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Prime Numbers
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This page is a collection of links related to prime numbers and factoring of very large numbers.
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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. The Prime Page Chris K. Caldwell's page on primes, especially large ones, with lots of links to related information and software. Links to...Tony Forbes' extensive collection of special types of prime clusters.
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Prime k-tuplets At this site we collect together all the largest known examples of certain types of dense clusters of prime numbers. The idea is to generalise the notion of prime twins pairs of prime numbers {p, p+2 to groups of three...Methods and definitions of finding prime numbers.
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prime This is the wonderful prime number page, the page where I show you how little I know in a subject where theres lots to know. Also, don't expect an orderly presentation, for any knowledge I have comes in small bundles,...Carlos Rivera's collection of problems and puzzles related to prime numbers.
http://www.primepuzzles.net/
Prime visualizations (both visual and auditory), applets, message board, links.
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Aesthetics of the Prime Sequence Primes and nucleotide basesGraphicsAutism and primesSoftwareRelated LinksCopyrights Contemporary Research Contact...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
Twin primes and Brun's number up to 10^14.
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Thomas R. Nicely's Home Page Table of all known first occurrence and maximal prime gaps Tables of first known occurrence prime gaps Instructions for submitting prime gaps Discovery of the P*ntium FDIV flaw P*ydirt and B*wl B*und Other works Tables of prime counts Tables of...Notes and links compiled by Mark Watkins on the relation of the Riemann zeta function to the distribution of prime numbers.
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Introductory prime number theory resources This excellent and thorough article is intended as a commentary to supplement the first half of a popular talk on the Riemann Hypothesis given by Peter Sarnak at a 1998 MSRI conference [a video recording is available here how the...Description of prime k-tuples, the first Hardy-Littlewood conjecture and the Hardy-Littlewood constants.
http://mathworld.wolfram.com/PrimeConstellation.html
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
Test numbers for primality and pseudoprimality in Java.
http://www.math.fau.edu/Richman/carm.htm
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
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
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
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/
With applets to demonstrate properties of primes.
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Notes and Literature on Prime Numbers A prime number is a natural number greater than 1 that can be divided evenly only by 1 and itself. Thus the first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 You can see...Lists of prime numbers to download in plain ASCII or MS-Excel format.
http://www.svobodat.com/primes/
Entropy of a nonnegative adjacency matrix related to prime numbers.
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Entropy and prime numbers I found during my work for graduation in Mathematics. I’d like to know your opinion about it, so you can send me an e-mail to carla@x-planet.net. You can also visit my new site: http www.x-planet.net Thank you anyway. An application...Contains a formula by Jones, Sato, Wada and Wiens. The set of primes is the set of positive values taken by this expression.
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Formulae for Primes The set of prime numbers is identical with the set of positive values of as the variables range over the nonnegative integers. This seems superficially implausible because the expression is a product: the (k 2) term at the start is...All of the prime numbers less than 2000000000.
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Print Prime Numbers This page is sponsored by http www.A-Wee-Bit-of-Ireland.com/ Your source in the USA for the finest Irish wool sweaters, celtic ruanas, capes, scarves and hats. Here is fun story about a curious sheep A sieve was used to generate a list...Includes biographies on many mathematicians.
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Prime numbers Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians. The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality...By Paul Zimmermann.
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See also the excellent page of Chris Caldwell. The largest known prime is 225964951-1 (7816230 digits found by Nowak, Woltman, Kurowski, et al. from GIMPS on February 18, 2003. The largest known ordinary prime is 44052638+26384405 (15071 decimal digits proved...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/
A group with new propositions in various areas of number theory.
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Benford sets had been added on 26 may 2000 A new Theorem on Zeta functions had been added on 22 sept. 2000 A new Law on (first digit distributions) had been added on 17 oct. 2002 New number theoretical identities...Factorization and weights of Proth coefficients.
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Brennen.Net Number Theory Prime Links All applets require a browser that supports version 1.1 of the Java AWT. If your browser fails to execute an applet, make sure you're running the latest version of the browser before reporting a bug Curious primes of the form...Examples of mostly digit patterns collected by Harvey Heinz.
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Prime Patterns This palindromic prime number reads the same upside down or when viewed in a mirror. CONTENTS Primes From Factorials PRIME is Prime Sum of 5 7 Primes More Prime series Near Repdigit Primes Smallest Largest Primes 5 71 Fortunate Primes...Investigation into patterns in the distribution of the primes by visualizing them.
http://yoyo.cc.monash.edu.au/~bunyip/primes/
Software, results and other resources.
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Generalized Fermat Primes Search Mersenne studied two particular forms of numbers, thinking that they could produce a large amount of prime numbers or even to be ever prime. Mersenne communicated a list of the primes of the form 2n-1, for all n 257. It...Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number information.
http://www.hypography.com/topics/searchingforprimes.cfm
Archived questions and answers at different levels.
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Math Forum: Ask Dr. Math FAQ: Prime Numbers How can you find prime numbers? What's the Sieve of Eratosthenes What's the largest known prime? A prime number is a positive integer that has exactly two positive integer factors, 1 and itself. For example, if we list the factors...Records, statistics, curios and puzzles about primes reading the same backwards. Compiled by Patrick De Geest.
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World of Palindromic Primes Primes are primes that read the same left to right (forwards) as from the right to left (backwards) Here are a few random examples 3, 131, 71317, 134757431 This study exposes some statistics concerning palindromic primes. For every length it...An article by Pascal Sebah with the results of computation of the twin primes up to 5.10^15.
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Introduction to twin primes and Brun's constant computation Introduction to twin primes and Brun's constant computation (Click here for a Postscript version of this page and here for a pdf version) 1Introduction It's a very old fact (Euclid 325-265 B.C in Book IX of the Elements) that the...Record list for twin and Sophie Germaine primes.
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World records in computational number theory World records in computational number theory Our joint work with Prof. Dr. Karl-Heinz Indlekofer in this field started in 1992. I worked in his research group from 1992 until 1997 as a project manager. During this period I designed most...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.
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This page gives 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 A coordinated search for primes of the form n!+1 can be found at Nuuti Kuosa's page www.hut.fi/~nkuosa/primeform/...An organized search for primes of the form n*b^n-1.
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Generalized Woodall Numbers Woodall number is a number of the form A Woodall prime is any prime number of the same form. This notion can be generalized to numbers of the form where The following is a list of generalized Woodall primes. Initially...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/
Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.
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Mathematical Constants My website is smaller than it once was. Please visit again, however, since new materials will continue to appear occasionally My book Mathematical Constants is now available for online purchase from Cambridge University Press (in the United Kingdom and in...Notes on primality tests by Anuj Seth.
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Data Encryption Page www.anujseth.com] ...Searchable database of these numbers. Lists largest primes by type and who discovered them.
http://www.utm.edu/research/primes/largest.html
Web article by Johan G. van der Galiën showing that the primes do not satisfy certain statistical tests for randomness.
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prime numbers The article below is about the question: Is the distribution of the prime numbers randomly? Applied mathematics in a PASCAL program clearly gives the answer: NO, the distribution of the prime numbers is not random! This might have consequences for...The discovery of nine and finally ten consecutive primes in arithmetic progression.
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The Search for Nine and Ten Consecutive Primes in Arithmetic Progression The amazing story of the discovery of nine and finally ten consecutive primes in arithmetic progression) Background Search for nine consecutive primes in arithmetic progression Progress The Result The official announcement on the NMBRTHRY-Server, 1998 January 24 To see the...Tables for K=300 to 999.
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Primes of the form K 2N -1 for K=301 to 399 Therefore the partial list of primes for N Nx+1, Nx+2 may or may not be complete up to the highest prime known. Many people have contributed to the creation of this collection of data. Too many in fact to list...Visualization of prime numbers resembling an astronomical radiant or celestial pathway.
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Radiant Prime Each prime number is converted to every base up to itself minus 1. Reversed, some numbers will form another prime number. The marks indicate where another prime exists. The primes on the left start at 2 and continue down the...A coordinated project extending the list of Wieferich primes to 10^15.
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We have surpassed our goal of reaching 1015 (we got to 1.25 1015 but no new Wieferich primes were found. The status page is still up with final results, but the information is static. Thanks to everyone who helped in...The top 10 k consecutive primes in arithmetic progression for each k.
http://hjem.get2net.dk/jka/math/cpap.htm
Short lesson.
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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. Definitions are...E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal digits.
http://www.lix.polytechnique.fr/...orain/Primes/MC7331.english.html
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
An interactive animation of the sieve of Eratosthenes to obtain prime numbers (JavaScript required).
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Eratosthenes Prime Number Sieve with JavaScript Click on any number and all its proper multiples will be removed from the table. Prime Number Sieve: Repeat the action Remove all proper multiples of the next remaining number Start with the number 2. When all proper multiples of...Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
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Prime number You can browse all small prime numbers(small than 10,000,000,000) here. There's totally 455042511 prime numbers. Input a number to check is it a prime number or not Browse the prime numbers from this number to upper. You can also send...Findings using an exhaustive search by Thomas J Engelsma.
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K-Tuple Permissible Patterns Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have no reason to believe that it is a mystery into which the mind will ever penetrate. LeonardEuler A mathematician...Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.
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The Prime Machine The applet on this page lets you explore the set of prime numbers. You do need a Java compatible browser. However, your browser does not support Java. If it did you would not see this message! Get a java compatible...A musical piece translating prime factorizations to frequencies. Requires RealPlayer.
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priemmuziek This is a musical piece that is counting from 1 to infinity. It steps from one to the next number. From the number thats up, the factors are calculated. They are translated in Herz and send to the soundcard. When...Explains this method of visually representing the distribution of primes and the relationships between factors and products.
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NumberSpiral.com Home Page Number spirals are very simple. To make one, we just write the non-negative integers on a ribbon and roll it up with zero at the center. The trick is to arrange the spiral so all the perfect squares (1, 4,...The largest known prime gaps measured by absolute or relative size, or a combination.
http://hjem.get2net.dk/jka/math/primegaps/gaps20.htm
Graduation address by former professor of philosophy Garrett Barden. Mentions primes as sign of human curiosity.
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ref grad.doc Jarrell describes the graduation address at a girls’ college in New England. Here is part of the account Mr Daudier spoke for for years, we felt Gertrude had heard him give the speech before so had I; Gottfried never had;...Sequences of nearly doubled primes, maintained by Dirk Augustin.
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Cunningham Chain records Record list created and maintained by Dirk Augustin. Hosted by Jens Kruse Andersen (home) Part 1, longest CC's Part 2, smallest existing CC's of given length Part 3, largest known CC's of given length Part 4, record history Part 5,...A compilation of links related to prime numbers including primality tests, lists of prime numbers, factoring, Mersenne numbers and the Goldbach conjecture.
http://cochise.mta.ac.il:8080/~liorb/servlet/Categories
Maintained bt the Electronic Frontier Foundation.
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Prime Number Resources and Information Hundreds of thousands of primes (a growing list) How many primes are there? Frequently Asked Questions about Primes How to prove that a large number is prime Finding prime numbers an introduction The quick tests The classical tests General purpose...A repository maintained by Warut Roonguthai. One project is a search for six titanic primes in arithmetic progression.
http://ksc9.th.com/warut/ap/
Introductory text on the theory of prime numbers. Contains proofs of some important theorems including the fundamental theorem of arithmetic.
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Minimal polynomials and conjugates) endobj 54 0 obj endobj 56 0 obj (Algebraic number fields) endobj 58 0 obj endobj 60 0 obj (Algebraic integers) endobj 62 0 obj endobj 64 0 obj (Units) endobj 66 0 obj endobj 68...Prime constellation records. Arithmetic progressions, simultaneous primes, prime gaps.
http://hjem.get2net.dk/jka
A proof is offered by Martin Winer for the prime twin problem by defining randomness for a binary sequence.
http://www.rankyouragent.com/primes/primes.htm
A collection of interesting Cunningham chains plus how to find some with Yves Gallot's Proth.exe.
http://ksc9.th.com/warut/cunningham/
An organized search for primes of the form (n)(n-k)(n-2k)...+/-1. Includes table of numbers searched and primes found.
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Status of Search for Multifactorial Primes ...A compilation of records and resources by Jens Kruse Andersen.
http://hjem.get2net.dk/jka/math/myrecords.htm
Includes twin prime counts, tables of first occurrence prime gaps, papers.
http://www.trnicely.net
Index to hundreds of prime-related articles in Eric Weisstein's MathWorld.
http://mathworld.wolfram.com/topics/PrimeNumbers.html
Index to many prime-related articles.
http://en.wikipedia.org/wiki/Category:Prime_numbers
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
Site includes known primes k*2^n-1 for k=301 to 999.
http://www.geocities.com/primes_r_us
Information by Joe McLean. Includes fundamentals, frequency, primality proofs and special types. Many definitions and theorems.
http://www.glasgowg43.freeserve.co.uk/primefaq.htm