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Search Home : Science : Math : Number Theory : Prime Numbers
See Also:
- The Prime Page (An Index of Information on Prime Numbers): The prime source for information about prime numbers!
- The Prime Puzzles & Problems Connection: Carlos Rivera's collection of problems and puzzles related to prime numbers.
- A List of Prime Numbers: All of the prime numbers less than 2000000000.
- Aesthetics of the Prime Numbers Sequence: Prime visualizations (both visual and auditory), applets, message board, links.
- 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.
- Ask Dr. Math: What is a prime number? How can you find prime numbers? What's the 'Sieve of Eratosthenes'? What's the largest known prime?
- Basic Theorems Concerning Prime Numbers: An introductory page on the theory of prime numbers with proofs of some important theorems including the infinitude of primes, Euclid's algorithm and the fundamental theorem of arithmetic.
- Bipeds and Prime Numbers: Address by Professor Garrett Barden.
- Cunningham Chain Records: Sequences of nearly doubled primes, maintained by Dirk Augustin.
- Deficient Factorials: A summary of all known searches for primes of the form n!/k+-1 (with k>1), n!/k!+-1 (k>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.
- Dr. Nicely's Home Page: Twin primes and Brun's number up to 10^14.
- EFF Cooperative Computing Awards: Between $100,000 and $250,000 will go to the first individual or `group` who discovers a new prime number above 10 million digits.
- Elliptic Curve Primality Proving Algorithm: The ECPP is a modern method of primality proving that does not require auxiliary factorizations. Instead, ECPP uses the sizes of groups of rational points on elliptic curves modulo n.
- Entropy and Prime Numbers: Entropy of a nonnegative adjacency matrix related to prime numbers.
- Formulae for Determining Primality or Compositeness: This is a method to produce formulas of various complexities with real coeffecients whose itereation indicate whether a given integer is prime or composite.
- Formulae for Primes: The formula of 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.
- K-Tuples: Findings using an exhaustive search by Thomas J Engelsma.
- Large Primes in Arithmetic Progression: A repository maintained by Warut Roonguthai. One project is a search for six titanic primes in arithmetic progression.
- Largest Known Primes: Searchable database of these numbers. Lists largest primes by type and who discovered them.
- Multifactorial Primes: An organized search for primes of the form n!!!...!!!! +/-1. Includes table of numbers searched and primes found.
- New Primality Record: E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal digits.
- 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.
- PRIMES is in P.: A paper by Manindra Agrawal, Neeraj Kayal, Nitin Saxena that presents a polynomal-time algorithm that determines whether an input number n is prime or composite [PS].
- Patterns in Primes: Examples of digital patterns in prime numbers collected by Harvey Heinz.
- Primality Testing with Fermat's Little Theorem: Test numbers for primality and pseudoprimality in Java.
- Prime Constellations: Description of prime k-tuples, the first Hardy-Littlewood conjecture and the Hardy-Littlewood constants.
- Prime Music: A musical pieve based on the sieve of Eratosthenes. Requires Realplayer.
- Prime Number Generation: Notes on primality tests by Anuj Seth.
- Prime Number Records: By Paul Zimmermann.
- Prime Number Resources and Information: Maintained bt the Electronic Frontier Foundation.
- Prime Numbers: Short lesson.
- Prime Numbers Directory: A compilation of links related to prime numbers including primality tests, lists of prime numbers, factoring, Mersenne numbers and the Goldbach conjecture.
- Prime Numbers History: Historical topics about prime numbers.
- Prime Numbers List: Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
- Prime Numbers and Factoring: This page is a collection of links related to prime numbers and factoring of very large numbers.
- Prime k-tuplets: Tony Forbes' extensive collection of special types of prime clusters.
- Primes of the Form K * 2^N -1: Tables for K=300 to 999.
- Proof of Bertrand's Postulate: International Mathematics Olympiad tutorial proving the theorem of Chebyshef that there is a prime between n and 2n for all positive integers n > 1.
- Pseudoprimes/Probable Primes: Recent developments in primality testing. Here are slides of Jon Grantham's talk on this subject.
- Radiant Primes: Visualization of prime numbers resembling an astronomical radiant or celestial pathway.
- Random Small Primes: A site which gives some random primes up to 300 digits and more , also gives related information on primes.
- Randomness and Prime Twin Proof: A proof is offered by Martin Winer for the prime twin problem by defining randomness for a binary sequence.
- Searching for Primes: Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number information.
- Tables of Prime Numbers: Lists of prime numbers to download in plain ASCII or MS-Excel format.
- Testing for Primality: Since ancient times, mathematicians have been fascinated by problems concerning prime numbers, and many people have worked on the problem of determining ways to test if numbers are prime. One way to test if a number is prime is to find the number's divisors. The following program finds the smallest integral divisor (greater than 1) of a given number n. It does this in a straightforward way, by testing n for divisibility by successive integers starting with 2.
- 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 Largest Known CPAP's: The top 10 k consecutive primes in arithmetic progression for each k.
- The New Book of Prime Number Records, Additions and Errata: Paulo Ribenboim has named this the "official" site for the collections of typos and errata from his text.
- The Nine and Ten Primes Project: The discovery of nine and finally ten consecutive primes in arithmetic progression.
- The Nth Prime Page: This online calculator finds the Nth prime, with N up to 10^12. It also finds the pi function (given a number, this function returns the number of primes below that number).
- The Prime Glossary: The award wining Prime Glossary has over 150 pages of definitions and terms related to prime numbers and factoring.
- 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.
- The Time Traveler: A `group` with new propositions in various areas of number theory.
- The Top-20 Prime Gaps: The largest known prime gaps measured by absolute or relative size, or a combination.
- Twin Primes: A computation of the number up to 10^14, by Jörg Richstein.
- Visualizing the Distribution of Prime Numbers: Investigation into patterns in the distribution of the primes by visualizing them.
- Wieferich Prime Number Search: A coordinated project extending the list of Wieferich primes to 10^15.
- World Records in Computational Number Theory: Record list for twin and Sophie Germaine primes.
- World of Palindromic Primes: Records, statistics, and other interesting facts about palindromic primes compiled by Patrick De Geest.
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