 Science: Math: Number_Theory: Prime_Numbers

 Goldbach Conjecture@  (13) Mersenne  (9) Primality Proving Software@  (9) Primality Tests  (21)

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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.

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).

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.

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.

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.

The First 5,800,000 Prime Numbers
Site includes known primes k*2^n-1 for k=301 to 999.

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.

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.

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.

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.

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.

Patterns in Primes
Examples of mostly digit patterns collected by Harvey Heinz.

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 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 Music
A musical piece translating prime factorizations to frequencies. Requires RealPlayer.

Prime Numbers
Short lesson.

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

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.

Visualization of prime numbers resembling an astronomical radiant or celestial pathway.

Some Prime Numbers

Status of Search for Multifactorial Primes
An organized search for primes of the form (n)(n-k)(n-2k)...+/-1. Includes table of numbers searched and primes found.

Thomas R. Nicely
Includes twin prime counts, tables of first occurrence prime gaps, papers.

The Time Traveler
A group with new propositions in various areas of number theory.

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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