Prime Numbers (Number Theory)

Prime Numbers further on these related pages:

Goldbach Conjecture@ Mersenne Primality Tests

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Prime Numbers Sites:

Number Spiral Number Spiral: Explains this method of visually representing the distribution of primes and the relationships between factors and products. (Prime Numbers) http://www.numberspiral.com/ Prime Numbers List Prime Numbers List: Browse all prime numbers of less than 10 digits. A prime number checker facility is also included. (Prime Numbers) http://www.prime-numbers.org Elliptic Curve Primality Proving Algorithm 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. (Prime Numbers) http://www.utm.edu/research/primes/glossary/ECPP.html Formulae for Determining Primality or Compositeness 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. (Prime Numbers) http://www.mathematical.com/mathprimetest.html Hardy-Littlewood Constants Hardy-Littlewood Constants: Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant. (Prime Numbers) http://pauillac.inria.fr/algo/bsolve/constant/hrdyltl/hrdyltl.html Searching for Primes Searching for Primes: Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number information. (Prime Numbers) http://www.hypography.com/topics/searchingforprimes.cfm The Largest Known CPAP's The Largest Known CPAP's: The top 10 k consecutive primes in arithmetic progression for each k. (Prime Numbers) http://hjem.get2net.dk/jka/math/cpap.htm Basic Theorems Concerning Prime Numbers 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. (Prime Numbers) http://www.maths.tcd.ie/pub/coursework/374/Primality.pdf. The Time Traveler The Time Traveler: A group with new propositions in various areas of number theory. (Prime Numbers) http://www.geocities.com/timeparadox/ Generalized Woodall Numbers Generalized Woodall Numbers: An organized search for primes of the form n*b^n-1. (Prime Numbers) http://science.kennesaw.edu/~jdemaio/generali.htm Testing for Primality 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 divis (Prime Numbers) http://www-mitpress.mit.edu/sicp/chapter1/node17.html Random Small Primes Random Small Primes: A site which gives some random primes up to 300 digits and more , also gives related information on primes. (Prime Numbers) http://www.utm.edu/research/primes/lists/small/small.html The Prime Page (An Index of Information on Prime Numbers) The Prime Page (An Index of Information on Prime Numbers): The prime source for information about prime numbers! (Prime Numbers) http://www.utm.edu/research/primes/ Prime Number Generation Prime Number Generation: Notes on primality tests by Anuj Seth. (Prime Numbers) http://www.anujseth.com/crypto/ Primes of the Form K * 2^N -1 Primes of the Form K * 2^N -1: Tables for K=300 to 999. (Prime Numbers) http://www.geocities.com/primes_r_us/riesel/prime300.html Prime Music Prime Music: A musical pieve based on the sieve of Eratosthenes. Requires Realplayer. (Prime Numbers) http://www.xs4all.nl/~limonade/limonades/priem/primemusic.html Notes and Literature on Prime Numbers Notes and Literature on Prime Numbers: With applets to demonstrate properties of primes. (Prime Numbers) http://www.math.utah.edu/%7Ealfeld/math/prime.html Animation of Eratosthenes' Prime Sieve Animation of Eratosthenes' Prime Sieve: An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript required). (Prime Numbers) http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm Prime Number Records Prime Number Records: By Paul Zimmermann. (Prime Numbers) http://www.loria.fr/~zimmerma/records/primes.html Prime Numbers Directory Prime Numbers Directory: A compilation of links related to prime numbers including primality tests, lists of prime numbers, factoring, Mersenne numbers and the Goldbach conjecture. (Prime Numbers) http://cochise.mta.ac.il:8080/~liorb/servlet/Categories Prime Numbers History Prime Numbers History: Historical topics about prime numbers. (Prime Numbers) http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html The Prime Page The Prime Page: Methods and definitions of finding prime numbers. (Prime Numbers) http://www.fortunecity.com/meltingpot/manchaca/799/prime.html Visualizing the Distribution of Prime Numbers Visualizing the Distribution of Prime Numbers: Investigation into patterns in the distribution of the primes by visualizing them. (Prime Numbers) http://yoyo.cc.monash.edu.au/~bunyip/primes/ Ask Dr. Math 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? (Prime Numbers) http://mathforum.org/dr.math/faq/faq.prime.num.html Deficient Factorials 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. (Prime Numbers) http://www.denhulster.nl/primeform/deffac.html A List of Prime Numbers A List of Prime Numbers: All of the prime numbers less than 2000000000. (Prime Numbers) http://www.rsok.com/~jrm/printprimes.html World Records in Computational Number Theory World Records in Computational Number Theory: Record list for twin and Sophie Germaine primes. (Prime Numbers) http://compalg.inf.elte.hu/~ajarai/worldr.htm The Nine and Ten Primes Project The Nine and Ten Primes Project: The discovery of nine and finally ten consecutive primes in arithmetic progression. (Prime Numbers) http://members.aon.at/toplicm/cp09.html Prime Numbers and Factoring Prime Numbers and Factoring: This page is a collection of links related to prime numbers and factoring of very large numbers. (Prime Numbers) http://www.ontko.com/~rayo/primes/index.html K-Tuples K-Tuples: Findings using an exhaustive search by Thomas J Engelsma. (Prime Numbers) http://www.opertech.com/primes/k-tuples.html Primality Testing with Fermat's Little Theorem Primality Testing with Fermat's Little Theorem: Test numbers for primality and pseudoprimality in Java. (Prime Numbers) http://www.math.fau.edu/Richman/carm.htm Radiant Primes Radiant Primes: Visualization of prime numbers resembling an astronomical radiant or celestial pathway. (Prime Numbers) http://www.radiantprimes.com/ Aesthetics of the Prime Numbers Sequence Aesthetics of the Prime Numbers Sequence: Prime visualizations (both visual and auditory), applets, message board, links. (Prime Numbers) http://www.2357.a-tu.net/ Introduction to Twin Primes and Brun's Constant 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. (Prime Numbers) http://numbers.computation.free.fr/Constants/Primes/twin.html Wieferich Primes Wieferich Primes: Miscellaneous notes and graphics about Wieferich primes by Joe Crump. (Prime Numbers) http://www.spacefire.com/numbertheory/Wieferich.htm Henri Lifchitz 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. (Prime Numbers) http://ourworld.compuserve.com/homepages/hlifchitz/ The Top-20 Prime Gaps The Top-20 Prime Gaps: The largest known prime gaps measured by absolute or relative size, or a combination. (Prime Numbers) http://hjem.get2net.dk/jka/math/primegaps/gaps20.htm Distribution of the Prime Numbers 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. (Prime Numbers) http://www.home.zonnet.nl/galien8/prime/prime.html Tables of Prime Numbers Tables of Prime Numbers: Lists of prime numbers to download in plain ASCII or MS-Excel format. (Prime Numbers) http://www.svobodat.com/primes/ Largest Known Primes Largest Known Primes: Searchable database of these numbers. Lists largest primes by type and who discovered them. (Prime Numbers) http://www.utm.edu/research/primes/largest.html The Prime Glossary The Prime Glossary: The award wining Prime Glossary has over 150 pages of definitions and terms related to prime numbers and factoring. (Prime Numbers) http://www.utm.edu/research/primes/glossary/ World of Palindromic Primes World of Palindromic Primes: Records, statistics, and other interesting facts about palindromic primes compiled by Patrick De Geest. (Prime Numbers) http://www.worldofnumbers.com/palpri.htm Some Results on the Number of Non-Witnesses to Compositeness 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. (Prime Numbers) http://www.geocities.com/SiliconValley/Network/2811/primes/higgins.htm Patterns in Primes Patterns in Primes: Examples of digital patterns in prime numbers collected by Harvey Heinz. (Prime Numbers) http://www.geocities.com/~harveyh/primes.htm The New Book of Prime Number Records, Additions and Errata 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. (Prime Numbers) http://www.utm.edu/research/primes/notes/errata/ The Prime Machine The Prime Machine: Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem. (Prime Numbers) http://www.math.utah.edu/~alfeld/math/machine.html Dr. Nicely's Home Page Dr. Nicely's Home Page: Twin primes and Brun's number up to 10^14. (Prime Numbers) http://www.trnicely.net/index.html Bipeds and Prime Numbers Bipeds and Prime Numbers: Address by Professor Garrett Barden. (Prime Numbers) http://www.ucc.ie/opa/conferspech/gbarden.html Twin Primes Twin Primes: A computation of the number up to 10^14, by Jörg Richstein. (Prime Numbers) http://www.informatik.uni-giessen.de/staff/richstein/res/tp-en.html Entropy and Prime Numbers Entropy and Prime Numbers: Entropy of a nonnegative adjacency matrix related to prime numbers. (Prime Numbers) http://web.tiscali.it/GEB/sfteng.htm Applets for Prime Numbers Applets for Prime Numbers: Factorization and weights of Proth coefficients. (Prime Numbers) http://www.brennen.net/primes/ The Distribution of the Primes 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. (Prime Numbers) http://www.srcf.ucam.org/~dmo25/Primes Proof of Bertrand's Postulate 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. (Prime Numbers) http://matholymp.com/TUTORIALS/Bertrand.pdf Wieferich Prime Number Search Wieferich Prime Number Search: A coordinated project extending the list of Wieferich primes to 10^15. (Prime Numbers) http://torch.cs.dal.ca/~knauer/wieferich/ Pseudoprimes/Probable Primes Pseudoprimes/Probable Primes: Recent developments in primality testing. Here are slides of Jon Grantham's talk on this subject. (Prime Numbers) http://www.pseudoprime.com/pseudo.html Introductory Prime Number Theory Resources 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. (Prime Numbers) http://www.maths.ex.ac.uk/~mwatkins/zeta/tutorial.htm New Primality Record New Primality Record: E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal digits. (Prime Numbers) http://www.lix.polytechnique.fr/~morain/Primes/MC7331.english.html The Prime Puzzles & Problems Connection The Prime Puzzles & Problems Connection: Carlos Rivera's collection of problems and puzzles related to prime numbers. (Prime Numbers) http://www.primepuzzles.net/ The Nth Prime Page 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). (Prime Numbers) http://www.math.Princeton.EDU/~arbooker/nthprime.html Yves Gallot's Proth.exe and Cunningham Chains 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. (Prime Numbers) http://ksc9.th.com/warut/cunningham/ PRIMES is in P. 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]. (Prime Numbers) http://www.cse.iitk.ac.in/users/manindra/ Large Primes in Arithmetic Progression Large Primes in Arithmetic Progression: Join the search for an example of 6 titanic primes in arithmetic progression. (Prime Numbers) http://ksc9.th.com/warut/ap/ Prime Number Resources and Information Prime Number Resources and Information: prime number basics (Prime Numbers) http://www.eff.org/coop-awards/prime-info.html Prime k-tuplets Prime k-tuplets: Tony Forbes' extensive collection of special types of prime clusters. (Prime Numbers) http://www.ltkz.demon.co.uk/ktuplets.htm Randomness and Prime Twin Proof Randomness and Prime Twin Proof: A proof is offered by Martin Winer for the prime twin problem by defining randomness for a binary sequence. (Prime Numbers) http://members.rogers.com/mwiner/primes.htm Prime Constellations Prime Constellations: Description of prime k-tuples, the first Hardy-Littlewood conjecture and the Hardy-Littlewood constants. (Prime Numbers) http://mathworld.wolfram.com/PrimeConstellation.html Cunningham Chain Records Cunningham Chain Records: Sequences of nearly doubled primes, maintained by Dirk Augustin. (Prime Numbers) http://hjem.get2net.dk/jka/math/Cunningham_Chain_records.htm Generalized Fermat Prime Search Generalized Fermat Prime Search: Software, results and other resources. (Prime Numbers) http://perso.wanadoo.fr/yves.gallot/primes/gfn.html Multifactorial Primes Multifactorial Primes: An organized search for primes of the form n!!!...!!!! +/-1. Includes table of numbers searched and primes found. (Prime Numbers) http://www.geocities.com/kraden/mfprimes.html EFF Cooperative Computing Awards 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. (Prime Numbers) http://www.eff.org/awards/coop.html Prime Numbers Prime Numbers: Short lesson. (Prime Numbers) http://odin.mdacc.tmc.edu/~krc/numbers/prime.html Formulae for Primes Formulae for Primes: GIF images of a paper by A. Venugopalan in Proc. Indian Acad. Sci. (1983). (Prime Numbers) http://www.geocities.com/Paris/Arc/5654/formulaforprimes.html