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Prime Numbers
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Goldbach Conjecture (12)
Mersenne (9)
Primality Proving Software (9)
Primality Tests (24)
Web Pages
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  The Prime Pages http://primes.utm.edu/
Prime number research, records and resources. Includes largest known primes, finding and proving primes, glossary, curios, links.
  Electronic Frontier Foundation: Cooperative Computing Awards http://www.eff.org/awards/coop.php
Offers $100000, $150000 and $250000 for the first discovery of a prime above 10, 100 and 1000 million digits.
  MathWorld: Prime Numbers http://mathworld.wolfram.com/topics/PrimeNumbers.html
Index to hundreds of prime-related articles in Eric Weisstein's MathWorld.
  Hardy-Littlewood Constants http://pauillac.inria.fr/algo/bsolve/constant/hrdyltl/hrdyltl.html
Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.
  Visualizing the Distribution of Prime Numbers http://yoyo.cc.monash.edu.au/~bunyip/primes/
Investigation into patterns in the distribution of the primes by visualizing them.
  Ask Dr. Math FAQ: Prime Numbers http://mathforum.org/dr.math/faq/faq.prime.num.html
Archived questions and answers at different levels.
  Wikipedia: Prime Numbers http://en.wikipedia.org/wiki/Category:Prime_numbers
Index to many prime-related articles.
  The Prime Puzzles & Problems Connection http://www.primepuzzles.net/
Carlos Rivera's collection of problems and puzzles related to prime numbers.
  Thomas R. Nicely http://www.trnicely.net
Includes twin prime counts, tables of first occurrence prime gaps, papers.
  Generalized Fermat Prime Search http://pagesperso-orange.fr/yves.gallot/primes/gfn.html
Software, results and other resources.
  Animation of Eratosthenes' Prime Sieve http://www.hbmeyer.de/eratosiv.htm
An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript required).
  On-Line Encyclopedia of Integer Sequences (OEIS): Primes http://www.research.att.com/~njas/sequences/Sindx_Pri.html
Index to information about many integer sequences involving primes. Site includes numerous other prime-related sequences.
  Number Spiral http://www.numberspiral.com/
Explains this method of visually representing the distribution of primes and the relationships between factors and products.
  K-Tuple Permissible Patterns http://www.opertech.com/primes/k-tuples.html
Findings using an exhaustive search by Thomas J Engelsma.
  Introduction to Twin Primes and Brun's Constant http://numbers.computation.free.fr/Constants/Primes/twin.html
An article by Pascal Sebah with the results of computation of the twin primes up to 5.10^15.
  Prime Numbers Generator and Checker http://www.numberempire.com/primenumbers.php
Enter a natural number, check it and find the nearest prime.
  Natural Numbers http://www.naturalnumbers.org
Provides a collection of tools and interesting pages for testing, visualizing, and understanding natural numbers.
  Cunningham Chain Records http://users.cybercity.dk/~dsl522332/math/Cunningham_Chain_records.htm
Sequences of nearly doubled primes, maintained by Dirk Augustin.
  Generalized Woodall Numbers http://science.kennesaw.edu/~jdemaio/generali.htm
An organized search for primes of the form n*b^n-1.
  Some Prime Numbers http://www.rsok.com/~jrm/printprimes.html
Sieves and factoring for small numbers. Download primes below 8 billion.
  Prime Numbers and Factoring http://www.ontko.com/~rayo/primes/index.html
Links and references related to primes and factoring.
  Prime Numbers List http://www.prime-numbers.org
Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
  Jens Kruse Andersen http://users.cybercity.dk/~dsl522332/
Prime constellation records. Arithmetic progressions, simultaneous primes, prime gaps.
  Bipeds and Prime Numbers http://www.ucc.ie/opa/conferspech/gbarden.html
Graduation address by former professor of philosophy Garrett Barden. Mentions primes as sign of human curiosity.
  Primality Testing with Fermat's Little Theorem http://www.math.fau.edu/Richman/carm.htm
Test numbers for primality and pseudoprimality in Java.
  Prime Numbers http://odin.mdacc.tmc.edu/~krc/numbers/prime.html
Short lesson.
  Introductory Prime Number Theory Resources http://www.secamlocal.ex.ac.uk/~mwatkins/zeta/tutorial.htm
Notes and links compiled by Mark Watkins on the relation of the Riemann zeta function to the distribution of prime numbers.
  The Prime Page http://www.fortunecity.com/meltingpot/manchaca/799/prime.html
Methods and definitions of finding prime numbers.
  Applets for Prime Numbers http://www.brennen.net/primes/
Factorization and weights of Proth coefficients.
  Primality http://www.maths.tcd.ie/pub/coursework/374/Primality.pdf
Introductory text on the theory of prime numbers and number fields. Contains proofs of some important theorems including the fundamental theorem of arithmetic.
  Gebhard Glöggler http://www.g-gloeggler.de
Makes a statement about the number of primes between the squares of odd numbers, and provides a proof of Goldbach's conjecture.
  World of Numbers: World of Palindromic Primes http://www.worldofnumbers.com/palpri.htm
Records, statistics, curios and puzzles about primes reading the same backwards. Compiled by Patrick De Geest.
  Are the Prime Numbers Randomly Distributed? http://www.members.tele2.nl/galien8/prime/prime.html
Web article by Johan G. van der Galiën. Shows that smaller starting digits are more common for primes below 10^9.
  Entropy and Prime Numbers http://web.tiscali.it/GEB/sfteng.htm
Entropy of a nonnegative adjacency matrix related to prime numbers.
  Bertrand's Postulate http://www.lacim.uqam.ca:16080/~plouffe/OEIS/archive_in_pdf/Bertrand.pdf
International Mathematics Olympiad tutorial proving there is always a prime between n and 2n.
  Notes and Literature on Prime Numbers http://www.math.utah.edu/~alfeld/math/prime.html
With applets to demonstrate properties of primes.
  Prime k-tuplets http://anthony.d.forbes.googlepages.com/ktuplets.htm
Tony Forbes' extensive collection of special types of prime clusters.
  Formulae for Primes http://www.bath.ac.uk/~ensab/Primes/
Includes a formula by Jones, Sato, Wada and Wiens. The set of primes is the set of positive values taken by this expression.
  MacTutor History of Mathematics: Prime Numbers http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html
Includes biographies on many mathematicians.
  The Prime Machine http://www.math.utah.edu/~alfeld/math/machine.html
Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.
  The Nine and Ten Primes Project http://members.aon.at/toplicm/cp09.html
The discovery of nine and finally ten consecutive primes in arithmetic progression.

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