Germain Prime
Largest Known Prime: 2 raised to the 32,582,657 (9,808,358 digits long, 44th Mersenne Prime)
Applications: Cryptography, srts and literature, nature

History

The history of primes begins with Euclid, who, circa 300 BC, discovered there was an infinite number of prime numbers. Eratosthenes developed a simple, yet useful method to determine primes called the Sieve of Eratosthenes around 200 BC. In the 17th century Pierre de Fermat developed the Fermat Primes. French mathematician Marin Mersenne developed the definition of a Mersenne Prime during the same time period. During the late 19th century the proof of the Prime Number Theorem was completed by Jacques Hadamard and Charles Jean de la Valle Poussin. Modern computers have accelerated the search for the largest prime number.

Determining if a number is prime

While Eratosthenes method for finding primes is simple and effective for small numbers, the modern Sieve of Atkin, although more complex, is faster when properly used. One simple method for determining whether a number is prime is to divide by all primes less than or equal to the square root of that number. If the divisions yield a remainder, the number is not prime. Otherwise the number is prime. Mathematicians can also determine whether or not a number of prime by using Primality Tests. These tests include Pepin's Test, Proth's Theorem and the Lucas Lehmer Test.

Applications for prime numbers

Primes are used today in cryptography, hash tables and pseudorandom number generators.

Prime numbers in popular culture

Primes are also seen in arts and literature, such as in the the novel Contact, the play Arcadia and in several films (The Cube, Sneakers, The Mirror Has Two Faces and A Beautiful Mind).

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