-->

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

• Fast Facts:

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

• Related Mahalo Pages

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

Categories

• View History
• Discuss on the Message Board
• Embed this Page
• Share this page