Prime Numbers Number Theory Math

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• - Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
  
• - Between $100,000 and $250,000 will go to the first individual or group who discovers a new prime number above 10 million digits.
  
• - Short lesson.
  
• - Test numbers for primality and pseudoprimality in Java.
  
• - Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number information.
  
• - Searchable database of these numbers. Lists largest primes by type and who discovered them.
  
• - Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.
  
• - A coordinated project extending the list of Wieferich primes to 10^15.
  
• - Methods and definitions of finding prime numbers.
  
• - A computation of the number up to 10^14, by Jörg Richstein.
  
• - A compilation of links related to prime numbers including primality tests, lists of prime numbers, factoring, Mersenne numbers and the Goldbach conjecture.
  
• - 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 divis
  
• - A musical pieve based on the sieve of Eratosthenes. Requires Realplayer.
  
• - Explains this method of visually representing the distribution of primes and the relationships between factors and products.
  
• - Address by Professor Garrett Barden.
  
• - A compilation of records and resources by Jens Kruse Andersen.
  
• - The discovery of nine and finally ten consecutive primes in arithmetic progression.
  
• - 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.
  
• - Historical topics about prime numbers.
  
• - 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.
  
• - Tables for K=300 to 999.
  
• - Recent developments in primality testing. Here are slides of Jon Grantham's talk on this subject.
  
• - Web article by Johan G. van der Galiën showing that the primes do not satisfy certain statistical tests for randomness.
  
• - International Mathematics Olympiad tutorial proving the theorem of Chebyshef that there is a prime between n and 2n for all positive integers n > 1.
  
• - 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.
  
• - An article by Pascal Sebah with the results of computation of the twin primes up to 5.10^15.
  
• - E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal digits.
  
• - With applets to demonstrate properties of primes.
  
• - Records, statistics, and other interesting facts about palindromic primes compiled by Patrick De Geest.
  
• - An organized search for primes of the form n!!!...!!!! +/-1. Includes table of numbers searched and primes found.
  
• - A proof is offered by Martin Winer for the prime twin problem by defining randomness for a binary sequence.
  
• - This is a method to produce formulas of various complexities with real coeffecients whose itereation indicate whether a given integer is prime or composite.
  
• - Tony Forbes' extensive collection of special types of prime clusters.
  
• - Research in number theory, prime numbers and parity of arithmetic functions. Includes primality testing theorems and prime number chains. In English and French.
  
• - Entropy of a nonnegative adjacency matrix related to prime numbers.
  
• - A site which gives some random primes up to 300 digits and more, also gives related information on primes.
  
• - What is a prime number? How can you find prime numbers? What's the 'Sieve of Eratosthenes'? What's the largest known prime?
  
• - An organized search for primes of the form n*b^n-1.
  
• - An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript required).
  
• - Lists of prime numbers to download in plain ASCII or MS-Excel format.
  
• - Sequences of nearly doubled primes, maintained by Dirk Augustin.
  
• - A collection of interesting Cunningham chains plus how to find some with Yves Gallot's Proth.exe.
  
• - Maintained bt the Electronic Frontier Foundation.
  
• - All of the prime numbers less than 2000000000.
  
• - 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.
  
• - Description of prime k-tuples, the first Hardy-Littlewood conjecture and the Hardy-Littlewood constants.
  
• - Visualization of prime numbers resembling an astronomical radiant or celestial pathway.
  
• - The formula of Jones, Sato, Wada and Wiens: the set of primes is the set of positive values taken by this expression.
  
• - The award wining Prime Glossary has over 150 pages of definitions and terms related to prime numbers and factoring.
  
• - Paulo Ribenboim has named this the "official" site for the collections of typos and errata from his text.
  
• - Twin primes and Brun's number up to 10^14.
  
• - This page is a collection of links related to prime numbers and factoring of very large numbers.
  
• - Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.
  
• - Notes on primality tests by Anuj Seth.
  
• - Software, results and other resources.
  
• - Notes and links compiled by Mark Watkins on the relation of the Riemann zeta function to the distribution of prime numbers.
  
• - Record list for twin and Sophie Germaine primes.
  
• - By Paul Zimmermann.
  
• - 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].
  
• - Findings using an exhaustive search by Thomas J Engelsma.
  
• - The largest known prime gaps measured by absolute or relative size, or a combination.
  
• - The top 10 k consecutive primes in arithmetic progression for each k.
  
• - Factorization and weights of Proth coefficients.
  
• - Prime visualizations (both visual and auditory), applets, message board, links.
  
• - Examples of digital patterns in prime numbers collected by Harvey Heinz.
  
• - A group with new propositions in various areas of number theory.
  
• - A repository maintained by Warut Roonguthai. One project is a search for six titanic primes in arithmetic progression.
  
• - Investigation into patterns in the distribution of the primes by visualizing them.