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 Science > Math > Number Theory > Prime Numbers

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Science > Math > Number Theory > Prime Numbers

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/

Graand

Free Classified Ads Portal

www.graand.com

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 Numbers

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. (September 18, 2001)

http://www.ucc.ie/opa/conferspech/gbarden.html