Prime Numbers

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

1. The only even prime number is 2,
2. Early 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: 2^43112609 - 1. It was found in 2008 and has 12978189 digits; it is a Mersenne primehttp://primes.utm.edu/largest.html.

The history of primes begins with Euclid, who, circa 300 BC, discovered there is an infinite number of prime numbers. Eratosthenes, about 200 BC developed a simple, yet useful method to determine the primes called the Sieve of Eratosthenes. In the 17th century Pierre de Fermat studied the Fermat Primes. The French mathematician Marin Mersenne defined the Mersenne Primes during the same time period. In 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.

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.

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

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).

• Wolfram Mathworld: Prime Number Theorem | Fibonacci Prime | Legendre's Conjecture | Mersenne Prime

• Wikipedia: Cramer's Conjecture | Schinzel's hypothesis H | Fermat Prime

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