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

The Largest Known Primes - An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself. For example, the prime divisors of 10 are 2 and 5; and the first six primes are 2, 3, 5, 7,11 and 13.

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.

Prime Numbers - Largest known Mersenne primes

Problems of the Millenium: The Riemann Hypothesis - Description of the Riemann hypothesis by Enrico Bombieri discussing the problems history and significance, and the evidence to support the hypothesis.

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.

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

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.

Publications of famous François Morain on Primality. - A web page describing the various publications of F. Morain

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

It's About Prime - Capable of factoring numbers as large as 2^64 - 1 with the standard Macintosh Interface using custom routines.

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 Distribution of the Primes and the Underlying Order to Chaos - Summary of research into second Hardy-Littlewood conjecture by Esat Young Scientist of the Year 2002 David Michael O'Doherty.

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.

Detecting False Reports In Primality Tests By The Oddcomp(z) Method - Public-key algorithms need plenty of prime numbers. There are more primes than the number of atoms in the universe. All standing trees on planet Earth will not be sufficient to produce paper pulp to publish all the 512-bit primes in bound volumes. How do we detect false reports by probabilistic primality tests?

Timing Tests on Three Primality Test Formulations. - Y.K.Huen. It is well known that whilst primality algorithms are extremely efficient when compared to brute force trial divisions, they yield probabilistic results meaning that there is a remote chance that one could find a counterexample.

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

Brief Findings From Primality Tests On (2^i+1) Family Of Sequences - The number theoretic properties of the i^j+1 type of number sequences are investigated within the computing capabilities of a Pentium Pro PC. This paper reports briefly on some of the findings.

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

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 5000 largest known primes! - This is the official page for the searchable database of the 5000 largest known primes--updated weekly! Do you want to know the largest prime, Mersenne, twin, Sophie Germain...? We start with the definition of prime and list many records.

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.

Perrin Numbers - Perrin pseudoprimes with lists and Perrin number calculator.

Pseudoprimes Based On Symmetric Functions - Basic propositions and computational techniques.

Mika Kojo - Tables and programs, especially suggested IKE primes.

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 fexpression.

k-tuple Checker and Extender - Javascript program that checks for admissible prime k-tuples.

Prime Numbers - Mathematicians have a special fondness for definitions. The objects they study often have no physical presence: you can't touch them, weigh them, or smell them. So, precise definitions are used to provide a solid underpinning to their subject.

Prime Number Resources and Information - prime number basics

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

Prime Number Spiral - Windows software exploring the prime number spiral. Online ordering.

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

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.

A Monte-Carlo Primality Tester - The factoring problem seems very hard. But to test a number for having factors turns out to be much easier than to find them. It also helps if we supply the computer with a coin-flipping device. We now consider a Monte Carlo algorithm, i.e. one that with high probability rejects any composite number, but never a prime.

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.

Cryptography and Coding Theory with MAPLE page - Some coding theory and cryptography links (most of which use MAPLE).

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

Prime Numbers - Historical topics about prime numbers.

Twin Primes - Up to 10^14.

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

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.

Search of the Next Prime of the Form n!+1 - The purpose of this page is to coordinate effort to search for the next prime of the form n!+1. At the moment our purpose is to search the range between 23,000!+1 - 30,000!+1.

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.

Pulchritudinous Primes - Graphics and images related to prime numbers.

Generalized Fermat Prime Search - Software, results and other resources.

Prime Number Generation - Notes on primality tests by Anuj Seth.

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.