61. Twin Prime Conjecture - Wikipedia, The Free Encyclopedia twin prime conjecture. (Redirected from twin Prime conjecture). The 2k.The case k = 1 is the twin prime conjecture. Partial results. http://en.wikipedia.org/wiki/Twin_Prime_Conjecture

Twin prime conjecture From Wikipedia, the free encyclopedia. (Redirected from 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 Such a pair of prime numbers is called a twin prime . The conjecture has been researched by many number theorists. A proof developed by Richard Arenstorf claims to have proven this conjecture, and if verified by the mathematical community, will be considered a proof of this conjecture. Previous to Arenstorf's proof mathematicians believed 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 Table of contents 1 Partial results 2 Hardy-Littlewood conjecture 3 Potential proof 1 See also ... edit Partial results In Erdös showed that there is a constant c p such that p p c p , where p ' denotes the next prime after p . This result was successively improved; in

62. Twin Prime - Wikipedia, The Free Encyclopedia most number theorists believe this to be true. This is the contentof the twin Prime conjecture. A strong form of the twin Prime http://en.wikipedia.org/wiki/Twin_prime

Twin prime From Wikipedia, the free encyclopedia. A twin prime is a prime number that differs from another prime number by two . Except for the pair (2, 3), this is the smallest possible difference between two primes. Some examples of twin prime pairs are 5 and 7, 11 and 13, and 821 and 823. (Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin The question of whether there exist infinitely many twin primes has been one of the great open questions in number theory for many years. On May 26, 2004, however, Richard Arenstorf of Vanderbilt University submitted a 38-page proof that there exist, in fact, infinitely many twin primes. This is the content of the Twin Prime Conjecture . A strong form of the Twin Prime Conjecture, the Hardy-Littlewood conjecture , postulates a distribution law for twin primes akin to the prime number theorem , Arenstorf's proof also holds true for this conjecture. . This result implies that the sum of the reciprocals of all twin primes converges (see Brun's constant ). This is in stark contrast to the sum of the reciprocals of all primes, which diverges. He also shows that every even number can be represented in infinitely many ways as a difference of two numbers both having at most 9 prime factors. Chen Jing Run's well known theorem states that for any m even, there are infinitely many primes that differs by m from a number having at most two prime factors. (Before Brun attacked to the twin prime problem, Merlin had also attempted to solve this problem using sieve method. But unfortunately he was killed in WWI)

63. Mathenomicon.net : News : A Step Towards The Twin Prime Conjecture? An important advance has been made in prime number theory that maypave the way towards a proof of the twin prime conjecture. http://www.cenius.net/news/news.php?ArticleID=8

64. PrimePair Show graph. Requires Java. Relations. broader (en) Prime number referenced(en) Brun s constant (en) twin prime conjecture. Funded http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=1294

65. PlanetMath: Twin Prime Conjecture twin prime conjecture, (conjecture). But is there an infinite number of twinprimes ? twin prime conjecture is owned by vladm. (view preamble). http://planetmath.org/encyclopedia/TwinPrimesTheNumberOfConjuncture.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List twin prime conjecture (Conjecture) Two consecutive odd numbers which are both prime are called twin primes, e.g. 5 and 7, or 41 and 43, or 1,000,000,000,061 and 1,000,000,000,063. But is there an infinite number of twin primes ? "twin prime conjecture" is owned by vladm view preamble View style: HTML with images page images TeX source See Also: prime triples conjecture Cross-references: infinite prime odd numbers This is version 4 of twin prime conjecture , born on 2003-01-07, modified 2003-07-13. Object id is 3883, canonical name is TwinPrimesTheNumberOfConjuncture. Accessed 656 times total. Classification: AMS MSC (Number theory :: Multiplicative number theory :: Distribution of primes) Pending Errata and Addenda None.

66. Twin Prime Conjecture - InformationBlast twin prime conjecture Information Blast. twin prime conjecture. The 2k.The case k = 1 is the twin prime conjecture. Partial results. http://www.informationblast.com/Twin_Prime_Conjecture.html

Twin prime conjecture Categories: Analytic number theory Number theory Conjectures 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. A proof developed by Richard Arenstorf claims to have proven this conjecture, and if verified by the mathematical community, will be considered a proof of this conjecture. Previous to Arenstorf's proof mathematicians believed 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. 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

67. Twin Prime Conjecture TutorGig.com Encyclopedia twin prime conjecture. The twin prime conjecture is a famous unsolvedproblem in number theory that involves prime numbers. It states http://www.tutorgig.com/encyclopedia/getdefn.jsp?keywords=Twin_Prime_Conjecture

68. Page 015 In this paper, Jing Run Chen states his famous theorem saying that both Goldbach sconjecture and the twin prime conjecture are almost true . http://www.math.utoledo.edu/~jevard/Page015.htm

Almost twin primes and Chen's theorem Page maintained by Jean-Claude Evard. Last update: June 23, 2003. AMS classification numbers Link Link Link Copies of reviews from Mathematical Review cannot be posted on Web pages, but they can be seen through links to MathSciNet. These links work only in the networks of institutions or on the computers of users who are current subscribers to MathSciNet. Definitions 1. We say that an integer greater than 1 is an r-almost prime if and only if it is the product of at most r primes. 2. The set of all r-almost primes is denoted by P r 3. We say that a positive integer is an almost prime if and only if it is a 2-almost prime 4. We say that a pair of positive integers are r-almost twin primes if and only if one integer of the pair is a prime and the other is an r-almost prime. 5. We say that a pair of positive integers are almost twin primes if and only if they are 2-almost twin primes Historical result about almost twin primes Chen's theorem says that both the Goldbach's conjecture and the twin prime conjecture are almost true, in the following sense:

69. Twin Prime Conjecture The twin prime conjecture is a famous unsolved problem in number theory that involvesprime numbers. It states The case k = 1 is the twin prime conjecture. http://www.xasa.com/wiki/en/wikipedia/t/tw/twin_prime_conjecture_1.html

Twin prime conjecture Wikipedia 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. A proof developed by Richard Arenstorf claims to have proven this conjecture, and if verified by the mathematical community, will be considered a proof of this conjecture. Previous to Arenstorf's proof mathematicians believed 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 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

70. BBC NEWS | Science/Nature | Prime Number Breakthrough 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. http://news.bbc.co.uk/1/hi/sci/tech/2911945.stm

Home TV Radio Talk ... Programmes 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.

71. Definition Of Twin Prime Conjecture - WordIQ Dictionary & Encyclopedia twin prime conjecture. The twin prime conjecture is a famous unsolvedproblem in number theory that involves prime numbers. It states http://www.wordiq.com/definition/Twin_Prime_Conjecture

Encyclopedia Dictionary Thesaurus The Web eBooks loadkeyword("Twin prime conjecture"); Twin prime conjecture Encyclopedia Definition: Twin Prime Conjecture fr:Conjecture des jumeaux premiers 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. Partial results 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 Maier showed that a constant c In Chen Jingrun showed that there are infinitely many primes p such that p + 2 is a either a prime or a semiprime (i.e., the product of two primes). The approach he took involved a topic called

72. Unsolved Problem 2 Unsolved Problem 2 Are there an infinite number of twin primes? twin primes aretwo prime numbers that differ by 2. For example, 17 and 19 are twin primes. 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

73. Math Trek: Prime Twins, Science News Online, June 2, 2001 Although most mathematicians believe that there are infinitely manytwin primes, no one has yet proved this conjecture to be true. http://www.sciencenews.org/articles/20010602/mathtrek.asp

Math Trek Prime Twins Food for Thought Dietary protection against sunburn (with recipe) Science Safari Daily Planet Earth TimeLine 70 Years Ago in Science News Week of June 2, 2001; Vol. 159, No. 22 Prime Twins 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 numbers—integers 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.

74. Prime Numbers And Twin Primes - National Curve Bank 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. http://curvebank.calstatela.edu/prime/prime.htm

Back to . . . . Curve Bank Home Page 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.

75. Twin Prime Conjecture Article on twin prime conjecture from WorldHistory.com, licensed fromWikipedia, the free encyclopedia. Return Index twin prime conjecture. http://www.worldhistory.com/wiki/T/Twin-Prime-Conjecture.htm

World History (home) Encyclopedia Index Localities Companies Surnames ... This Week in History Twin prime conjecture Twin prime conjecture in the news The twin prime conjecture is a famous unsolved problem in number theory that involves prime number s. 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. Partial results In 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 1966, Chen Jingrun showed that there are infinitely many primes p such that p + 2 is a either a prime or a semiprime (i.e., the product of two primes). The approach he took involved a topic called sieve theory, and he managed to treat the twin prime conjecture and

76. Twin_Prime_Conjecture Information, Explanation, Recent Texts patents.) twin prime conjecture. (Redirected from twin Prime of 2k.The case k = 1 is the twin prime conjecture. Partial results In http://essential-facts.com/primary/math-plus/Twin_Prime_Conjecture.html

refined (including recent related patents.) Twin prime conjecture (Redirected from 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 2k. The case k = 1 is the twin prime conjecture. Partial results In p p ' denotes the next prime after p. This result was successively improved; in Chen Jingrun showed that there are infinitely many primes p such that p + 2 is a either a prime or a semiprime (i.e., the product of two primes). The approach he took involved a topic called sieve theory , and he managed to treat the twin prime conjecture and Goldbach's conjecture in similar manners.

77. 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

78. Twin Prime Conjecture twin Prime conjecture. The twin prime conjecture is a special case of themore general Prime Patterns conjecture corresponding to the set . http://icl.pku.edu.cn/yujs/MathWorld/math/t/t436.htm

Twin Prime Conjecture Adding a correction proportional to to a computation of Brun's Constant ending with will give an estimate with error less than . An extended form of the conjecture states that where is the Twin Primes Constant . The twin prime conjecture is a special case of the more general Prime Patterns Conjecture corresponding to the set See also Brun's Constant Prime Arithmetic Progression Prime Constellation Prime Patterns Conjecture ... Twin Primes Eric W. Weisstein

79. [Seminar] (Fwd) Prime Number Result Wrong? (Jyxo Usenet) also marked the biggest step in decades toward proving one of the oldest and mostfamous hypotheses in number theory the twin Prime conjecture, which posits http://usenet.jyxo.cz/cz.sci.informatics.announce.seminar/0305/seminar-fwd-prime

[Seminar] (Fwd) prime number result wrong? jyxo archiv usenet seminar květen 2003 Jiri Wiedermann jiri.wiedermann z cs.cas.cz Ponděl­ 19 kvě 2003 08:41:53 Za obsah pà ™­spěvkà ¯ odpov­d¡ autor. O Jyxo Usenet Sluà ¾by Kontakt Vyhled¡vač Jyxo

80. Now Playing At STAGE 3 THEATRE COMPANY - Sonora, California Brilliant mathematician Linda Ruether has spent her life trying to unlockthe ageold mathematical mystery of the twin Prime conjecture. http://www.stage3.org/current.htm

Double the thrills – "Twin Primes" at Stage 3 "Lead us not into temptation" says the prayer. Sometimes temptation is too great. But heed a word of warning: Before you take another step, you better check your math. Stage 3 is one of those courageous theater companies willing to take a risk on bringing exciting new works to the stage. In this case the gamble pays off in the form of Alex Lewin's captivating intellectual thriller, "Twin Primes". Winner of the 2003 Festival of New Plays, "Twin Primes" is a psychological spine-tingler in the vein of Alfred Hitchcock and Orson Welles, taut, gripping storytelling full of surprises and a dash of humor. Brilliant mathematician Linda Ruether has spent her life trying to unlock the age-old mathematical mystery of the Twin Prime Conjecture. She has sacrificed everything but this tantalizing dream has remained just out of reach. When an eighteen-year-old genius stumbles upon the solution, she can't resist the temptation to gain her own intellectual immortality, whatever the cost. She might just succeed. She might be able to join the pantheon of giants. Or is there something that she has overlooked? Something that was before our very eyes the entire time. Can ambition blind us to the obvious? Maybe. Maybe not. We never know until the final few seconds.

Page 4     61-80 of 90    Back | 1  | 2  | 3  | 4  | 5  | Next 20