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In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. There exists an infinitude of prime numbers, as demonstrated by Euclid in about 300 B.C.. The first 30 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, and 113 ; see the list of prime numbers for a longer list.
The property of being a prime is called primality, and the word prime is also used as an adjective. Since 2 is the only even prime number, the term odd prime refers to all prime numbers greater than 2.
The study of prime numbers is part of number theory, the branch of mathematics which encompasses the study of natural numbers. Prime numbers have been the subject of intense research, yet some fundamental questions remain such as the Riemann hypothesis or the Goldbach conjecture, which have been open for more than a century. The problem of modeling the distribution of prime numbers is a popular subject of investigation for number theorists: When looking at individual numbers, the primes seem to be randomly distributed, but the "global" distribution of primes follows well-defined laws.
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RT @OMGFacts: 2 and 5 are the only prime numbers that end in 2 and 5. #omgfacts
snideba (Barry Snider) Fri, 18 Dec 2009 05:48:59 -0000
RT @OMGFacts: 2 and 5 are the only prime numbers that end in 2 and 5. #omgfacts
RT @OMGFacts: 2 and 5 are the only prime numbers that end in 2 and 5. #omgfacts
mangatrai (Mangat Rai Goyal) Fri, 18 Dec 2009 05:47:37 -0000
RT @OMGFacts: 2 and 5 are the only prime numbers that end in 2 and 5. #omgfacts
RT @OMGFacts: 2 and 5 are the only prime numbers that end in 2 and 5. #omgfacts
Gaga4Gokey (Renée ⥠:]) Fri, 18 Dec 2009 05:29:07 -0000
RT @OMGFacts: 2 and 5 are the only prime numbers that end in 2 and 5. #omgfacts
RT @OMGFacts: 2 and 5 are the only prime numbers that end in 2 and 5. #omgfacts
Gonzacos (Gonzalo Acosta) Fri, 18 Dec 2009 05:15:05 -0000
RT @OMGFacts: 2 and 5 are the only prime numbers that end in 2 and 5. #omgfacts
2 and 5 are the only prime numbers that end in 2 and 5.
KevinDimock (Kevin Dimock) Fri, 18 Dec 2009 04:25:10 -0000
2 and 5 are the only prime numbers that end in 2 and 5.
RT @OMGFacts: 2 and 5 are the only prime numbers that end in 2 and 5. #omgfacts
calarthy2 (callan mccarthy) Fri, 18 Dec 2009 04:23:55 -0000
RT @OMGFacts: 2 and 5 are the only prime numbers that end in 2 and 5. #omgfacts
Problems Connection - Carlos Rivera's collection of problems and puzzles related to prime numbers.
The Prime Pages - Prime number research, records and resources. Includes largest known primes, finding and proving primes, glossary, curios, links.
Meta Description: [ Access to hundreds of pages of award-winning information on prime
numbers--with links to thousands of pages elsewhere. We host the searchable database of the 5000
largest known primes (updated weekly). We also have a glossary, top 10 records lists, prime-music,
programs, free downloads, an... ]
All You Wanted to Know about Primes - Information by Joe McLean. Includes fundamentals, frequency, primality proofs and special types. Many definitions and theorems.
Animation of Eratosthenes' Prime Sieve - An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript required).
Meta Description: [ Interactive animation of the sieve of Eratosthenes to obtain prime numbers, using JavaScript. ]
Applets for Prime Numbers - Factorization and weights of Proth coefficients.
Ask Dr. Math FAQ: Prime Numbers - Archived questions and answers at different levels.
Meta Description: [ What is a prime number? How can you find prime numbers? What's the 'Sieve of Eratosthenes'? How can you decide if a number is prime? What's the largest known prime? ]
Bipeds and Prime Numbers - Graduation address by former professor of philosophy Garrett Barden. Mentions primes as sign of human curiosity.
Cunningham Chain Records - Sequences of nearly doubled primes, maintained by Dirk Augustin.
Meta Description: [ Cunningham Chain records ]
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Deficient Factorials - A summary of searches for primes of the form n!/k+-1 (k above 1), n!/k!+-1 (k above 3) and n!/n#+-1.
Distribution of the Prime Numbers - Web article by Johan G. van der Galiën showing that the primes do not satisfy certain statistical tests for randomness.
Meta Description: [ prime numbers are not random! ]
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Electronic Frontier Foundation: Cooperative Computing Awards - Offers $100000, $150000 and $250000 for the first discovery of a prime above 10, 100 and 1000 million digits.
Meta Description: [ Electronic Frontier Foundation is a nonprofit group working to protect your digital rights. ]
Entropy and Prime Numbers - Entropy of a nonnegative adjacency matrix related to prime numbers.
Formulae for Primes - Contains a formula by Jones, Sato, Wada and Wiens. The set of primes is the set of positive values taken by this expression.
Generalized Fermat Prime Search - Software, results and other resources.
Meta Description: [ Generalized Fermat Prime Search. ]
Generalized Woodall Numbers - An organized search for primes of the form n*b^n-1.
Hardy-Littlewood Constants - Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.
Meta Description: [ This website aims to show that there are many constants in mathematics other than just e and pi! ]
Henri Lifchitz - Research in number theory, prime numbers and parity of arithmetic functions. Includes primality testing theorems and prime number chains. In English and French.
Meta Description: [ Recherches en théorie des nombres, nombres premiers et parité des fonctions arithmétiques. Research in number theory, prime numbers and parity of arithmetic functions, top prp 10000. ]
Introduction to Twin Primes and Brun's Constant - An article by Pascal Sebah with the results of computation of the twin primes up to 5.10^15.
Introductory Prime Number Theory Resources - Notes and links compiled by Mark Watkins on the relation of the Riemann zeta function to the distribution of prime numbers.
Jens Kruse Andersen - Prime constellation records. Arithmetic progressions, simultaneous primes, prime gaps.
K-Tuple Permissible Patterns - Findings using an exhaustive search by Thomas J Engelsma.
MacTutor History of Mathematics: Prime Numbers - Includes biographies on many mathematicians.
MathWorld: Prime Numbers - Index to hundreds of prime-related articles in Eric Weisstein's MathWorld.
Notes and Literature on Prime Numbers - With applets to demonstrate properties of primes.
Number Spiral - Explains this method of visually representing the distribution of primes and the relationships between factors and products.
Meta Description: [ This site is devoted to the number spiral, a type of graph that reveals the distribution of primes and other properties of integers. ]
On-Line Encyclopedia of Integer Sequences (OEIS): Primes - Index to information about many integer sequences involving primes. Site includes numerous other prime-related sequences.
Primality - Introductory text on the theory of prime numbers and number fields. Contains proofs of some important theorems including the fundamental theorem of arithmetic.
Primality Testing with Fermat's Little Theorem - Test numbers for primality and pseudoprimality in Java.
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Prime k-tuplets - Tony Forbes' extensive collection of special types of prime clusters.
Meta Description: [ A collection of prime k-tuplets. ]
Prime Music - A musical piece translating prime factorizations to frequencies. Requires RealPlayer.
Prime Numbers - Short lesson.
Prime Numbers and Factoring - This page is a collection of links related to prime numbers and factoring of very large numbers.
Prime Numbers List - Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
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Proof of Bertrand's Postulate - International Mathematics Olympiad tutorial proving there is always a prime between n and 2n.
Radiant Primes - Visualization of prime numbers resembling an astronomical radiant or celestial pathway.
Some Prime Numbers - Sieves and factoring for small numbers. Download primes below 8 billion.
Meta Description: [ A list of prime numbers. ]
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The Distribution of the Primes - Project Report on research into the 2nd Hardy-Littlewood conjecture and the relationship between the primes and chaotic systems by David O'Doherty. Includes program downloads.
The First 5,800,000 Prime Numbers - Site includes known primes k*2^n-1 for k=301 to 999.
Meta Description: [ Over 5 million smallest primes plus lists of specialized primes. ]
The Nine and Ten Primes Project - The discovery of nine and finally ten consecutive primes in arithmetic progression.
The Prime Machine - Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.
The Prime Page - Methods and definitions of finding prime numbers.
Thomas R. Nicely - Includes twin prime counts, tables of first occurrence prime gaps, papers.
Visualizing the Distribution of Prime Numbers - Investigation into patterns in the distribution of the primes by visualizing them.
Wikipedia: Prime Numbers - Index to many prime-related articles.
World of Numbers: World of Palindromic Primes - Records, statistics, curios and puzzles about primes reading the same backwards. Compiled by Patrick De Geest.
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