Number Theory Don H. Tucker and I have been working on the twin Prime conjecture forabout six or seven years now. We have developed a mathematical http://www.math.utah.edu/~gold/numbertheory.html
Extractions: 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
Twin Prime Conjecture twin prime conjecture. The twin prime conjecture is a famous unsolvedproblem in number theory that involves prime numbers. It states http://www.sciencedaily.com/encyclopedia/twin_prime_conjecture_1
Extractions: Front Page Today's Digest Week in Review Email Updates ... Outdoor Living Main Page See live article 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.
Goldston_tech The twin prime conjecture, which asserts that infinitely often is oneof the oldest problems; it is difficult to trace its origins. http://aimath.org/goldston_tech/
Extractions: What are the shortest intervals between consecutive prime numbers? The twin prime conjecture, which asserts that infinitely often is one of the oldest problems; it is difficult to trace its origins. In the 1960's and 1970's sieve methods developed to the point where the great Chinese mathematician Chen was able to prove that for infinitely many primes the number is either prime or a product of two primes. However the well-known ``parity problem'' in sieve theory prevents further progress. What can actually be proven about small gaps between consecutive primes? A restatement of the prime number theorem is that the average size of is where denotes the th prime. A consequence is that In 1926, Hardy and Littlewood, using their ``circle method'' proved that the Generalized Riemann Hypothesis (that neither the Riemann zeta-function nor any Dirichlet L-function has a zero with real part larger than 1/2) implies that . Rankin improved this (still assuming GRH) to . In 1966 Bombieri and Davenport, using the newly developed theory of the large sieve (in the form of the Bombieri - Vinogradov theorem) in conjunction with the Hardy - Littlewood approach, proved
Mathsoft: Number Theory Constants: Hardy-Littlewood Constants Extended twin Prime conjecture. where. conjectures involving two differentkinds of prime triples. where D=2.858248596 . conjectures http://www.mathsoft.com/mathresources/constants/numbertheory/article/0,,2000,00.
Extractions: The sequence of prime numbers p = 2, p = 3, p = 5, p = 7, p = 11, p = 13, p where where Extended Goldbach Conjecture if R(n) is defined to be the number of representations of an even integer n as the sum of two primes (order counts), then It's intriguing that both the Extended Twin Prime Conjecture and the Extended Goldbach Conjecture involve the same constant, C twin The Hardy-Littlewood constants discussed above all involve infinite products over primes. Other such products occur in our essays on Infinite series over primes are the main topic in Artin's constant Landau-Ramanujan constant Hafner-Sarnak-McCurley constant Euler Totient Function Asymptotic constants ... Meissel-Mertens constants and in Artin's constant Landau-Ramanujan constant Hafner-Sarnak-McCurley constant Euler Totient Function Asymptotic constants ... Brun's constant . We will mention C twin again in connection with Artin's constant Landau-Ramanujan constant Hafner-Sarnak-McCurley constant Euler Totient Function Asymptotic constants ... Artin's constant since the two constants are quite similar. Linnik's constant also involves prime numbers.
Gustavo Lacerda - April 16th, 2004 It is believed that there are infinitely many twin pairs (the famous twinprime conjecture), yet the problem remains unsolved up to day. http://www.livejournal.com/users/gustavolacerda/2004/04/16/
Extractions: It is believed that there are infinitely many twin pairs (the famous twin prime conjecture), yet the problem remains unsolved up to day. Suppose, someone has proved that the twin prime conjecture is unprovable in set theory. Do you believe that, still, the twin prime conjecture possesses an "objective truth value"? Imagine, you are moving along the natural number system:
Extractions: Working with a Turkish colleague, a San Jose State University math professor has solved one of the most important problems in prime number theory a solution that took him 20 years. ``There wasn't any rush, you know,'' Dan Goldston said. ``You just work away. And really, neither of us ever expected to get particularly good results by this method. It's actually completely amazing to me.'' Mathematicians described the advance announced at a conference in Germany as the most important breakthrough in the field in decades. Like many mathematical developments it has no immediate practical application but may open the door to a wealth of further advances. ``He's done something that a lot of people thought couldn't be done, really,'' said Hugh Montgomery, a mathematician at the University of Michigan in Ann Arbor. ``He's really broken a barrier.''
MercuryNews.com | 05/07/2003 | A Good Proof Despite Goof Goldston s work involves the twin prime conjecture the idea that there arean infinite number of pairs of prime numbers that differ only by two. http://www.siliconvalley.com/mld/siliconvalley/5804885.htm
Extractions: A few weeks after announcing that he and a colleague had solved an important math problem one he had labored on for 20 years Daniel Goldston had an experience familiar to anyone dipping a toe into the mathematical realm: He found he'd goofed. ``It's not unheard of,'' said Goldston, a professor at San Jose State University. ``Even if I had spent another year very carefully going over everything, I think I still would have missed that error.'' Goldston's advance in the field of prime numbers, announced in March, was initially hailed as the most important breakthrough in this particular area of mathematics in decades. Now he must try to salvage it. A number of famous mathematical proofs also had errors but were eventually fixed to everyone's satisfaction. Goldston hopes he can do the same. ``I will have to see how far I can recover from it,'' he said. It will mean months of work, maybe more, much of it done at his dining room table while his wife and three children watch TV.
Ben's Beta Blog Ben s Beta Blog. math Insomniaand-the-twin-Prime-conjecture.writeback. 2003/04/25- Apr, Fri. 0557 h -0500Z - Insomnia and the twin Prime conjecture. http://cpe000103c34069-cm014300001653.cpe.net.cable.rogers.com/weblogs/ben/math/
Extractions: math It's late and I'm exhausted. Only short linkage today. twin-prime conjecture My alarm goes off at 0600h today, though, so I have a little over an hour to sleep. This means lots of linkage and little to no writing. Apologies all 'round. Science News Online - Prime Finding: Mathematicians mind the gap Then again, it is math. Section: /math permalink Hmm... There doesn't seem to be too much coverage of this development anywhere online yet. I can't seem to find the actual paper anywhere either. I really want to read it... I'll have to keep an eye on Goldston's site for the appearance of that paper. Things are getting interesting these days! TrackBack ping me at this URI Comment...
NMBRTHRY Archives -- August 2002 (#18) single error! Also I was interested to check how the twin prime conjectureprediction fits with computed datas. All computations http://listserv.nodak.edu/scripts/wa.exe?A2=ind0208&L=nmbrthry&P=1968
Number Theory Definition Meaning Information Explanation problem (representing a given integer as a sum of squares, cubes etc.), the TwinPrime conjecture (finding infinitely many prime pairs with difference 2) and http://www.free-definition.com/Number-theory.html
Extractions: Google News about your search term Traditionally, number theory is that branch of pure mathematics concerned with the properties of integer s and contains many open problems that are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arose naturally from the study of integers. Number theory may be subdivided into several fields according to the methods used and the questions investigated. See for example the list of number theory topics In elementary number theory , the integers are studied without use of techniques from other mathematical fields. Questions of divisibility, the Euclidean algorithm to compute greatest common divisor s, factorization of integers into prime number s, investigation of perfect number s and congruences belong here. Typical statements are Fermat's little theorem and Euler's theorem extending it, the Chinese remainder theorem and the law of quadratic reciprocity . The properties of multiplicative function s such as the M¶bius function integer sequence s such as factorial s and Fibonacci number s.
