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Open Directory - Science: Math: Number Theory: Prime Numbers
Primality Proving Software
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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.
Animation of Eratosthenes' Prime Sieve
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.
Entropy and Prime Numbers
- Entropy of a nonnegative adjacency matrix related to prime numbers.
- 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.
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.
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.
- 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.
- Explains this method of visually representing the distribution of primes and the relationships between factors and products.
- 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.
- 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 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.
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.
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