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Prime Numbers

Science > Math > Number Theory > Prime Numbers

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Goldbach Conjecture (12)
Mersenne (9)
Primality Proving Software (9)
Primality Tests (24)

Web Pages

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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).

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

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.

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

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.

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.

Cunningham Chain Records - http://users.cybercity.dk/~dsl522332/math/Cunningham_Chain_records.htm
Sequences of nearly doubled primes, maintained by Dirk Augustin.

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.

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

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.

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.

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

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

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.

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.

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.

Jens Kruse Andersen - http://users.cybercity.dk/~dsl522332/
Prime constellation records. Arithmetic progressions, simultaneous primes, prime gaps.

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

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

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

Natural Numbers - http://www.naturalnumbers.org
Provides a collection of tools and interesting pages for testing, visualizing, and understanding natural numbers.

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

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

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.

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.

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

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

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

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

Prime Numbers Generator and Checker - http://www.numberempire.com/primenumbers.php
Enter a natural number, check it and find the nearest prime.

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.

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

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.

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

The Prime Pages - http://primes.utm.edu/
Prime number research, records and resources. Includes largest known primes, finding and proving primes, glossary, curios, links.

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.

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.

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

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.

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