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This page was last updated on August 20th, 2008
This page was last updated on August 20th, 2008
Prime Numbers (from Number Theory)
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Animation of Eratosthenes' Prime Sieve
An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript required).
Generalized Fermat Prime Search
Software, results and other resources.
The Prime Machine
Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.
Largest Known Primes
Searchable database of these numbers. Lists largest primes by type and who discovered them.
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.
Notes and Literature on Prime Numbers
With applets to demonstrate properties of primes.
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.
Primality Testing with Fermat's Little Theorem
Test numbers for primality and pseudoprimality in Java.
World Records in Computational Number Theory
Record list for twin and Sophie Germaine primes.
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.
Radiant Primes
Visualization of prime numbers resembling an astronomical radiant or celestial pathway.
Prime Number Generation
Notes on primality tests by Anuj Seth.
Twin Primes
A computation of the number up to 10^14, by Jörg Richstein.
Tables of Prime Numbers
Lists of prime numbers to download in plain ASCII or MS-Excel format.
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).
Prime Numbers and Factoring
This page is a collection of links related to prime numbers and factoring of very large numbers.
The Top-20 Prime Gaps
The largest known prime gaps measured by absolute or relative size, or a combination.
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.
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.
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.
Prime Music
A musical pieve based on the sieve of Eratosthenes. Requires Realplayer.
Prime Number Resources and Information
prime number basics
Pseudoprimes/Probable Primes
Recent developments in primality testing. Here are slides of Jon Grantham's talk on this subject.
Searching for Primes
Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number information.
Patterns in Primes
Examples of digital patterns in prime numbers collected by Harvey Heinz.
Random Small Primes
A site which gives some random primes up to 300 digits and more , also gives related information on primes.
Applets for Prime Numbers
Factorization and weights of Proth coefficients.
Cunningham Chain Records
Sequences of nearly doubled primes, maintained by Dirk Augustin.
The Largest Known CPAP's
The top 10 k consecutive primes in arithmetic progression for each k.
A List of Prime Numbers
All of the prime numbers less than 2000000000.
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?
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.
The Nine and Ten Primes Project
The discovery of nine and finally ten consecutive primes in arithmetic progression.
Entropy and Prime Numbers
Entropy of a nonnegative adjacency matrix related to prime numbers.
Wieferich Primes
Miscellaneous notes and graphics about Wieferich primes by Joe Crump.
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].
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.
Aesthetics of the Prime Numbers Sequence
Prime visualizations (both visual and auditory), applets, message board, links.
Yves Gallot's Proth.exe and Cunningham Chains
A collection of interesting Cunningham chains plus how to find some with Yves Gallot's Proth.exe.
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 divis
Large Primes in Arithmetic Progression
Join the search for an example of 6 titanic primes in arithmetic progression.
Primes of the Form K * 2^N -1
Tables for K=300 to 999.
Prime Numbers List
Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
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.
The Prime Page (An Index of Information on Prime Numbers)
The prime source for information about prime numbers!
Prime k-tuplets
Tony Forbes' extensive collection of special types of prime clusters.
K-Tuples
Findings using an exhaustive search by Thomas J Engelsma.
Bipeds and Prime Numbers
Address by Professor Garrett Barden.
Multifactorial Primes
An organized search for primes of the form n!!!...!!!! +/-1. Includes table of numbers searched and primes found.
Number Spiral
Explains this method of visually representing the distribution of primes and the relationships between factors and products.
The Prime Puzzles & Problems Connection
Carlos Rivera's collection of problems and puzzles related to prime numbers.
The Time Traveler
A group with new propositions in various areas of number theory.
Prime Number Records
By Paul Zimmermann.
World of Palindromic Primes
Records, statistics, and other interesting facts about palindromic primes compiled by Patrick De Geest.
Prime Numbers
Short lesson.
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.
Randomness and Prime Twin Proof
A proof is offered by Martin Winer for the prime twin problem by defining randomness for a binary sequence.
Some Results on the Number of Non-Witnesses to Compositeness
This paper introduces the reader to the Rabin-Miller probabilistic primality test, the concept of non-witnesses to compositeness, and the problem of determining the number of non-witnesses to compositeness.
Visualizing the Distribution of Prime Numbers
Investigation into patterns in the distribution of the primes by visualizing them.
The Prime Glossary
The award wining Prime Glossary has over 150 pages of definitions and terms related to prime numbers and factoring.
Prime Numbers History
Historical topics about prime numbers.
Hardy-Littlewood Constants
Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.
Prime Constellations
Description of prime k-tuples, the first Hardy-Littlewood conjecture and the Hardy-Littlewood constants.
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.
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.
The Prime Page
Methods and definitions of finding prime numbers.
New Primality Record
E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal digits.
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.
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.
Generalized Woodall Numbers
An organized search for primes of the form n*b^n-1.
Wieferich Prime Number Search
A coordinated project extending the list of Wieferich primes to 10^15.
Dr. Nicely's Home Page
Twin primes and Brun's number up to 10^14.
An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript required).
Software, results and other resources.
Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.
Searchable database of these numbers. Lists largest primes by type and who discovered them.
Paulo Ribenboim has named this the "official" site for the collections of typos and errata from his text.
With applets to demonstrate properties of primes.
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.
Test numbers for primality and pseudoprimality in Java.
Record list for twin and Sophie Germaine primes.
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.
Visualization of prime numbers resembling an astronomical radiant or celestial pathway.
Notes on primality tests by Anuj Seth.
A computation of the number up to 10^14, by Jörg Richstein.
Lists of prime numbers to download in plain ASCII or MS-Excel format.
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).
This page is a collection of links related to prime numbers and factoring of very large numbers.
The largest known prime gaps measured by absolute or relative size, or a combination.
A compilation of links related to prime numbers including primality tests, lists of prime numbers, factoring, Mersenne numbers and the Goldbach conjecture.
International Mathematics Olympiad tutorial proving the theorem of Chebyshef that there is a prime between n and 2n for all positive integers n > 1.
The formula of Jones, Sato, Wada and Wiens: the set of primes is the set of positive values taken by this expression.
A musical pieve based on the sieve of Eratosthenes. Requires Realplayer.
prime number basics
Recent developments in primality testing. Here are slides of Jon Grantham's talk on this subject.
Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number information.
Examples of digital patterns in prime numbers collected by Harvey Heinz.
A site which gives some random primes up to 300 digits and more , also gives related information on primes.
Factorization and weights of Proth coefficients.
Sequences of nearly doubled primes, maintained by Dirk Augustin.
The top 10 k consecutive primes in arithmetic progression for each k.
All of the prime numbers less than 2000000000.
What is a prime number? How can you find prime numbers? What's the 'Sieve of Eratosthenes'? What's the largest known prime?
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.
The discovery of nine and finally ten consecutive primes in arithmetic progression.
Entropy of a nonnegative adjacency matrix related to prime numbers.
Miscellaneous notes and graphics about Wieferich primes by Joe Crump.
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].
This is a method to produce formulas of various complexities with real coeffecients whose itereation indicate whether a given integer is prime or composite.
Prime visualizations (both visual and auditory), applets, message board, links.
A collection of interesting Cunningham chains plus how to find some with Yves Gallot's Proth.exe.
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
Join the search for an example of 6 titanic primes in arithmetic progression.
Tables for K=300 to 999.
Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
An article by Pascal Sebah with the results of computation of the twin primes up to 5.10^15.
The prime source for information about prime numbers!
Tony Forbes' extensive collection of special types of prime clusters.
Findings using an exhaustive search by Thomas J Engelsma.
Address by Professor Garrett Barden.
An organized search for primes of the form n!!!...!!!! +/-1. Includes table of numbers searched and primes found.
Explains this method of visually representing the distribution of primes and the relationships between factors and products.
Carlos Rivera's collection of problems and puzzles related to prime numbers.
A group with new propositions in various areas of number theory.
By Paul Zimmermann.
Records, statistics, and other interesting facts about palindromic primes compiled by Patrick De Geest.
Short lesson.
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.
A proof is offered by Martin Winer for the prime twin problem by defining randomness for a binary sequence.
This paper introduces the reader to the Rabin-Miller probabilistic primality test, the concept of non-witnesses to compositeness, and the problem of determining the number of non-witnesses to compositeness.
Investigation into patterns in the distribution of the primes by visualizing them.
The award wining Prime Glossary has over 150 pages of definitions and terms related to prime numbers and factoring.
Historical topics about prime numbers.
Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.
Description of prime k-tuples, the first Hardy-Littlewood conjecture and the Hardy-Littlewood constants.
Web article by Johan G. van der Galiën showing that the primes do not satisfy certain statistical tests for randomness.
Notes and links compiled by Mark Watkins on the relation of the Riemann zeta function to the distribution of prime numbers.
Methods and definitions of finding prime numbers.
E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal digits.
Research in number theory, prime numbers and parity of arithmetic functions. Includes primality testing theorems and prime number chains. In English and French.
Between $100,000 and $250,000 will go to the first individual or group who discovers a new prime number above 10 million digits.
An organized search for primes of the form n*b^n-1.
A coordinated project extending the list of Wieferich primes to 10^15.
Twin primes and Brun's number up to 10^14.
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Harper`s Numbers
January 22nd, 2006, 12:35 AM First of all, I will say that I am disgusted with this Liberal governm
January 22nd, 2006, 12:35 AM First of all, I will say that I am disgusted with this Liberal governm
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