Number Theory

See also:

• Computers: Computer Science: Distributed Computing: Projects: Cryptography  (13)
• Science: Math: Number Theory: Factoring  (44)
• Science: Math: Recreations: Specific Numbers  (170)

• The Prime Pages   - Prime number research, records and resources. Includes largest known primes, finding and proving primes, glossary, curios, links.
• The Prime Puzzles & Problems Connection   - Carlos Rivera's collection of problems and puzzles related to prime numbers.

  Animation of Eratosthenes' Prime Sieve - An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript required)..

  Applets for Prime Numbers - Factorization and weights of Proth coefficients..

  Are the Prime Numbers Randomly Distributed? - Web article by Johan G. van der Galiën. Shows that smaller starting digits are more common for primes below 10^9..

  Ask Dr. Math FAQ: Prime Numbers - Archived questions and answers at different levels..

  Bertrand's Postulate - International Mathematics Olympiad tutorial proving there is always a prime between n and 2n. [PDF].

  Cunningham Chain Records - Sequences of nearly doubled primes, maintained by Dirk Augustin..

  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..

  Entropy and Prime Numbers - Entropy of a nonnegative adjacency matrix related to prime numbers..

  Formulae for Primes - Includes a formula by Jones, Sato, Wada and Wiens. The set of primes is the set of positive values taken by this expression..

  Gebhard Glöggler - Makes a statement about the number of primes between the squares of odd numbers, and provides a proof of Goldbach's conjecture..

  Generalized Fermat Prime Search - Software, results and other resources..

  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..

  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..

  Natural Numbers - Provides a collection of tools and interesting pages for testing, visualizing, and understanding natural numbers..

  The Nine and Ten Primes Project - The discovery of nine and finally ten consecutive primes in arithmetic progression..

  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..

  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. [PDF].

  Primality Testing with Fermat's Little Theorem - Test numbers for primality and pseudoprimality in Java..

  Prime Constellation Counting Functions - Techniques for counting prime constellations between P(n) and P(n)^2. [PDF].

  Prime k-tuplets - Tony Forbes' extensive collection of special types of prime clusters..

  The Prime Machine - Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem..

  Prime Number Lists - Downloads of over 100 million prime numbers. Each link contains 1 million primes in a .7z file. A special link allows for downloads of all primes at once..

  Prime Numbers - Short lesson..

  Prime Numbers and Factoring - Links and references related to primes and factoring..

  Prime Numbers Generator and Checker - Enter a natural number, check it and find the nearest prime..

  Prime Numbers List - Browse all prime numbers of less than 10 digits. A prime number checker facility is also included..

  The Prime Page - Methods and definitions of finding prime numbers..

  Some Prime Numbers - Sieves and factoring for small numbers. Download primes below 8 billion..

  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..

  Bipeds and Prime Numbers - Graduation address by former professor of philosophy Garrett Barden. Mentions primes as sign of human curiosity. (September 18, 2001).

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