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Goldbach's Conjecture:     more books (25)

Conjecture: Conjecture de Poincaré, Conjecture de Goldbach, Hypothèse de Riemann Généralisée, Conjecture de Syracuse (French Edition) Nombre Premier: Nombre Premier de Mersenne, Nombre de Fermat, Théorème Des Nombres Premiers, Crible D'ératosthène, Conjecture de Goldbach, 7, 5 (French Edition) Arithmétique: Conjecture de Goldbach, Axiomes de Peano, Table Des Bases, Partition D'un Entier, Tétration, Algorithme de Décalage N-Racines (French Edition) Uncle Petros/Goldbachs Conjecture Poster by Apostolos Doxiadis, 2001-03-05 Checking the Goldbach conjecture on a vector computer (Report. Centrum voor Wiskunde en Informatica) by A Granville, 1988 Uncle Peteros & Goldbach's Conjecture by Apostolos Doxiadis, 2000 Goldbach Conjecture Uncle Petros and Goldbach's Conjecture. by Apostolos. DOXIADIS, 2000-01-01 Goldbach's Conjecture and Structures of Primes in Number Theory (Berichte aus der Mathematik) by Uwe Kraeft, 2010-06-15 Number Theory Seven by K. Savithri, 1986

lists with details

21. Goldbach's Conjecture (II)
    Goldbach s conjecture (II) Goldbach s conjecture For any even number ngreater than or equal to 4, there exists at least one pair of prime numbers p1  
    http://acm.uva.es/p/v6/686.html
    
    Extractions: This conjecture has not been proved nor refused yet. No one is sure whether this conjecture actually holds. However, one can find such a pair of prime numbers, if any, for a given even number. The problem here is to write a program that reports the number of all the pairs of prime numbers satisfying the condition in the conjecture for a given even number. A sequence of even numbers is given as input. Corresponding to each number, the program should output the number of pairs mentioned above. Notice that we are interested in the number of essentially different pairs and therefore you should not count p p ) and p p ) separately as two different pairs. An integer is given in each input line. You may assume that each integer is even, and is greater than or equal to 4 and less than 2 . The end of the input is indicated by a number 0. Each output line should contain an integer number. No other characters should appear in the output.

22. Goldbach's Conjecture
    I studied Goldbach s conjecture, but did not solve it. Goldbach s conjecturehas two boundaries that set limits on how masking may occur.  
    http://www.geocities.com/CapeCanaveral/Launchpad/5577/musings/goldbach.htm
    
    Extractions: The Conjecture : All even numbers larger than 4 are the sum of two primes. For example: 18 = 13 + 5, or 102 = 97 + 5. This conjecture is simple enough that a sixth grader can understand it or demonstrate examples, yet the worlds best mathematicians have not solved it in over 200 years. Math teachers : all too often we fail to demonstrate to students the value of making mistakes, and learning from false paths and divergent concepts. Sometimes what we learn along the way is more important than what we intended to discover at the beginning. Use this page to show what learning or new ideas might occur from studying arcane conjectures such as Goldbach's. The goal is either to prove Goldbach or to disprove Goldbach. There is one obvious way to disprove Goldbach, simply, find one exception to the rule. There is no obvious way to prove Goldbach, and other methods of disproving Goldbach are not so obvious. I studied Goldbach's Conjecture, but did not solve it. Neither has anyone else since Goldbach first proposed it. But here are some ideas I stumbled on in the process of studying it. Will any of these ideas help you solve it? Some Important Notes about Primes Critical Factors - The Largest Prime Needed to Test a Larger Number for Primality All composite numbers are multiples of numbers equal to or smaller than their square root. Example: All composite numbers smaller than 121 are multiples numbers smaller than 11, where 11 = sqrt(121). Since 4,6,8,9, and 10 are composite, we need only test 2,3,5, and 7. Thus, all numbers between 49 = 7^2 and 121 = 11^2 are either multiples 2,3,5, or 7, or they are prime. So we may consider 2,3,5, and 7 the

23. Uncle Petros And Goldbach's Conjecture By Apostolos Doxiadis
    AuthorTrek reviews a centuries old mathematical puzzle.  
    http://www.geocities.com/SoHo/Nook/1082/uncle_petros.html
    
    Extractions: for new fiction Genre Bookshop under constant (de)construction Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis This is a highly stimulating novel about the mathematician as artist, following the trend laid down by Simon Singh's 'Fermat's Last Theorem'. And it is attractive to watch artists suffering, as Petros Anargyros does here. For Petros dares solve Goldbach's Conjecture... I do have some literary complaint about Doxiadis though: he makes Petros more romantic than his successful peers, and the narrator writes his account in the style of a math paper. It may as well be a cryptic crossword clue (very apt in the case of one of the mathematicians Doxiadis mentions), with the answer lying in the body of the question. This novel certainly makes you want go out and try and prove Goldbach's Conjecture - you'll wake up in the middle of the night, thinking about it. At first glance, it seems very appropriate that 2 (the only even prime), is mentioned in the conjecture. After all, it's common sense that there can only even be one even prime. If there was an even prime number larger than 2, then it could be divided by 2, and therefore it could not have been prime in the first place. The fact that there is no even prime larger than 2 goes very much in favour of Goldbach's Conjecture, since this discounts a possible exception. However, this is too simplistic. It is not true to say that the higher the even number, the higher the number of pairs of primes. Look at these:

24. Goldbach's Conjecture
    Verifying Goldbach s conjecture up to 4 × 1014. Diese Seite auf Deutsch. Introduction In 1855, A. Desboves verified Goldbach s conjecture up to 10000.  
    http://www.mathstat.dal.ca/~joerg/res/g-en.html
    
    Extractions: Publication Introduction In his famous letter to Leonhard Euler dated June 7th 1742, Christian Goldbach first conjectures that every number that is a sum of two primes can be written as a sum of "as many primes as one wants". Goldbach considered 1 as a prime and gives a few examples. On the margin of his letter, he then states his famous conjecture that every number is a sum of three primes: This is easily seen to be equivalent to that every even number is a sum of two primes which is referred to as the (Binary) Goldbach Conjecture . Its weaker form, the Ternary Goldbach Conjecture states that every odd number can be written as a sum of three primes. The ternary conjecture has been proved under the assumption of the truth of the generalized Riemann hypothesis and remains unproved unconditionally for only a finite (but yet not computationally coverable) set of numbers. Although believed to be true, the binary Goldbach conjecture is still lacking a proof. . The program was distributed to various workstations. It kept track of maximal values of the smaller prime p in the minimal partition of the even numbers, where a minimal partition is a representation 2n = p + q with 2n - p' being composite for all p'

25. Example Of Response With Extension Questions
    It is called Goldbach s Ternary conjecture, while the better known part isGoldbach s Binary I see you are quite interested in Goldbach s conjecture.  
    http://mathforum.org/dr.math/guide/extension4.html

26. Example Of Response With Extension Questions
    LAWRENCE MARTIN Re Goldbach s conjecture It is called Goldbach s Ternaryconjecture, while the better known part is Goldbach s Binary conjecture.  
    http://mathforum.org/dr.math/guide/extension3.html

27. Goldbach's Conjecture -- Facts, Info, And Encyclopedia Article
    Goldbach s conjecture. Categories Analytic number theory, conjectures Inmathematics, Goldbach s conjecture is one of the oldest (Click link for more  
    http://www.absoluteastronomy.com/encyclopedia/g/go/goldbachs_conjecture.htm
    
    Extractions: var dc_UnitID = 10; var dc_PublisherID = 512; var dc_BackgroundColor1 = 'white'; var dc_BackgroundColor2 = 'white'; var dc_TitleColor = 'blue'; var dc_TextColor = 'black'; var dc_URLColor = 'blue'; var dc_URLVisitedColor = 'green'; var dc_sm_type = 'horizontal'; var dc_Width = 700; var dc_Height = 75; var dc_caption_font_bgColor = 'white'; var dc_caption_font_color = 'blue'; var dc_OutBorder = 'no'; var dc_adprod='TM'; [Categories: Analytic number theory, Conjectures] In mathematics, Goldbach's conjecture is one of the oldest (Click link for more info and facts about unsolved problem) unsolved problem s in (Click link for more info and facts about number theory) number theory and in all of (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics . It states:

28. Mathematical Mysteries: The Goldbach Conjecture
    who at first treated the letter with some disdain, regarding the result astrivial. Goldbach s conjecture, however, remains unproved to this day.  
    http://plus.maths.org/issue2/xfile/
    
    Extractions: Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Issue 2 May 1997 Contents Features Call routing in telephone networks Agner Krarup Erlang (1878 - 1929) Testing Bernoulli: a simple experiment Are the polls right? ... What mathematicians get up to Career interview Student interviews Career interview - Accountant Regulars Plus puzzle Pluschat Mystery mix Letters Staffroom New GCE AS/A-level Cores The Open Learning Foundation Mathematics Working Group Running before we can walk? Delegate's diary: CAL97 ... posters! May 1997 Regulars Prime numbers provide a rich source of speculative mathematical ideas. Some of the mystical atmosphere that surrounds them can be traced back to Pythagoras and his followers who formed secret brotherhoods in Greece, during the 5th Century BC. The Pythagoreans believed that numbers had spiritual properties. The discovery that some numbers such as the square root of 2 cannot be expressed exactly as the ratio of two whole numbers was so shocking to Pythagoras and his followers that they hushed up the proof! Today, prime numbers are fascinating but they are also of commercial importance, since the best commercial and military ciphers depend on their properties. (See "

29. Gold For Goldbach
    is the sum of two primes , the standard description of Goldbach s conjecture .In 1998, Goldbach s conjecture was shown by computer to be true for even  
    http://plus.maths.org/issue11/news/Goldbach/
    
    Extractions: 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! June 2000 News In Issue 2 of Plus , we introduced you to Goldbach's Conjecture , the speculation by mathematician Christian Goldbach in a 1742 letter to Leonhard Euler that every even integer greater than 2 can be expressed as the sum of two (not necessarily different) prime numbers. (An alternative way of expressing this is that every even integer greater than 4 can be expressed as the sum of two odd primes). To give Euler some credit, in fact in his letter Goldbach expressed the belief that "Every integer

30. PlanetMath: Goldbach's Conjecture
    Goldbach s conjecture, (conjecture) Goldbach s conjecture is owned by drini . This is version 6 of Goldbach s conjecture, born on 200201-24,  
    http://planetmath.org/encyclopedia/GoldbachsConjecture.html
    
    Extractions: Goldbach's conjecture (Conjecture) The conjecture states that every even integer is expressible as the sum of two primes In 1966 Chen proved that every sufficiently large even number can be expressed as the sum of a prime and a number with at most two prime divisors Vinogradov proved that every sufficiently large odd number is a sum of three primes. In 1997 it was shown by J.-M. Deshouillers, G. Effinger, H. Te Riele, and D. Zinoviev that assuming Generalized Riemann Hypothesis every odd number can be represented as sum of three primes. The conjecture was first proposed in a 1742 letter from Christian Goldbach to Euler and still remains unproved.

31. Read About Goldbach's Conjecture At WorldVillage Encyclopedia. Research Goldbach
    Goldbach s conjecture. Everything you wanted to know about Goldbach s conjecturebut had no clue how to find it.. Learn about Goldbach s conjecture here!  
    http://encyclopedia.worldvillage.com/s/b/Goldbach's_conjecture
    
    Extractions: edit In , the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler in which he proposed the following conjecture: He considered 1 to be a prime number , a convention subsequently abandoned. So today, Goldbach's original conjecture would be written: Euler, becoming interested in the problem, answered with an equivalent version of the conjecture: The former conjecture is today known as the "ternary" Goldbach conjecture, the latter as the "strong" Goldbach conjecture. The conjecture that all odd numbers greater than 9 are the sum of three odd primes is called the "weak" Goldbach conjecture. Both questions have remained unsolved ever since, although the weak form of the conjecture is much closer to resolution than the strong one. edit The majority of mathematicians believe the conjecture (in both the weak and strong forms) to be true, at least for

32. Mudd Math Fun Facts: Goldbach's Conjecture
    Goldbach s conjecture. Here s a famous unsolved problem is every even numbergreater than 2 the sum of 2 primes? The Goldbach conjecture, dating from 1742,  
    http://www.math.hmc.edu/funfacts/ffiles/10002.5.shtml

33. 2262 Goldbach S Conjecture
    Anyway, your task is now to verify Goldbach s conjecture for all even If thereis no such pair, print a line saying Goldbach s conjecture is wrong.  
    http://acm.pku.edu.cn/JudgeOnline/showproblem?problem_id=2262

34. Biography Of Goldbach
    Although it has not been proved Goldbach s conjecture has been verified up to Desboves did one of the earliest verifications of Goldbach s conjecture to  
    http://www.andrews.edu/~calkins/math/biograph/biogoldb.htm
    
    Extractions: Back to the Table of Contents Biographies of Mathematicians - Goldbach Christian Goldbach was a famous mathematician. He was born on March 18, 1690 in Konigsberg, Prussia (now Kaliningrad, Russia). He died on November 20, 1764 in Moscow, Russia. So he lived to be 74 and 9/12 and 2 days old. In St. Petersburg he became a professor of mathematics and historian. After that, in 1728, he tutored Tsar Peter II in Moscow. He traveled around Europe and met mathematicians. He was able to meet Leibniz, Nicolaus Bernoulli, Nicolaus(2) Bernoulli, de Moivre, Daniel Bernoulli, and Hermann. Goldbach did much of his work in correspondence with Euler. He did some important mathematical work on number theory. One of his best known works is on his conjecture. Goldbach also did some work with infinite sums, the theory of curves, and the theory of equations. He was born March 18, 1690, died November 20, 1764 Goldbach did much of his work in correspondence with Euler. Goldbach's Conjecture Christian Goldbach's first conjecture is that every even number > 4 is a sum of two primes. It dates from 1742 and it was discovered in correspondence between Goldbach and Euler. A conjecture based on Goldbach's original conjecture is that every odd number > 6 is equal to the sum of three primes. Christian Goldbach's first conjecture is that every even number > 4 is a sum of two primes.

35. Goldbach's Conjecture
    Goldbach s conjecture. His famous conjecture was made in 1742 and for 255 It is thought that Goldbach s conjecture will be settled before 12/31/2020.  
    http://www.andrews.edu/~calkins/math/biograph/199899/biogoldb.htm
    
    Extractions: Back to the Table of Contents Christian Goldbach Christian Goldbach was born in Konigsberg, Prussia (now Kaliningrad, Russia) on March 18, 1690. He lived in Russia his entire life and died in Moscow in 1764. In 1725 Goldbach became professor of mathematics and historian at St. Petersburg. Then, in 1728, he went to Moscow as tutor to Tsar Peter II. He traveled around Europe meeting mathematicians. Goldbach did important work in number theory. A lot of it corresponded with Euler. He is remembered best for his conjecture, made in 1742 in a letter to Euler and still an open question, that every even integer greater than 2 can be represented as the sum of two primes. Goldbach also conjectured that every odd number is the sum of three primes. Goldbach also studied infinite sums, the theory of curves and the theory of equations. Goldbach's Conjecture His famous conjecture was made in 1742 and for 255 years, no one has succeeded in proving or disproving the correctness of this conjecture. It is thought that Goldbach's Conjecture will be settled before 12/31/2020. If it becomes "settled", this means it will be either proven, refuted, or proven undecidable. Links to find interesting facts about Goldbach and his Conjecture: This project was presented by students Risa Zander and Kaleena Katz in 1998.

36. Editorial Reviews: Uncle Petros And Goldbach's Conjecture
    Reviews of Uncle Petros and Goldbach s conjecture by Apostolos Doxiadis one of the greatest mathematical challenges of all time Goldbach s conjecture,  
    http://www.maths.ex.ac.uk/~mwatkins/isoc/doxiadis.htm
    
    Extractions: A mathematical conjecture unsolved for two centuries; a mathematical genius uncle driven mad trying to solve it; an ambiguous relation with a mathematically-minded nephew; and acute human observation all come together in Uncle Petros to make a very funny, tender, charming and, to my mind, irresistable novel. Book Description In the tradition of Fermat's Last Theorem and Einstein's Dreams, a novel about mathematical obsession. Petros Papachristos devotes the early part of his life trying to prove one of the greatest mathematical challenges of all time: Goldbach's Conjecture, the deceptively simple claim that every even number greater than two is the sum of two primes. Against a tableau of famous historical figuresamong them G.H. Hardy, the self-taught Indian genius Srinivasa Ramanujan, and a young Kurt GodelPetros works furiously to prove the notoriously difficult conjecture, but suddenly disappears into a solitary existence playing chess in the Greek countryside. To his nephew, he is known as the solitary, eccentric Uncle Petros, but when the young man finds out that his uncle is an esteemed professor of mathematics, he searches out his uncle's hidden past. Through an adversarial friendship based on chess and mathematics, he drives the retired mathematician back into the hunt to prove Goldbach's Conjecture... but at the cost of the old man's sanity, and perhaps even his life.

37. Goldbach's Conjecture
    Encyclopedia Goldbach s conjecture. In mathematics, Goldbach s conjectureis one of the oldest unsolved problems in number theory and in all of  
    http://encyclopedie-en.snyke.com/articles/goldbach_s_conjecture.html
    
    Extractions: 7 References In , the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler in which he proposed the following conjecture: He considered 1 to be a prime number , a convention subsequently abandoned. So today, Goldbach's original conjecture would be written: Euler, becoming interested in the problem, answered with an equivalent version of the conjecture: The former conjecture is today known as the "ternary" Goldbach conjecture, the latter as the "strong" Goldbach conjecture. The conjecture that all odd numbers greater than 9 are the sum of three odd primes is called the "weak" Goldbach conjecture. Both questions have remained unsolved ever since, although the weak form of the conjecture is much closer to resolution than the strong one. The majority of mathematicians believe the conjecture (in both the weak and strong forms) to be true, at least for

38. Goldbach's Conjecture Number Primes Sum Prime Goldbach Odd
    Goldbach s conjecture Number Primes Sum Prime Goldbach Odd Economy.  
    http://www.economicexpert.com/a/Goldbach:s:conjecture.html
    
    Extractions: 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 ... First Prev [ 1 Next Last In mathematics, Goldbach's conjecture is one of the oldest unsolved problem s in number theory and in all of mathematics . It states: For example, In 1742, the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler in which he proposed the following conjecture: Euler, becoming interested in the problem, answered with a stronger version of the conjecture: The former conjecture is known today as the 'weak' Goldbach conjecture , the latter as the 'strong' Goldbach conjecture. (The strong version implies the weak version, as any odd number greater than 5 can be obtained by adding 3 to any even number greater than 2). Without qualification, the strong version is meant. Both questions have remained unsolved ever since, although the weak form of the conjecture is much closer to resolution than the strong one. The majority of mathematicians believe the conjecture (in both the weak and strong forms) to be true, at least for

39. Goldbach's Conjecture
    Goldbach s conjecture Every even integer n greater than two is the sum of twoprimes. This is easily seen to be equivalent to  
    http://library.thinkquest.org/C006364/ENGLISH/problem/goldbach.htm
    
    Extractions: Goldbach wrote a letter to Euler dated June 7, 1742 suggesting (roughly) that every even integer is the sum of two integers p and q where each of p and q are either one or odd primes. Now we often word this as follows: Goldbach's conjecture : Every even integer n greater than two is the sum of two primes. This is easily seen to be equivalent to Every integer n greater than five is the sum of three primes. There is little doubt that this result is true, as Euler replied to Goldbach: That every even number is a sum of two primes, I consider an entirely certain theorem in spite of that I am not able to demonstrate it. Progress has been made on this problem, but slowlyit may be quite awhile before the work is complete. For example, it has been proven that every even integer is the sum of at most six primes (Goldbach suggests two) and in 1966 Chen proved every sufficiently large even integer is the sum of a prime plus a number with no more than two prime factors (a P Vinogradov in 1937 showed that every sufficiently large odd integer can be written as the sum of at most three primes, and so every sufficiently large integer is the sum of at most four primes. One result of Vinogradov's work is that we know Goldbach's theorem holds for almost all even integers.

40. Read This: Uncle Petros And Goldbach's Conjecture
    Read This! The MAA Online book review column review of Uncle Petros andGoldbach s conjecture, by Apostolos Doxiadis.  
    http://www.maa.org/reviews/petros.html
    
    Extractions: by Apostolos Doxiadis Although Uncle Petros remained expressionless, I noticed a slight tremor run down his hand. "Who's spoken to you about Goldbach's Conjecture?" he asked quietly. "My father," I murmured. :And what did he say, precisely?" "That you tried to prove it." "Just that?" "And.... that you didn't succeed." His hand was steady again. "Nothing else?" "Nothing else." "Hm," he said. "Suppose we make a deal?" "What sort of deal?" Intrigued? Then read on. Uncle Petros and Goldbach's Conjecture Pi, it is not clear that nonmathematicians who read the book will view mathematics as an attractive pursuit, or mathematicians as completely sane. But most nonmathematicians probably think that already anyway.) The book is really the story of two generations of obsession, the one a quest for the solution to a mathematical problem, the other a young man's search for the truth about the uncle his family shuns and derides for having thrown away his life. The story is told in the words of the young nephew, who has just completed his own mathematics degree. He discovers that his Uncle Petros Papachristos, whom he has known hitherto solely as a reclusive gardener his father refuses to talk about, was a child prodigy in mathematics, the youngest ever professor of mathematics at the University of Munich, and at one point a collaborator of Hardy and Littlewood. (Ramanujan, Gödel, and Turing also make cameo appearances in the novel.)

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