Mathematics Resources Mathematicians close to cracking twin prime conjecture. Source Adfero Ltd.A group of international mathematicians has made major advances towards cracking http://www.scenta.co.uk/scenta/library/mathematics.cfm?cit_id=21556&FAArea1=cust
Isabel’s Math Blog » Prime Twin Conjecture Prime twin conjecture. Filed under. Number theory. Izzy @ 1125 pm. The Primetwin conjecture has been (tentatively) proven by RF Arenstorf at Vanderbilt http://www.izzycat.org/math/index.php?p=23
MercuryNews.com 05/25/2005 Mathematician Lauded For (corrected Goldston s work involves the twin prime conjecture the idea that there are aninfinite While the new work doesn t prove the twin Prime conjecture, http://www.mercurynews.com/mld/mercurynews/news/11732485.htm
NMBRTHRY Archives - June 2004 Arenstorf s paper on the twin Prime conjecture (14 lines) From PieterMoree moree@science.uva.nl ; Re Arenstorf s paper on the twin Prime conjecture (22 http://listserv.nodak.edu/cgi-bin/wa.exe?A1=ind0406&L=nmbrthry&D=0
NMBRTHRY Archives -- August 2002 (#18) in agreement with the twin prime conjecture prediction and my estimation of Brun sconstantis. B = 1.90216 05831 04 The results are in perfect agreement http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0208&L=nmbrthry&P=1968
Welcome To Mathsoft It s intriguing that both the Extended twin Prime conjecture and the ExtendedGoldbach conjecture involve the same constant, Ctwin. http://www.mathsoft.com/mathsoft_resources/mathsoft_constants/Number_Theory_Cons
Extractions: Print this page 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 Meissel-Mertens constants and in Brun's constant . We will mention C twin again in connection with Artin's constant since the two constants are quite similar. Linnik's constant also involves prime numbers.
Math Trek: Prime Twins, Science News Online, June 2, 2001 Indeed, the twin prime conjecture is considered one of the major unsolved problemsin number theory. It was even mentioned in the 1996 movie A Mirror Has http://www.sciencenews.org/articles/20010602/mathtrek.asp
Extractions: Week of June 2, 2001; Vol. 159, No. 22 Ivars Peterson Number theory offers a host of problems that are remarkably easy to state but fiendishly difficult to solve. Many of these questions and conjectures feature prime numbersintegers evenly divisible only by themselves and 1. For instance, primes often occur as pairs of consecutive odd integers: 3 and 5, 5 and 7, 11 and 13, 17 and 19, and so on. So-called twin primes are scattered throughout the list of all prime numbers. There are 16 twin prime pairs among the first 50 primes. The largest known twin prime is the 32,220-digit pair 318032361 x 2 +/1, found recently by David Underbakke and Phil Carmody. Although most mathematicians believe that there are infinitely many twin primes, no one has yet proved this conjecture to be true. Indeed, the twin prime conjecture is considered one of the major unsolved problems in number theory. It was even mentioned in the 1996 movie A Mirror Has Two Faces , which starred Barbra Streisand.
Slashdot | Twin Prime Proof Proffered twin Prime Proof Proffered article related to Education and Science. there was a proposed proof to the Poincare conjecture not the Perelman proof http://science.slashdot.org/article.pl?sid=04/11/04/0544229&tid=146&tid=14
Slashdot | There Are Infinitely Many Prime Twins twin primes are pairs of primes where both p and p + 2 are prime. It is conjecturedthat there are an infinite number of twin primes but proving this http://science.slashdot.org/article.pl?sid=04/05/28/2012209&tid=146
Page 015 and the twin prime conjecture are almost true, in the following sense. 1.There exist an integer N such that every even integer greater than N is the http://www.math.utoledo.edu/~jevard/Page015.htm
American Institute Of Mathematics Number theorists moved a step closer to the resolving the twin prime conjecturethis week when a new paper appeared on the internet, see the AIM preprint, http://aimath.org/primegaps/
Extractions: submitting Conferences Projects ... Visitors May 2005: Breakthrough in Prime Number theory Number theorists moved a step closer to the resolving the twin prime conjecture this week when a new paper appeared on the internet, see the AIM preprint , which gives a proof that the spacing between consecutive primes is sometimes very much smaller than the average spacing. This result was originally reported two years ago by Dan Goldston and Cem Yildirim (see the original AIM press release and technical description ) but was later retracted . Now, Janos Pintz has joined the team and completed the proof of this important result. Amazingly, the new proof can be given with full details in about 8 pages. Moreover, the techniques used are familiar to number theorists. The earlier version involved some new methods which turned out to be incorrect. There is a belief among some number theorists that a psychological barrier has been broken and that a proof of the twin prime conjecture may not be far away. Indeed, Goldston expressed such a belief during a presentation of this new work at AIM on May 24. The precise statement of the new theorem is that for any positive number there exist primes p and p' such that the difference between p and p' is smaller than . The proof of an even stronger statement, namely that the difference can be as small as
[math/0405509] There Are Infinitely Many Prime Twins There Are Infinitely Many Prime Twins. Authors RF Arenstorf Comments This paperhas been withdrawn Subjclass Number Theory MSC-class 11A41; 11N05 http://arxiv.org/abs/math.NT/0405509/
The Mathematical Tourist These twins are spread throughout the list of known prime numbers. To try toprove many conjectures about prime numbers, mathematicians therefore often http://www.fortunecity.com/emachines/e11/86/tourist2b.html
Extractions: The study of prime numbers has long been a central part of number theory, a field traditionally pursued for its own sake and for the beauty of its results . Once thought to be the purest of pure mathematics, this ancient pastime now figures prominently in modern computer science. The security of modern cryptosystems depends very strongly on the twin questions of how easy it is to identify primes and how hard it is to factor a large, random number. Neither question has a clear answer yet. Divisible evenly only by themselves and the number 1, the primes stand at the center of number theory. Like chemical elements in chemistry or fundamental particles in physics, they are building blocks in the mathematics of whole numbers. All other whole numbers, known as composites, can be written as the product of smaller prime numbers. In fact, according to the fundamental theorem of arithmetic , each composite number has a unique set of prime factors. Hence, the composite number 20 can be broken down into the prime factors 2, 2, and 5. No other composite number has the same set of factors. The number 1 is considered to be neither prime nor composite.
