61. Elusive Twins The twin prime conjecture is one of those tantalising problems in number theory that More support for the twin prime conjecture came in 1966 when Chen http://plus.maths.org/latestnews/may-aug05/twinprimes/

about Plus support Plus ... Plus search plus with google home latest issue explore the archive ... news Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Latest news Spaghetti breakthrough What happens to bent pasta? How to measure a million The risks in Who wants to be a millionaire? Not just knots: the secrets of khipu The Inka way of counting Machine prose A computer program that can learn languages A new time machine Take a journey to the limits of common sense Gene-ius The search for the maths gene Plus... more news from the world of maths Explore the news archive Subscribe to our free newsletter Get the ... posters! News Elusive twins How many twins are there? Just over two years ago, Plus reported on one of those times when the mathematical community held its breath (see Mind the gap Now, two years later, it looks as though the two mathematicians can finally breathe a sigh of relief. Having joined forces with Janos Pintz of the Hungarian Academy of Sciences, they managed to re-prove their result, and, according to Granville, this time the proof seems to bear up under scrutiny. How would you like your maths displayed?

62. Mind The Gap The twin Prime conjecture states that there are infinitely many pairs of prime The twin Prime conjecture is one of those annoying unsolved problems in http://plus.maths.org/issue25/news/twinprime/

about Plus support Plus ... Plus search plus with google home latest issue explore the archive ... news Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Latest news Spaghetti breakthrough What happens to bent pasta? How to measure a million The risks in Who wants to be a millionaire? Not just knots: the secrets of khipu The Inka way of counting Machine prose A computer program that can learn languages A new time machine Take a journey to the limits of common sense Gene-ius The search for the maths gene Plus... more news from the world of maths Explore the news archive Subscribe to our free newsletter Get the ... posters! News Mind the gap Mathematicians are holding their breath. Can Dan Goldston and Cem Yalcin Yildrim repair the hole in their proof to make the biggest breakthrough in prime number theory for 80 years? Goldston, of San Jose State University, and Cem Yalcin Yildrim, of Bogazici University, Istanbul, thought they had proved a result about the spacing of the prime numbers, which in turn could have led to a proof of the elusive Twin Prime conjecture. Their work, presented to colleagues in March, generated enormous excitement in the mathematical community. Unfortunately, on April 23, after closer examination, mathematicians spotted an error in the proof and now an effort is under way to resurrect their result. Prime numbers are the fundamental building blocks of number theory, with every integer being expressed in exactly one way as a product of primes. Mathematicians have known there are infinitely many primes since Euclid's proof over 2,000 years ago, but they have struggled for centuries to understand how the primes are spread among the integers. Prime numbers become sparser as you look further up the number line, but they are also clumpy, sometimes bunching together in groups. Goldston and Yildrim may still have brought mathematicians much closer to proving the Twin Prime Conjecture, by using a new method to attack the question of just how bunched together the prime numbers can be.

63. Article About "Twin Prime Conjecture" In The English Wikipedia On 24-Apr-2004 The twin prime conjecture reference article from the English Wikipedia on The twin prime conjecture is a famous unsolved problem in number theory that http://fixedreference.org/en/20040424/wikipedia/Twin_prime_conjecture

The Twin prime conjecture reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference : snapshots of Wikipedia from wikipedia.org) 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 the conjecture to be 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. Table of contents showTocToggle("show","hide") 1 Partial results 2 Hardy-Littlewood conjecture 3 See also 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

64. Proof Of Golbach's Conjecture And The Twin Prime Conjecture - Physics Help And M Physics Forums is a science and physics community. http://physicsforums.com/showthread.php?t=81643

65. Mersenneforum.org - Twin Prime Conjecture Work, Notation Question But it may help mathematicians tackle the famous twin prime conjecture, The twin prime conjecture doesn t seem impossible to prove anymore, Goldston http://www.mersenneforum.org/showthread.php?t=480

66. Forget Sudoku, Try Twin Prime Conjecture Mathematicians have taken a giant step towards cracking one of oldest and mostcomplex number puzzles without a Sudoku grid in sight. http://www.buzzle.com/editorials/5-25-2005-70533.asp

Home Web Directory What's the Buzz? Escape Hatch ... Free Email Friday, September 16, 2005 8:13:09 PM DIRECTORY Hobbies Amateur Radio Arts and Crafts Chapter Quicklink What's the Buzz Escape Hatch: Open Mic Forget Sudoku, Try Twin Prime Conjecture Mathematicians have taken a giant step towards cracking one of the oldest and most complex number puzzles - without a Sudoku grid in sight. By Guardian Newspapers, 5/25/2005 Mathematicians have taken a giant step towards cracking one of the oldest and most complex number puzzles - without a Sudoku grid in sight. The puzzle, known as the twin prime conjecture, has stumped the best mathematical brains for centuries. Of similar status to Fermat's last theorem, it even appeared as the subject of a chat-up line in the 1996 Hollywood film The Mirror Has Two Faces. Now, number experts Dan Goldston of San Jose State University in California and Cem Yildrim of Bogazici University in Istanbul, working with Janos Pintz of the Hungarian Academy of Sciences, have paved the way for a solution. Prof Goldston announced the breakthrough at the American Institute of Mathematics in Palo Alto, California. Brian Conrey, director of the institute, said: "A couple of months ago I would have told anybody who asked that no one has ever had a plausible idea for proving the twin prime conjecture. Today, I think it is feasible that it will be resolved in the next few years."

67. Foreign Dispatches: A Proof Of The Twin-Prime Conjecture? A Proof of the twinPrime conjecture? A Slashdot post pointed me to this purportedproof by Vanderbilt University s Richard Arenstorf of the twin-Prime http://reti.blogspot.com/2004/05/proof-of-twin-prime-conjecture.html

Foreign Dispatches Random remarks on current affairs. Saturday, May 29, 2004 A Proof of the Twin-Prime Conjecture? A Slashdot post pointed me to this purported proof by Vanderbilt University's Richard Arenstorf of the Twin-Prime Conjecture , which states that there are infinitely many primes of the form P P+2 , e.g, 5 and 7, 11 and 13, 17 and 19, or 29 and 31. This supposed proof, if correct, would be one of the most exciting results in number theory in quite some time. I'm not and never have been an analytic number theorist, and I can't say that I've ever heard of Mr. Arenstorf before today, so I'm in no position to assess the likelihood that his proof isn't just stuff and nonsense, at least not without getting a chance to actually read it through. Going from the comments of some of the Slashdot readers, this guy got his PhD 48 years ago, and hit his productive prime in the 1960s; prior to this, his most recent published paper was in 1993. This hardly makes one feel confident in the correctness of his work, as mathematics is notorious for being a young man's game, the likes of Paul Erdos aside. As another commenter noted, I'd feel far more confident that this guy's hit the mark if the likes of Peter Sarnak, Andrew Granville, Andrew Odlyzko or Preda Mihailescu were to give his paper a preliminary thumbs up - that would still be no guarantee that Arenstorf was correct, of course, but it would lessen the odds of his being wrong considerably. One thing I noticed in the abstract of the paper was that Arenstorf claimed that his proof depended only on methods from classical analytic number theory, and a quick scan through suggests that this is indeed the case, as it seems to lean most heavily on the theory of

68. MathForge.netPower Tools For Online Mathematics Note that this paper does not prove the twin prime conjecture, but a weaker (butstll very interesting) result. Granville thinks that this result might lead http://mathforge.net/index.jsp?page=seeReplies&messageNum=1989

69. Unsolved Problem 2 Are there an infinite number of twin primes? A prime number is an integer twin primes are two prime numbers that differ by 2. For example, 17 and 19 are http://cage.rug.ac.be/~hvernaev/problems/Problem2.html

8-Jan-1995 Unsolved Problem 2: Are there an infinite number of twin primes? A prime number is an integer larger than 1 that has no divisors other than 1 and itself. Twin primes are two prime numbers that differ by 2. For example, 17 and 19 are twin primes. Reference: [Sierpinski 1964] Waclaw Sierpinski, A Selection of Problems in the Theory of Numbers. Pergamon Press. New York: 1994. Pages 30-31. Each week, for your edification, we publish a well-known unsolved mathematics problem. These postings are intended to inform you of some of the difficult, yet interesting, problems that mathematicians are investigating. We do not suggest that you tackle these problems, since mathematicians have been unsuccessfully working on these problems for many years. general references previous problem problem archive next problem ... electronic publications

70. Twin Prime Conjecture twin prime conjecture The twin prime conjecture is a famous unsolved problem innumber theory that involves prime numbers. It states There are an infinite http://www.allabout.cc/wiki/Twin_Prime_Conjecture

Twin Prime Conjecture Courtesy of allabout.cc "The world has the habit of making room for the man whose actions show that he knows where he is going." Napoleon Hill Online Shops Click Shop E-Books Town Information ... Previous Page 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 p such that p p c ln p ), where

71. BBC NEWS | Science/Nature | Prime Number Breakthrough The advance is related to an idea called the twin prime conjecture. This idea,still unproved, is that there are an infinite number of pairs of prime http://news.bbc.co.uk/1/hi/sci/tech/2911945.stm

Home TV Radio Talk ... Newswatch Last Updated: Friday, 4 April, 2003, 11:11 GMT 12:11 UK Email this to a friend Printable version Prime number breakthrough By Dr David Whitehouse BBC News Online science editor Each one a prime A pair of mathematicians has made a breakthrough in understanding so-called prime numbers, numbers that can only be divided by themselves and one. Other mathematicians have described the advance as the most important in the field in decades. It was made by Dan Goldston, of San Jose State University, and Cem Yildirim, of Bogazici University in Istanbul, Turkey. It has just been announced at a conference in Germany on Algorithmic Number Theory. The advance is related to an idea called the twin prime conjecture. This idea, still unproved, is that there are an infinite number of pairs of prime numbers that differ only by two. Number building "Neither of us ever expected to get particularly good results by this method. It's actually completely amazing to me," says Goldston. Commenting on the breakthrough, Hugh Montgomery, a mathematician at the University of Michigan in Ann Arbor, US, says that Goldston has really broken a barrier.

72. Mathematicians Close To Cracking Twin Prime Conjecture 27 May 2005 difficult mathematical puzzles in the world the twin prime conjecture.Mathematicians close to cracking twin prime conjecture A group of international http://www.graduateengineer.com/eonicweb.asp?pgid=69&artid=2896

73. A Promising Approach To The Twin Prime Problem - Resonance - March 2003 The famous twin prime conjecture asserts that there are infinitely many pairs ofprimes differing by 2. More generally, it is conjectured that for any even http://www.ias.ac.in/resonance/Mar2003/Mar2003p26-32.html

journal of science education Advanced Search About Resonance Editorial ... Back Issues This Year January February A Promising Approach to the Twin Prime Problem Bhaskar Bagchi Bhaskar Bagchi is with the Indian Statistical Institute since 1971, first as a student and then as a member of the faculty. He is interested in diverse areas of mathematics like combinatorics, elementary and analytic number theory, functional analysis, combinatorial topology and statistics. The famous twin prime conjecture asserts that there are infinitely many pairs of primes differing by 2. More generally, it is conjectured that for any even number $h$, there are infinitely many pairs of primes differing by h. (This is obviously false for odd h.) Indeed, in a famous paper, G H Hardy and J E Littlewood made the following (much stronger) conjecture. Read full article (80 Kb) Address for Correspondence Bhaskar Bagchi Math. Stat. Unit

74. Platonism, Intuition And The Nature Of Mathematics. By K.Podnieks Do you believe that, still, the twin prime conjecture possesses an b) twinpairs appear over and again (ie the twin prime conjecture is true). http://www.ltn.lv/~podnieks/gt1.html

mathematics, what is mathematics, effectiveness, methodology, philosophy, foundations, formalism, Cantor, Frege, Platonism, intuition, nature, theories, axiomatic, formal, infinity, theory, Hilbert, program Back to title page Left Adjust your browser window Right PLATONISM, INTUITION AND THE NATURE OF MATHEMATICS by Karlis Podnieks Professor Karlis.Podnieks@mii.lu.lv University of Latvia Institute of Mathematics and Computer Science This paper presents the translation of the first chapter of my book "Around Goedel's theorem" published in 1992 in Russian. View copy of the Russian original Note. The 1st edition of the book was published in 1981 in Russian. In English, its concepts were first presented in 1988 at the (view copy of Abstract ), after that - in 1994, on the QED mailing list (in 5 parts: CONTENTS Platonism - the philosophy of working mathematicians Investigation of stable self-contained models - the true nature of the mathematical method Intuition and axioms Formal theories ... References 1. Platonism - the Philosophy of Working Mathematicians Charles Hermite once noted that, for him, numbers and functions are not mere inventions of mathematicians; that they do exist independently of us, as do things in our everyday practice... Some time ago, in the former USSR this proposition was quoted as the evidence for "the naive materialism of distinguished scientists".

75. Primarily Primes Here s some other conjectures about primes which are waiting for someone (you? As a side line, the twin primes are used to define one of mathematics http://www.lynnekelly.com.au/beingmathematical/numbers/primarily_primes.html

Primarily Primes Prime numbers have been the source of fascination for mathematicians for centuries. Nothing has changed! It has been known for over 2000 years that there are an infinite number of primes. Euclid's proof is claimed to be one of the most beautiful proofs ever written. Euclid's Proof of the existence of an infinite number of prime numbers Every number which is not a prime (called a composite number) is itself divisible by at least one prime. To prove there are an infinite number of primes, let us assume there are not. That is, let's assume P is the largest Prime. We can then prove this is impossible. The primes are - for our sake - 2, 3, 5, 7, 11 ...... P Let us then define Q as: Q = (2 x 3 x 5 x 7 x 11 x ..... x P) + 1. If Q is divided by any of the prime numbers below it, then the remainder will be 1. So it is not divisible by any number less than it other than 1. Hence Q is prime. But Q is bigger than our largest prime P. Hence there cannot ever be a P which is the largest Prime. There are many theories which have been tested without an exception found. But that doesn't mean there is a proof. Here's some:

76. Number Theory Don H. Tucker and I have been working on the twin Prime conjecture for about sixor seven years now. We have developed a mathematical algorithm which, http://www.math.utah.edu/~gold/numbertheory.html

Number Theory Jeffrey Frederick Gold Mathematical Interests: Twin Primes, Experimental Number Theory, Elementary Number Theory, Chinese Remainder Theorem, Covering Sets, Linear Congruences, Prime Numbers (of course), abundant numbers, odd perfect numbers, group theory, Galois theory, vectors, and more. Don H. Tucker and I have been working on the Twin Prime Conjecture for about six or seven years now. We have developed a mathematical algorithm which, when tested using a computer analogue, correctly predicted the twin primes in ascending order up to 5,000,000. Of course, the computer is never a proof (except maybe by intimidation), so we have been working on the induction argument for quite some time. It always seems to be within grasp, and just when I'm about to say, "Oh, to hell with it," I stare back down onto the page and the numbers give me something, they always give me something, something to come back and work on the problem again. Damn! I thought I'd get away!!!! A Characterization of Twin Prime Pairs, (with Don H. Tucker). Proceedings - Fifth National Conference on Undergraduate Research, Volume I, pp. 362-366, University of North Carolina Press, University of North Carolina at Asheville (UNCA), 1991. Abstract The basic idea of these remarks is to give a tight characterization of twin primes greater than three. It is hoped that this might lead to a decision on the conjecture that infinitely many twin prime pairs exist; that is, number pairs

77. Prime Numbers And Twin Primes - National Curve Bank twin primes are pairs of prime numbers that only differ by two. Until recently,it had been conjectured that there are infinitely many twin primes. http://curvebank.calstatela.edu/prime/prime.htm

Back to . . . . Curve Bank Home NCB Deposit # 19 Chris K. Caldwell Department of Mathematics University of Tennessee, Martin Martin, Tennessee caldwell@utm.edu Prime Numbers Twin Primes From ( IX, 20) of the Elements. Math in the news: Are there an infinite number of pairs of "twin primes?" For the student . . . . Background . . . . Twin primes are pairs of prime numbers that only differ by two. Examples: 3 and 5 5 and 7 11 and 13 17 and 19 29 and 31 41 and 43 59 and 61 Until recently, it had been conjectured that there are infinitely many twin primes. If the probability of a random integer n and the integer n+2 being prime were statistically independent events, then it would follow from the prime number theorem that there are about n/(log n) twin primes less than or equal to n. These probabilities are not independent. A famous team of British mathematicians - hmm, another pair so to speak, Hardy and Littlewood, conjectured that the correct estimate should be the following: But conjecture is not a proof. Recently, in March 2003, a new team of mathematicians - Dan Goldston of San Jose State University in California and Cem Yalcin Yildirim of Bogazici University in Istanbul, Turkey - announced they had at least made progress in proving the suspicion that pairs of primes keep going off to infinity.

78. Twin Peaks Series Pilot Lynch Set Released Episode Story Town Sometimes the, twin prime conjectureThe twin prime conjecture is a Such apair of prime numbers is called a twin prime. The conjecture has been res http://www.economicexpert.com/a/Twin:Peaks.htm

var GLB_RIS='http://www.economicexpert.com';var GLB_RIR='/cincshared/external';var GLB_MMS='http://www.economicexpert.com';var GLB_MIR='/site/image';GLB_MML='/'; document.write(''); document.write(''); document.write(''); document.write(''); A1('s',':','html'); Non User A B C ... Home First Prev [ 1 Next Last This article is about the television series. For alternative meanings, see: Twin Peaks (disambiguation) Twin Peaks was an American television series created by David Lynch and Mark Frost . The show is titled after the fictional town in northeastern Washington State wherein it is set. It aired on the ABC network in the United States from April 8 until June 10 . Some episodes were written/directed by Lynch and Frost, but most were directed by others who were invited by Lynch to guest-direct. The show was co-produced by Aaron Spelling 's production company and ran for 29 episodes over two seasons. 1 Overview Twin Peaks tells the story of FBI Special Agent Dale Cooper and his assignment of finding the killer of a young, popular local girl, Laura Palmer among the town folk of Twin Peaks. The program portrays small-town

79. Article About "Twin Prime Conjecture" In The English Wikipedia On 24-Jul-2004 The twin prime conjecture reference article from the English Wikipedia on 24Jul- The twin prime conjecture is a famous problem in number theory that http://july.fixedreference.org/en/20040724/wikipedia/Twin_prime_conjecture

The Twin prime conjecture reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference : snapshots of Wikipedia from wikipedia.org) Twin prime conjecture 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. Table of contents showTocToggle("show","hide") 1 Partial results 2 Hardy-Littlewood conjecture 3 Serious problem found in potential proof 4 See also ... 5 External links 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

80. Science -- Sign In As for the twin prime conjecture, Goldston doubts his method can be pushed so far.However, other experts say it s conceivable. We have more mathematicians http://www.sciencemag.org/cgi/content/full/300/5616/32

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