| Directory > Science > Math > Number Theory > Prime Numbers Number Spiral
Explains the number spiral, a method of visually representing the distribution of primes and the
relationships between factors and products.
http://www.numberspiral.com/
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Prime Music
A musical pieve based on the sieve of Eratosthenes. Requires Realplayer.
http://www.xs4all.nl/~limonade/limonades/priem/primemusic.html
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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
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K-Tuples
Findings using an exhaustive search by Thomas J Engelsma.
http://www.opertech.com/primes/k-tuples.html
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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
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Animation of Eratosthenes' Prime Sieve
An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript
required).
http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm
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The Distribution of the Primes
Project Report on research into the 2nd Hardy-Littlewood conjecture and the relationship between
the primes and chaotic systems by David O'Doherty. Includes program downloads.
http://www.srcf.ucam.org/~dmo25/Primes
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Prime Numbers Directory
A directory for prime numbers including primality tests, lists of prime numbers, factoring,
mersenne numbers and goldbach conjecture
http://cochise.mta.ac.il:8080/~liorb/servlet/Categories
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New Primality Record
E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal
digits.
http://www.lix.polytechnique.fr/~morain/Primes/MC7331.english.html
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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.
http://www.eff.org/awards/coop.html
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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.
http://odin.mdacc.tmc.edu/~krc/numbers/prime.html
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The Largest Known CPAP's
The top 10 k consecutive primes in arithmetic progression for each k.
http://hjem.get2net.dk/jka/math/cpap.htm
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Wieferich Prime Number Search
A coordinated project extending the list of Wieferich primes to 10^15.
http://torch.cs.dal.ca/~knauer/wieferich/
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Radiant Primes
Visualization of prime numbers resembling an astronomical radiant or celestial pathway.
http://www.radiantprimes.com/
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Multifactorial Primes
An organized search for primes of the form n!!!...!!!! +/-1. Includes table of numbers searched and
primes found.
http://www.geocities.com/kraden/mfprimes.html
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Primes of the Form K * 2^N -1
Tables for K=300 to 999.
http://www.geocities.com/primes_r_us/riesel/prime300.html
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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
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Twin Primes
A computation of the number up to 10^14, by Jörg Richstein.
http://www.informatik.uni-giessen.de/staff/richstein/res/tp-en.html
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Distribution of the Prime Numbers
Web article by Johan G. van der Galiën showing that the primes do not satisfy certain statistical
tests for randomness.
http://www.home.zonnet.nl/galien8/prime/prime.html
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Largest Known Primes
Searchable database of these numbers. Lists largest primes by type and who discovered them.
http://www.utm.edu/research/primes/largest.html
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PRIMES is in P.
A paper by Manindra Agrawal, Neeraj Kayal, Nitin Saxena that presents a polynomal-time algorithm
that determines whether an input number n is prime or composite [PS].
http://www.cse.iitk.ac.in/users/manindra/
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Prime Number Generation
Notes on primality tests by Anuj Seth.
http://www.anujseth.com/crypto/
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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
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Wieferich Primes
Miscellaneous notes and graphics about Wieferich primes by Joe Crump.
http://www.spacefire.com/numbertheory/Wieferich.htm
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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/
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Generalized Woodall Numbers
An organized search for primes of the form n*b^n-1.
http://science.kennesaw.edu/~jdemaio/generali.htm
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Deficient Factorials
A summary of all known searches for primes of the form n!/k+-1 (with k>1), n!/k!+-1 (k>3) and
n!/n#+-1.
http://www.denhulster.nl/primeform/deffac.html
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World Records in Computational Number Theory
Record list for twin and Sophie Germaine primes.
http://compalg.inf.elte.hu/~ajarai/worldr.htm
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Basic Theorems Concerning Prime Numbers
An introductory page on the theory of prime numbers with proofs of some important theorems
including the infinitude of primes, Euclid's algorithm and the fundamental theorem of arithmetic.
http://www.maths.tcd.ie/pub/coursework/374/Primality.pdf.
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Formulae for Primes
GIF images of a paper by A. Venugopalan in Proc. Indian Acad. Sci. (1983).
http://www.geocities.com/Paris/Arc/5654/formulaforprimes.html
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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
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World of Palindromic Primes
Records, statistics, and other interesting facts about palindromic primes compiled by Patrick De
Geest.
http://www.worldofnumbers.com/palpri.htm
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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?
http://mathforum.org/dr.math/faq/faq.prime.num.html
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Searching for Primes
Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number
information.
http://www.hypography.com/topics/searchingforprimes.cfm
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Generalized Fermat Prime Search
Software, results and other resources.
http://perso.wanadoo.fr/yves.gallot/primes/gfn.html
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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/
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Patterns in Primes
Examples of digital patterns in prime numbers collected by Harvey Heinz.
http://www.geocities.com/~harveyh/primes.htm
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Applets for Prime Numbers
Factorization and weights of Proth coefficients.
http://www.brennen.net/primes/
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The Time Traveler
A group with new propositions in various areas of number theory.
http://www.geocities.com/timeparadox/
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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.
http://www.hut.fi/~nkuosa/primeform/
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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.
http://www.utm.edu/research/primes/notes/errata/
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Prime Number Records
By Paul Zimmermann.
http://www.loria.fr/~zimmerma/records/primes.html
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Pseudoprimes/Probable Primes
Recent developments in primality testing. Here are slides of Jon Grantham's talk on this subject.
http://www.pseudoprime.com/pseudo.html
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Prime Numbers History
Historical topics about prime numbers.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html
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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.
http://ksc9.th.com/warut/cunningham/
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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.
http://www.cs.bu.edu/fac/lnd/toc/z/node21.html
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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.
http://www.geocities.com/SiliconValley/Network/2811/primes/higgins.htm
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Large Primes in Arithmetic Progression
Join the search for an example of 6 titanic primes in arithmetic progression.
http://ksc9.th.com/warut/ap/
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A List of Prime Numbers
All of the prime numbers less than 2000000000.
http://www.rsok.com/~jrm/printprimes.html
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Prime Number Resources and Information
prime number basics
http://www.eff.org/coop-awards/prime-info.html
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Formulae for Primes
The formula of 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/
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Entropy and Prime Numbers
Entropy of a nonnegative adjacency matrix related to prime numbers.
http://web.tiscali.it/GEB/sfteng.htm
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Pseudoprimes Based On Symmetric Functions
Basic propositions and computational techniques.
http://mathpages.com/symm/symmtoc.htm
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Tables of Prime Numbers
Lists of prime numbers to download in plain ASCII or MS-Excel format.
http://www.svobodat.com/primes/
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Notes and Literature on Prime Numbers
With applets to demonstrate properties of primes.
http://www.math.utah.edu/%7Ealfeld/math/prime.html
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The Prime Glossary
The award wining Prime Glossary has over 150 pages of definitions and terms related to prime
numbers and factoring.
http://www.utm.edu/research/primes/glossary/
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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.
http://www-mitpress.mit.edu/sicp/chapter1/node17.html
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Random Small Primes
A site which gives some random primes up to 300 digits and more , also gives related information
on primes.
http://www.utm.edu/research/primes/lists/small/small.html
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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.
http://www.utm.edu/research/primes/glossary/ECPP.html
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Primality Testing with Fermat's Little Theorem
Test numbers for primality and pseudoprimality in Java.
http://www.math.fau.edu/Richman/carm.htm
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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.
http://www.mathematical.com/mathprimetest.html
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Prime Constellations
Description of prime k-tuples, the first Hardy-Littlewood conjecture and the Hardy-Littlewood
constants.
http://mathworld.wolfram.com/PrimeConstellation.html
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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.maths.ex.ac.uk/~mwatkins/zeta/tutorial.htm
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Dr. Nicely's Home Page
Twin primes and Brun's number up to 10^14.
http://www.trnicely.net/index.html
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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.
http://matholymp.com/TUTORIALS/Bertrand.pdf
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Aesthetics of the Prime Numbers Sequence
Prime visualizations (both visual and auditory), applets, message board, links.
http://www.2357.a-tu.net/
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The Prime Puzzles & Problems Connection
Carlos Rivera's collection of problems and puzzles related to prime numbers.
http://www.primepuzzles.net/
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The Prime Page
Methods and definitions of finding prime numbers.
http://www.fortunecity.com/meltingpot/manchaca/799/prime.html
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Prime k-tuplets
Tony Forbes' extensive collection of special types of prime clusters.
http://www.ltkz.demon.co.uk/ktuplets.htm
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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).
http://www.math.Princeton.EDU/~arbooker/nthprime.html
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Prime Numbers and Factoring
This page is a collection of links related to prime numbers and factoring of very large numbers.
http://www.ontko.com/~rayo/primes/index.html
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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.
http://www.math.unicaen.fr/~reyssat/largest.html
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The Prime Page (An Index of Information on Prime Numbers)
The prime source for information about prime numbers!
http://www.utm.edu/research/primes/
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