Prime Numbers Historical topics about prime numbers.Category Science Math Number Theory Prime Numbers to prime numbers. Some unsolved problems The twin primes conjecturethat there are infinitely many pairs of primes only 2 apart. http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html
Ìàòåìàòè÷åñêèé æóðíàë â Èíòåðíåò wwwgap.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html =cut= 1. Thetwin primes conjecture that there are infinitely many pairs of primes only 2 http://mathmag.spbu.ru/conference/fido7.ru.math/12909/
Mathsoft: Mathsoft Unsolved Problems: Unsolved Problems On Other Sites MathPro Press Unsolved Math Problem of the Week column and General References;twin primes conjecture and Goldbach's Conjecture, discussed in Prime Numbers http://www.mathsoft.com/mathresources/problems/article/0,,1999,00.html
Extractions: search site map about us + news + ... Unsolved Problems Unsolved Problems Links On a Generalized Fermat-Wiles Equation Zero Divisor Structure in Real Algebras Sleeping Habits of Armadillos Engineering Standards ... Math Resources Unsolved Problems on Other Sites Jeff Lagarias' 3x+1 problem and related problems The Generalized 3x+1 Mapping (University of Queensland) and 1999 Conference on the Collatz Problem Proceedings Alex Lopez-Ortiz's sci.math FAQ on Famous Problems in Mathematics (University of New Brunswick) Chris Caldwell's Riemann Hypothesis (University of Tennessee at Martin); also Daniel Bump's Riemann Hypothesis (Stanford University) and Barry Cipra's A Prime Case of Chaos MathPro Press Unsolved Math Problem of the Week column and General References Twin Primes Conjecture and Goldbach's Conjecture, discussed in Prime Numbers: Some Unsolved Problems , part of MacTutor History of Mathematics (University of St Andrews); also Chris Caldwell's Prime Conjectures and Open Questions (University of Tennessee at Martin) Jan Otto Munch Pedersen's Known Amicable Pairs (Vejle Business College, Denmark) and Chris Caldwell's
Www.prism.uvsq.fr/~dedu/math/unsolvedPbs.txt (SOLVED RECENTLY, see http//www.spiegel.de/spiegel/0,1518,203235,00.html) UnsolvedProblem 2 (twin primes conjecture) Are there an infinite number of twin http://www.prism.uvsq.fr/~dedu/math/unsolvedPbs.txt
ABCNEWS.com : Prove A Theorem, Win $1,000,000! The twin primes conjecture is another There are an infinite number of prime pairs,prime numbers that differ by 2. Examples are 5 and 7, 11 and 13, 17 and 19 http://abcnews.go.com/sections/science/WhosCounting/whoscounting000401.html
Extractions: ABCNEWS.com var flash = 0; var ShockMode = 0; var Flash_File_Path = "http://akaads-abc.starwave.com/ad/sponsors/compaq/comp-log0302/comp-log0302.swf"; var default_image = "http://akaads-abc.starwave.com/ad/sponsors/compaq/comp-log0302/comp-log0302.gif"; var default_alttext = "visit hp.com"; var ad_width = "95"; var ad_height = "30"; on error resume next FlashInstalled = (IsObject(CreateObject("ShockwaveFlash.ShockwaveFlash.4"))) If FlashInstalled = "True" then flash = 1 End If GO TO: Select a Topic Sci/Tech Index HOMEPAGE SCIENCE WHO'S COUNTING? FEATURE Prove This, Win $1,000,000! Who Wants to Be a Millionaire Mathematician? Slowly, Uncle Petros is revealed to be a character of complexity and nuance, having devoted his considerable mathematical talents and much of his life to a futile effort to prove a classic unsolved problem. His solitary efforts give one a taste of the delight and the despair of mathematical research.
Unsolved Unsolved Problem 2 (twin primes conjecture) Are there an infinitenumber of twin primes? A prime number is an integer larger than http://mcraefamily.com/MathHelp/PuzzleUnsolved.htm
Twin Primes Brun's Constant, de Polignac's conjecture Prime Constellation, Sexy primes, twin Prime conjecture, twin primes Constant http://mathworld.pdox.net/math/t/t437.htm
Extractions: Let be the number of twin primes and such that . It is not known if there are an infinite number of such Primes (Shanks 1993), but all twin primes except (3, 5) are of the form . J. R. Chen has shown there exists an Infinite number of Primes such that has at most two factors (Le Lionnais 1983, p. 49). Bruns proved that there exists a computable Integer such that if , then where has been reduced to (Fouvry and Iwaniec 1983), (Fouvry 1984), 7 (Bombieri et al. 1986), 6.9075 (Fouvry and Grupp 1986), and 6.8354 (Wu 1990). The bound on is further reduced to 6.8325 (Haugland 1999). This calculation involved evaluation of 7-fold integrals and fitting of three different parameters. Hardy and Littlewood conjectured that (Ribenboim 1989, p. 202).
Prime Conjectures And Open Question consecutive primes with difference 2n. twin Prime conjecture Thereare infinitely many twin primes. In 1919 Brun proved that the http://www.utm.edu/research/primes/notes/conjectures/
Extractions: Submit primes Below are just a few of the many conjectures concerning primes. Goldbach's Conjecture: Every even n Goldbach wrote a letter to Euler in 1742 suggesting that . Euler replied that this is equivalent to this is now know as Goldbach's conjecture. Schnizel showed that Goldbach's conjecture is equivalent to distinct primes It has been proven that every even integer is the sum of at most six primes [ ] (Goldbach's conjecture suggests two) and in 1966 Chen proved every sufficiently large even integers is the sum of a prime plus a number with no more than two prime factors (a P ). In 1993 Sinisalo verified Goldbach's conjecture for all integers less than 4 ]. More recently Jean-Marc Deshouillers, Yannick Saouter and Herman te Riele have verified this up to 10 with the help, of a Cray C90 and various workstations. In July 1998, Joerg Richstein completed a verification to 4
The Prime Glossary: Twin Prime Conjecture twin primes are pairs of primes of the form (p, ). The term "twin prime" was coined by Paul Stäckel (18921919; Tietze 1965, p. 19). Proof of this conjecture would also imply the existence an infinite number of twin primes. http://primes.utm.edu/glossary/page.php/TwinPrimeConjecture.html
Extractions: (another Prime Pages ' Glossary entries) Glossary: Prime Pages: The (weak) twin prime conjecture is that there are infinitely many twin primes There is also a strong form of this conjecture [HL23] which states that there are about twin primes less than or equal to x . The constant written above as an infinite product is the twin primes constant. See the page "a simple heuristic " linked below for information on how this conjecture is formed. See Also: Brun's constant twin prime constant Related pages (outside of this work) References: G. H. Hardy and J. E. Littlewood , "Some problems of `partitio numerorum' : III: on the expression of a number as a sum of primes," Acta Math. (1923) 1-70. Reprinted in "Collected Papers of G. H. Hardy," Vol. I, pp. 561-630, Clarendon Press, Oxford, 1966.
Twin Primes -- From MathWorld for x n of is given by, (6). Proof of this conjecture would alsoimply the existence an infinite number of twin primes. Define, (7). http://mathworld.wolfram.com/TwinPrimes.html
Extractions: Twin primes are pairs of primes of the form p ). The term "twin prime" was coined by Paul Stäckel (1892-1919; Tietze 1965, p. 19). The first few twin primes are for n = 4, 6, 12, 18, 30, 42, 60, 72, 102, 108, 138, 150, 180, 192, 198, 228, 240, 270, 282, ... (Sloane's ). Explicitly, these are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), ... (Sloane's and The following table gives the first few p for the twin primes ( p cousin primes p sexy primes p ), etc. Triplet Sloane First Member p Sloane's p Sloane's p Sloane's p Sloane's p Sloane's p Sloane's Let be the number of twin primes p and such that . It is not known if there are an infinite number of such primes (Wells 1986, p. 41; Shanks 1993), but it seems almost certain to be true (Hardy and Wright 1979, p. 5). All twin primes except (3, 5) are of the form . J. R. Chen has shown there exists an infinite number of primes p such that has at most two factors (Le Lionnais 1983, p. 49). Bruns proved that there exists a computable integer such that if , then
Re: Twin Primes By Antreas P. Hatzipolakis (when n=1, the twin Prime conjecture) Source http// www. utm. edu/ research/ primes/ notes/ conject. http://mathforum.com/epigone/math-history-list/thahtwecha/v01540B00AF941276EFD7@
Twin Prime Conjecture -- From MathWorld sometimes called the strong twin prime conjecture (Shanks 1993, p. 30) or first HardyLittlewoodconjecture, states that the number of twin primes less than or http://mathworld.wolfram.com/TwinPrimeConjecture.html
Extractions: There are two related conjectures, each called the twin prime conjecture. The first version states that there are an infinite number of pairs of twin primes (Guy 1994, p. 19). It is not known if there are an infinite number of such primes (Wells 1986, p. 41; Shanks 1993, p. 30), but it seems almost certain to be true (Hardy and Wright 1979, p. 5). In the words of Shanks (1993, p. 219), "the evidence is overwhelming." The conjecture that there are infinitely many integers n such that is prime and n is twice a prime is very closely related (Shanks 1993, p. 30). A second twin prime conjecture states that 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 this conjecture, sometimes called the strong twin prime conjecture (Shanks 1993, p. 30) or first Hardy-Littlewood conjecture , states that the number of twin primes less than or equal to x is asymptotically equal to
Introduction To Twin Primes And Brun's Constant Computation An article by Pascal Sebah with the results of computation of the twin primes up to 5.10^15.Category Science Math Number Theory Prime Numbers According to this conjecture the density of twin primes is equivalent to the densityof cousin primes. For example, the exact computed values up to 10 12 are http://numbers.computation.free.fr/Constants/Primes/twin.html
Extractions: Introduction to twin primes and Brun's constant computation (Click here for a Postscript version of this page and here for a pdf version) It's a very old fact (Euclid 325-265 B.C., in Book IX of the Elements ) that the set of primes is infinite and a much more recent and famous result (by Jacques Hadamard (1865-1963) and Charles-Jean de la Vallee Poussin (1866-1962)) that the density of primes is ruled by the law where the prime counting function p (n) is the number of prime numbers less than a given integer n. This result proved in 1896 is the celebrated prime numbers theorem and was conjectured earlier, in 1792, by young Carl Friedrich Gauss (1777-1855) and by Adrien-Marie Legendre (1752-1833) who studied the repartition of those numbers in published tables of primes. This approximation may be usefully replaced by the more accurate logarithmic integral Li(n): However among the deeply studied set of primes there is a famous and fascinating subset for which very little is known and has generated some famous conjectures: the twin primes (the term prime pairs was used before [ Definition 1 A couple of primes (p,q) are said to be twins if q=p+2. Except for the couple (2,3), this is clearly the smallest possible distance between two primes.
Re: Twin Primes By Julio Gonzalez Cabillon primes which differ by k (which here I am calling "Polignac's conjecture") The mentioned article does not contain EXPLICITLY written the twin http://mathforum.com/epigone/math-history-list/thahtwecha/1.5.4.32.1997050804063
Twin Prime Conjecture - Wikipedia form of this conjecture, the so called Hardy Littlewood conjecture, which is concernedwith the distribution of twin primes, in analogy to the prime number http://www.wikipedia.org/wiki/Twin_Prime_Conjecture
Extractions: Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help (Redirected from Twin Prime Conjecture The twin prime conjecture is a famous unsolved problem in number theory that involves prime numbers . Its weak form states: 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 Alphonse 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.
Twin Prime - Wikipedia A strong form of the twin Prime conjecture, the HardyLittlewood conjecture, postulatesa distribution law for twin primes akin to the prime number theorem. http://www.wikipedia.org/wiki/Twin_prime
Extractions: Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help From Wikipedia, the free encyclopedia. A couple of two prime numbers p q ) are said to be twin primes if q p +2. This is the smallest possible distance between two primes. The first twin primes are: It is unknown whether there exist infinitely many twin primes, but most number theorists believe this to be true. 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 It is known 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.
The Prime Glossary: Twin Prime 19}. It has been conjectured that there are infinitely many twin primes(see the twin prime conjecture for further information). http://primes.utm.edu/glossary/page.php?sort=TwinPrime
The Prime Glossary: Twin Prime Conjecture There is also a strong form of this conjecture HL23 which states that there areabout twin primes less than or equal to x. The constant written above as an http://primes.utm.edu/glossary/page.php?next=twin prime
Project Proposals, Math 413 (Number Theory), Spring 2003, UMBC twin Prime conjecture If d n is the difference between the n th and the ( n +1)st primes, then d n =2 for an infinite number of values of n . Guy81, A8 http://www.math.umbc.edu/~campbell/Math413Spr03/projects.html
Extractions: Project Proposals Math 413, Spring 2003 Projects are not (generally) expected to contain extensive original work but can be expository or can apply existing methods. The project will be prosented both as a paper and orally. Expected as part of the paper is an abstract and references. Carmichael Numbers N composite with a N =1 (mod N for all a with gcd( a N N N
Page 012 Introduction to twin primes Link . The twin prime conjecture Link . Daniel Zwillinger,A Goldbach conjecture using twin primes, Math. Comp. 33 (1979), no. http://www.math.utoledo.edu/~jevard/Page012.htm
