The Prime Page (An Index of Information on Prime Numbers)
The prime source for information about prime numbers!

Prime Numbers and Factoring
This page is a collection of links related to prime numbers and factoring of very large numbers.

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 k-tuplets
Tony Forbes' extensive collection of special types of prime clusters.

The Prime Page
Methods and definitions of finding prime numbers.

The Prime Puzzles & Problems Connection
Carlos Rivera's collection of problems and puzzles related to prime numbers.

Aesthetics of the Prime Numbers Sequence
Prime visualizations (both visual and auditory), applets, message board, links.

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.

Dr. Nicely's Home Page
Twin primes and Brun's number up to 10^14.

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.

Prime Constellations
Description of prime k-tuples, the first Hardy-Littlewood conjecture and the Hardy-Littlewood constants.

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.

Primality Testing with Fermat's Little Theorem
Test numbers for primality and pseudoprimality in Java.

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.

Random Small Primes
A site which gives some random primes up to 300 digits and more , also gives related information on primes.

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 Prime Glossary
The award wining Prime Glossary has over 150 pages of definitions and terms related to prime numbers and factoring.

Notes and Literature on Prime Numbers
With applets to demonstrate properties of primes.

Tables of Prime Numbers
Lists of prime numbers to download in plain ASCII or MS-Excel format.

Entropy and Prime Numbers
Entropy of a nonnegative adjacency matrix related to prime numbers.

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 Number Resources and Information
prime number basics

A List of Prime Numbers
All of the prime numbers less than 2000000000.

Large Primes in Arithmetic Progression
Join the search for an example of 6 titanic primes in arithmetic progression.

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.

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.

Prime Numbers History
Historical topics about prime numbers.

Pseudoprimes/Probable Primes
Recent developments in primality testing. Here are slides of Jon Grantham's talk on this subject.

Prime Number Records
By Paul Zimmermann.

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

Applets for Prime Numbers
Factorization and weights of Proth coefficients.

Patterns in Primes
Examples of digital patterns in prime numbers collected by Harvey Heinz.

Visualizing the Distribution of Prime Numbers
Investigation into patterns in the distribution of the primes by visualizing them.

Generalized Fermat Prime Search
Software, results and other resources.

Searching for Primes
Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number information.

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?

World of Palindromic Primes
Records, statistics, and other interesting facts about palindromic primes compiled by Patrick De Geest.

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.

Formulae for Primes
GIF images of a paper by A. Venugopalan in Proc. Indian Acad. Sci. (1983).

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.

World Records in Computational Number Theory
Record list for twin and Sophie Germaine primes.

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.

Generalized Woodall Numbers
An organized search for primes of the form n*b^n-1.

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.

Wieferich Primes
Miscellaneous notes and graphics about Wieferich primes by Joe Crump.

Hardy-Littlewood Constants
Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.

Prime Number Generation
Notes on primality tests by Anuj Seth.

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].

Largest Known Primes
Searchable database of these numbers. Lists largest primes by type and who discovered them.

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.

Twin Primes
A computation of the number up to 10^14, by Jörg Richstein.

The Nine and Ten Primes Project
The discovery of nine and finally ten consecutive primes in arithmetic progression.

Primes of the Form K * 2^N -1
Tables for K=300 to 999.

Multifactorial Primes
An organized search for primes of the form n!!!...!!!! +/-1. Includes table of numbers searched and primes found.

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

Wieferich Prime Number Search
A coordinated project extending the list of Wieferich primes to 10^15.

The Largest Known CPAP's
The top 10 k consecutive primes in arithmetic progression for each k.

Prime Numbers
Short lesson.

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.

New Primality Record
E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal digits.

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.

Animation of Eratosthenes' Prime Sieve
An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript required).

Prime Numbers List
Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.

K-Tuples
Findings using an exhaustive search by Thomas J Engelsma.

The Prime Machine
Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.

Prime Music
A musical pieve based on the sieve of Eratosthenes. Requires Realplayer.

Number Spiral
Explains this method of visually representing the distribution of primes and the relationships between factors and products.

The Top-20 Prime Gaps
The largest known prime gaps measured by absolute or relative size, or a combination.

Bipeds and Prime Numbers
Address by Professor Garrett Barden.

Randomness and Prime Twin Proof
A proof is offered by Martin Winer for the prime twin problem by defining randomness for a binary sequence.

Cunningham Chain Records
Sequences of nearly doubled primes, maintained by Dirk Augustin.

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.