21. Twin Prime Conjecture The twin prime conjecture is a famous unsolved problem in number theory that Such a pair of prime numbers is called a twin prime. The conjecture has http://www.fact-index.com/t/tw/twin_prime_conjecture_1.html

Main Page See live article Alphabetical index Twin prime conjecture The twin prime conjecture is a famous unsolved problem in number theory that involves prime numbers . It states: There are an infinite number of primes p such that p + 2 is also prime. Such a pair of prime numbers is called a twin prime . The conjecture has been researched by many number theorists. The majority of mathematicians believe that the conjecture is true, based on numerical evidence and heuristic reasoning involving the probabilistic distribution of primes. In de Polignac made the more general conjecture that for every natural number k , there are infinitely many prime pairs which have a distance of 2 k . The case k =1 is the twin prime conjecture. Partial results In showed that there is a constant c < 1 and infinitely many primes p such that p p c ln p ), where p ' denotes the next prime after p . This result was successively improved; in Maier showed that a constant c < 0.25 can be used. In , Jing-run Chen showed that there are infinitely many primes p such that p +2 is a product of at most two prime factors. The approach he took involved a topic called Sieve theory, and he managed to treat the Twin Prime Conjecture and

22. Conjecture 3. Twin Prime's Conjecture This is the Twin prime Conjecture , which can be paraphrased this way There are infinite consecutive primes differing by 2 . http://www.primepuzzles.net/conjectures/conj_003.htm

Conjectures Conjecture 3. Twin Prime's Conjecture If we define d n as : d n = p n+1 - p n , is easy to see that d =1 and d n Now, that " for n>1, dn=2 infinitely often" (Ref. 2, p. 19). This is the "Twin prime Conjecture", which can be paraphrased this way : "There are infinite consecutive primes differing by 2". SOLUTION Mr Liu Fengsui has sent (3/9/01) an argument that proves - according to him - the well known and named " k-tuple conjecture " This conjecture can be expressed the following way (see " Any admissible constellation of primes occurs infinitely often ". Therefore, if this the Mr Liu's argument is correct then also the Twin Primes conjecture has been proved. As you soon will discover this argument is close related to the Liu's approach to the prime numbers definition, approach that has been exposed in detail in the Problem 37 of these pages. What follows is Mr Liu's argument. I should strongly point out that the most that Mr. Liu

23. Re: Twin Primes Conjecture I beg the pardon of the friends. My argument in favor of Twin Primes Conjecture is based in the http://sci.tech-archive.net/Archive/sci.math/2005-05/msg03179.html

Re: Twin Primes Conjecture From Date : 16 May 2005 16:17:13 -0700 Yes Robert I made a enormous blunder. I beg the pardon of the friends. My argument in favor of Twin Primes Conjecture is based in the following two facts: 1.- It is a proved thing , that the primes are divided 50%,50% in the sequences two 6n-1 , 6n-1. 2.- A twin pair is formed by one prime of the form 6n-1 and the other of the form 6n+1. And the following acceptable supposition: If we confront the two sequences, There is no reason for not having, from certain 6M - 1 onwards,more encounters between primes of this forms. On the contrary we would have a proposition very bizarre: "From certain p onwards, the primes 6n-1 and 6n+1 repel each other"!! Follow-Ups Re: Twin Primes Conjecture From: Robert Israel References Re: Twin Primes Conjecture From: Kamalu Re: Twin Primes Conjecture From: luiroto Re: Twin Primes Conjecture From: Robert Israel Prev by Date: Re: A record of mental computation Next by Date: Operator Norm Previous by thread: Re: Twin Primes Conjecture Next by thread: Re: Twin Primes Conjecture Index(es): Date Thread Relevant Pages twin primes and goldbach conjectures unprovable?

24. Www.math.niu.edu most my life to battling the Twin Primes Conjecture and I need as many theorems in my arsenal as I can get. any help wound be appreciated. http://www.math.niu.edu/~rusin/known-math/99/brun_const

From: Andreas Homrighausen Subject: Re: Twin Primes Date: Wed, 10 Feb 1999 13:13:54 +0100 Newsgroups: sci.math Keywords: Brun's constant Janus xPuN wrote: > > Hey, what are some already proven theorems about twin primes? I am devoting > most my life to battling the Twin Primes Conjecture and I need as many theorems > > in my arsenal as I can get. any help wound be appreciated. of course, > anything about just normal primes would also be quite handy. Thanks. Hello all! This is one of the most impressive theorem about twin primes: The sum of the reciprocals of the twin primes is convergent. B=(1/3+1/5)+(1/5+1/7)+... is called Brun's constant. The sum of the reciprocals of primes is divergent. Greetings, Andreas

25. Twin Prime Conjecture Proof The six wide array further helps to demonstrate the otherwise still unproven conjecture that there must be infinitely many twin primes, that is, http://www.recoveredscience.com/primes1ebook02.htm

recoveredscience .com We offer surprises about in our e-book Prime Passages to Paradise by H. PeterAleff Site Contents PRIME PATTERNS Table of Contents Rectangular arrays Twin prime proof Prime facts Prime problems Polygonal numbers Number pyramids ... Reader responses Visit our Sections: Constants Board Games Astronomy Medicine Store Stuff Home Page Search this site FAQ about e-books Download free e-books ... email us Footnotes : Paulo Ribenboim: "The New Book of Prime Number Records", Springer- Verlag, New York, 1996, pages 20 to 52. Calvin C. Clawson: "Mathematical Mysteries: The Beauty and Magic of Numbers", Plenum Press, New York, 1996, pages 64 and 65 Volume 1: Patterns of prime distribution in "polygonal - number pyramids" You are on page Twin Prime Proof (To German translation - zur deutschen Übersetzung) 1.2. Proving the twin prime conjecture The six- wide array further helps to demonstrate the otherwise still unproven conjecture that there must be infinitely many twin primes , that is, pairs of numbers where p and p + 2 are both prime. Here is how:

26. Additive Combinatorics And Theoretical Computer Science This is very exciting because many of the classical conjectures in number theory are about additive patterns in the primes the twin primes conjecture is the question of whether the http://www.cs.berkeley.edu/~luca/pubs/addcomb-sigact.pdf

27. Twin Prime Conjecture (number Theory) -- Britannica Online Encyclopedia twin prime conjecture (number theory), in number theory, assertion that there are infinitely many twin primes, or pairs of primes that differ by 2. http://www.britannica.com/EBchecked/topic/1556762/twin-prime-conjecture

document.write(''); Search Site: Advanced Search With all of these words With the exact phrase With any of these words Without these words Home SHOP BROWSE BLOG ... HELP Username: Password: Remember me Forgot your password? Help Email " is the e-mail address you used when you registered. Password " is case sensitive. If you need additional assistance, please contact customer support Enter the e-mail address you used when enrolling for Britannica Premium Service and we will e-mail your password to you. twin-prime-conjecture My Britannica CREATE MY twin prime c... NEW ARTICLE ... SAVE twin prime conjecture Table of Contents: twin prime conjecture Article Article Citations Article Citations ARTICLE from the twin prime conjecture also known as , in number theory , assertion that there are infinitely many twin primes, or pairs of primes that differ by 2. For example, 3 and 5, 5 and 7, 11 and 13, and 17 and 19 are twin primes. As numbers get larger, primes become less frequent and twin primes rarer still. Greek mathematician Euclid (flourished c.

28. Prime Numbers The Twin Primes Conjecture that there are infinitely many pairs of primes only 2 apart. Goldbach's Conjecture (made in a letter by C Goldbach to Euler in 1742) that every even integer http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html

Prime numbers Number theory index History Topics Index Version for printing 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 and were interested in perfect and amicable numbers. A perfect number is one whose proper divisors sum to the number itself. e.g. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has divisors 1, 2, 4, 7 and 14 and 1 + 2 + 4 + 7 + 14 = 28. A pair of amicable numbers is a pair like 220 and 284 such that the proper divisors of one number sum to the other and vice versa. You can see more about these numbers in the History topics article Perfect numbers By the time Euclid 's Elements appeared in about 300 BC, several important results about primes had been proved. In Book IX of the Elements Euclid proves that there are infinitely many prime numbers. This is one of the first proofs known which uses the method of contradiction to establish a result. Euclid also gives a proof of the Fundamental Theorem of Arithmetic: Every integer can be written as a product of primes in an essentially unique way.

29. Twin Prime Conjecture Reference - MathOverflow I m looking for a reference which has the first statement of the twin prime conjecture. According to wikipedia, nova, and several other quasireputable http://mathoverflow.net/questions/7639/twin-prime-conjecture-reference

login faq how to ask meta ... Twin Prime Conjecture Reference Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points I'm looking for a reference which has the first statement of the twin prime conjecture. According to wikipedia, nova, and several other quasi-reputable resources it is Euclid who first stated it, but according to Goldston http://www.math.sjsu.edu/~goldston/twinprimes.pdf it was stated nowhere until de Polignac. I'm hoping to resolve this issue by accessing either primary historical documents, or other reputable secondary sources (Goldston being one such example). I have looked at de Polignac's work, and he does indeed make a conjecture, but have been unable to find anything definitive (besides Goldston's statements) that there was no conjecture earlier. If this is too specific for MO, I'll remove the question. Thank you. reference-request nt.number-theory ho.history-overview prime-numbers flag edited Sep 13 at 5:09 Charles asked Dec 3 at 5:17 Ben Weiss 3 Answers oldest newest votes I don't have it to hand right at this moment, but Narkiewicz'

30. Twin Prime Conjecture Discovered By Euclid. Elearning Apr 19, 2009 Twin Prime Conjecture discovered by Euclid in 300 BC Song, Video. Elearning. http://www.gogeometry.com/geometry/twin_prime_number_conjecture_euclid.htm

31. Twin Prime Conjecture - Definition The twin prime conjecture is a famous problem in number theory that Such a pair of prime numbers is called a twin prime. The conjecture has been http://www.wordiq.com/definition/Twin_Prime_Conjecture

Twin Prime Conjecture - Definition The twin prime conjecture is a famous problem in number theory that involves prime numbers . It states: There are an infinite number of primes p such that p + 2 is also prime. Such a pair of prime numbers is called a twin prime . The conjecture has been researched by many number theorists. Mathematicians believe the conjecture to be true, based only on numerical evidence and heuristic reasoning involving the probabilistic distribution of primes. In de Polignac made the more general conjecture that for every natural number k , there are infinitely many prime pairs which have a distance of 2 k . The case k = 1 is the twin prime conjecture. Contents showTocToggle("show","hide") 1 Partial results 2 Hardy-Littlewood conjecture 3 Serious problem found in potential proof 1 See also ... 2 External links Partial results In Viggo Brun showed that the sum of reciprocals of the twin primes was convergent. This famous result was the first use of the Brun sieve and helped initiate the development of modern sieve theory . The modern version of Brun's argument can be used to show that the number of twin primes less than N In showed that there is a constant c p such that p p c ln p , where p ' denotes the next prime after p . This result was successively improved; in

32. Open Problems: Twin Prime Conjecture « The Math Less Traveled Apr 10, 2007 Today, I m going to talk about the twin prime conjecture. A prime number, as you may recall, is a positive integer greater than 1 which has http://www.mathlesstraveled.com/?p=62

33. Twin Primes -- From Wolfram MathWorld Twin primes are pairs of primes of the form (p, p+2). The term twin prime was coined by Paul St ckel (18621919; Tietze 1965, p. 19). The first few twin primes are n+/-1 for n=4 http://mathworld.wolfram.com/TwinPrimes.html

34. Twin Prime Conjecture - Simple English Wikipedia, The Free Encyclopedia For example 3 and 5 are both prime and differ by two. They are twin primes. 23 is prime, but it is not a twin prime. The primes nearest to 23 are 19 and 29. http://simple.wikipedia.org/wiki/Twin_Prime_Conjecture

Twin Prime Conjecture From Wikipedia, the free encyclopedia Jump to: navigation search This page or section does not have any sources . You can help Wikipedia by finding sources, and adding them. Tagged since April 2009 The twin prime conjecture is a mathematical theory . It says that it is possible to find two twin primes that are as big as wanted. Twin primes are prime numbers that differ by two. For example 3 and 5 are both prime and differ by two. They are twin primes. 23 is prime, but it is not a twin prime. The primes nearest to 23 are 19 and 29. Twin primes were discovered by Euclid in 300 B.C. Since Euclid's time mathematicians have wondered whether there are an infinite number of twin primes. Many mathematicians are still trying to find the answer. This short article about mathematics or a similar topic can be made longer. You can help Wikipedia by adding to it Retrieved from " http://simple.wikipedia.org/wiki/Twin_Prime_Conjecture Category Number theory Hidden categories: Articles lacking sources Math stubs Personal tools New features Log in / create account Namespaces Page Talk Variants Views Read Change View history Actions Search Getting around Main Page Simple start Simple talk New changes ... Give to Wikipedia Print/export Make a book Download as PDF Page for printing Toolbox What links here Related changes Special pages Permanent link ... Cite this page In other languages English Español Esperanto Français ... Svenska This page was last changed on 20 August 2010, at 14:44.

35. Twin Primes Conjecture / Prime Sieve Note This work is not finished, but if you notice errors or have comments, please let me know. http://austininc.com/SciRealm/TwinPrimes.html

Twin Primes Conjecture / Proof via Prime Sieve Method An almost proof of the The Twin Primes Conjecture... About John Send email to John John's Science, Math, Philosophy Stuff: The Science Realm: John's Virtual Sci-Tech Universe 4-Vectors Antipodes Cyrillic Projector ... Turkish Grammar FHS Business Websites: FHS Supply, Inc. FHS Racing Oils FHS Red Max Model Fuels FHS SmokeLess Oil Welcome to Quantum Reality: Virtual worlds of imaginary particles: The dreams stuff is made of: Life, the eternal ghost in the machine... This site is dedicated to the quest for knowledge and wisdom, through science, mathematics, philosophy, invention, and technology. May the treasures buried herein spark the fires of imagination like the twinkling jewels of celestial light crowning the midnight sky... ***Learn, Discover, Explore*** Site last modified: 2005-Feb-17-7pm Note: This work is not finished, but if you notice errors or have comments, please let me know. Twin Primes Conjecture / Proof via Prime Sieve Method The Prime Sieve is a constructive method or algorithm for finding prime numbers. This document will analyze the method in some detail, hopefully adding to our mathematical knowledge. Summary of Twin Primes Conjecture Proof.

36. PBS Discussions :: View Topic - Twin Prime Conjecture 12 posts 10 authors - Last post Jul 10, 2007Great song, twin prime conjecture song. Did you know there is already a well known twin prime song? yes indeed, the hit song from a few http://discussions.pbs.org/viewtopic.pbs?t=45116

37. The Twin Primes Conjecture - Mathematics Discussion Debate Everything The Twin Primes Conjecture is discussed at protheory.com Mathematics Discussion http://www.fprotheory.com/showthread.php?t=42

38. YouTube - Theory Of Everything - Twin Primes Conjecture If you would like to discuss any of my videos please join me on my new theory of everything (TOE) forums http//www.protheory.com (My Website) http//www.fprotheory.com (My http://www.youtube.com/watch?v=nFEyZ7eWh6I

39. Note On Twin Primes - A NOTE ON TWIN PRIMES The Twin Prime File Format PDF/Adobe Acrobat Quick View http://www.math.sjsu.edu/~goldston/twinprime.pdf

40. F. Conjectures (Math 413, Number Theory) The Twin Primes Conjecture Prime Gaps; Fermat Numbers; Goldbach's Conjecture; Catalan's Conjecture; Totient Function Conjectures; The Collatz Problem http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html

F. Conjectures Number Theory, Math 413, Fall 1998 A collection of easily stated number theory conjectures which are still open. Each conjecture is stated along with a collection of accessible references. The Riemann Hypothesis Fermat Numbers Goldbach's Conjecture Catalan's Conjecture ... The Collatz Problem The Riemann Hypothesis Def: Riemann's Zeta function, Z(s), is defined as the analytic extension of sum n infty n s Thm: Z( s )=prod i infty p i s , where p i is the i th prime. Thm: The only zeros of Z( s ) are at s s Conj: The only zeros of Z( s ) are at s =-2, -4, -6, ... and on the line Re( s Thm: The Riemann Conjecture is equivalent to the conjecture that for some constant c x )-li( x c sqrt( x )ln( x where pi( x ) is the prime counting function. Refs: Unsolved Problems Elementary Number Theory http://www.utm.edu/research/primes/notes/rh.html (notes in Chris Caldwell's Prime Pages) http://match.stanford.edu/rh/ (Dan Bump's notes) Def: n is perfect if it is equal to the sum of its divisors (except itself). Examples are 6=1+2+3, 28, 496, 8128, ... Def: The n th Mersenne Number, M

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