Prime Numbers

Animation of Eratosthenes' Prime Sieve
An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript required).
http://www.hbmeyer.de/eratosiv.htm

Applets for Prime Numbers
Factorization and weights of Proth coefficients.
http://www.brennen.net/primes/

Are the Prime Numbers Randomly Distributed?
Web article by Johan G. van der Galiën. Shows that smaller starting digits are more common for primes below 10^9.
http://www.home.zonnet.nl/galien8/prime/prime.html

Ask Dr. Math FAQ: Prime Numbers
Archived questions and answers at different levels.
http://mathforum.org/dr.math/faq/faq.prime.num.html

Bertrand's Postulate
International Mathematics Olympiad tutorial proving there is always a prime between n and 2n. [PDF]
http://www.lacim.uqam.ca:16080/~plouffe/OEIS/archive_in_pdf/Bertrand.pdf

Cunningham Chain Records
Sequences of nearly doubled primes, maintained by Dirk Augustin.
http://hjem.get2net.dk/jka/math/Cunningham_Chain_records.htm

Electronic Frontier Foundation: Cooperative Computing Awards
Offers $100000, $150000 and $250000 for the first discovery of a prime above 10, 100 and 1000 million digits.
http://www.eff.org/awards/coop.php

Entropy and Prime Numbers
Entropy of a nonnegative adjacency matrix related to prime numbers.
http://web.tiscali.it/GEB/sfteng.htm

The First 5,800,000 Prime Numbers
Site includes known primes k*2^n-1 for k=301 to 999.
http://www.geocities.com/primes_r_us/

Formulae for Primes
Includes a formula by Jones, Sato, Wada and Wiens. The set of primes is the set of positive values taken by this expression.
http://www.bath.ac.uk/~ensab/Primes/

Generalized Fermat Prime Search
Software, results and other resources.
http://pagesperso-orange.fr/yves.gallot/primes/gfn.html

Generalized Woodall Numbers
An organized search for primes of the form n*b^n-1.
http://science.kennesaw.edu/~jdemaio/generali.htm

Hardy-Littlewood Constants
Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.
http://pauillac.inria.fr/algo/bsolve/constant/hrdyltl/hrdyltl.html

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.
http://ourworld.compuserve.com/homepages/hlifchitz/

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.
http://numbers.computation.free.fr/Constants/Primes/twin.html

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.
http://www.secamlocal.ex.ac.uk/~mwatkins/zeta/tutorial.htm

Jens Kruse Andersen
Prime constellation records. Arithmetic progressions, simultaneous primes, prime gaps.
http://hjem.get2net.dk/jka

K-Tuple Permissible Patterns
Findings using an exhaustive search by Thomas J Engelsma.
http://www.opertech.com/primes/k-tuples.html

MacTutor History of Mathematics: Prime Numbers
Includes biographies on many mathematicians.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html

MathWorld: Prime Numbers
Index to hundreds of prime-related articles in Eric Weisstein's MathWorld.
http://mathworld.wolfram.com/topics/PrimeNumbers.html

The Nine and Ten Primes Project
The discovery of nine and finally ten consecutive primes in arithmetic progression.
http://members.aon.at/toplicm/cp09.html

Notes and Literature on Prime Numbers
With applets to demonstrate properties of primes.
http://www.math.utah.edu/~alfeld/math/prime.html

Number Spiral
Explains this method of visually representing the distribution of primes and the relationships between factors and products.
http://www.numberspiral.com/

On-Line Encyclopedia of Integer Sequences (OEIS): Primes
Index to information about many integer sequences involving primes. Site includes numerous other prime-related sequences.
http://www.research.att.com/~njas/sequences/Sindx_Pri.html

Patterns in Primes
Examples of mostly digit patterns collected by Harvey Heinz.
http://www.geocities.com/~harveyh/primes.htm

Primality
Introductory text on the theory of prime numbers and number fields. Contains proofs of some important theorems including the fundamental theorem of arithmetic. [PDF]
http://www.maths.tcd.ie/pub/coursework/374/Primality.pdf

Primality Testing with Fermat's Little Theorem
Test numbers for primality and pseudoprimality in Java.
http://www.math.fau.edu/Richman/carm.htm

Prime k-tuplets
Tony Forbes' extensive collection of special types of prime clusters.
http://anthony.d.forbes.googlepages.com/ktuplets.htm

The Prime Machine
Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.
http://www.math.utah.edu/~alfeld/math/machine.html

Prime Music
A musical piece translating prime factorizations to frequencies. Requires RealPlayer.
http://www.xs4all.nl/~limonade/limonades/priem/primemusic.html

Prime Numbers
Short lesson.
http://odin.mdacc.tmc.edu/~krc/numbers/prime.html

Prime Numbers and Factoring
Links and references related to primes and factoring.
http://www.ontko.com/~rayo/primes/index.html

Prime Numbers List
Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
http://www.prime-numbers.org

The Prime Page
Methods and definitions of finding prime numbers.
http://www.fortunecity.com/meltingpot/manchaca/799/prime.html

Some Prime Numbers
Sieves and factoring for small numbers. Download primes below 8 billion.
http://www.rsok.com/~jrm/printprimes.html

Status of Search for Multifactorial Primes
An organized search for primes of the form (n)(n-k)(n-2k)...+/-1. Includes table of numbers searched and primes found.
http://www.geocities.com/kradenken/mfprimes.html

Thomas R. Nicely
Includes twin prime counts, tables of first occurrence prime gaps, papers.
http://www.trnicely.net

The Time Traveler
A group with new propositions in various areas of number theory.
http://www.geocities.com/timeparadox/

Visualizing the Distribution of Prime Numbers
Investigation into patterns in the distribution of the primes by visualizing them.
http://yoyo.cc.monash.edu.au/~bunyip/primes/

Wikipedia: Prime Numbers
Index to many prime-related articles.
http://en.wikipedia.org/wiki/Category:Prime_numbers

World of Numbers: World of Palindromic Primes
Records, statistics, curios and puzzles about primes reading the same backwards. Compiled by Patrick De Geest.
http://www.worldofnumbers.com/palpri.htm

Bipeds and Prime Numbers
Graduation address by former professor of philosophy Garrett Barden. Mentions primes as sign of human curiosity. <small>(September 18, 2001)</small>
http://www.ucc.ie/opa/conferspech/gbarden.html