21. Goldbach’S Conjecture From A Dictionary Of Philosophy, Third Edition | BookRag Goldbach’S Conjecture from A Dictionary of Philosophy, Third Edition. Goldbach’S Conjecture summary with 1 pages of research material. http://www.bookrags.com/tandf/goldbachs-conjecture-tf/

22. The Simple Proof Of Goldbach's Conjecture The Simple Proof of Goldbach's Conjecture by miles mathis return to updates. THE SIMPLE PROOF OF GOLDBACH'S CONJECTURE by Miles Mathis http://milesmathis.com/gold3.html

return to homepage return to updates THE SIMPLE PROOF OF GOLDBACH'S CONJECTURE by Miles Mathis Euler Abstract : Here I solve Goldbach's Conjecture by the simplest method possible. I do this by first calculating probabilites for prime and non-prime meetings. Then I redefine and transform these probability fractions into densities, allowing me to develop a proof without probabilities. These densities allow me to calculate minimum numbers of pair meetings for any given prime density. These minimum pair meetings create a new rule that disallows certain meetings and requires others. One pair meeting that is required is at least one prime pair. Goldbach's Conjecture is that any even number may be expressed as the sum of two primes. If this conjecture is false, then there must be at least one even number that cannot be expressed as two primes. I will show that this is impossible, thereby confirming Goldbach's Conjecture. It has always been thought that there may be a simple solution to Goldbach's Conjecture. In this paper I will show that solution. If you want to see the proof stated in the baldest possible way, with no commentary or explanation, you can skip to the last paragraph, which simply states the new rule. Or you can go to my

23. Goldbach Conjecture - Wolfram Demonstrations Project Goldbach's conjecture is one of the oldest open problems in mathematics. The strong version reformulated by Euler states that every even positive integer greater than or equal http://demonstrations.wolfram.com/GoldbachConjecture/

24. The Prime Glossary: Goldbach's Conjecture Welcome to the Prime Glossary a collection of definitions, information and facts all related to prime numbers. This pages contains the entry titled http://primes.utm.edu/glossary/xpage/GoldbachConjecture.html

Goldbach's conjecture (another Prime Pages ' Glossary entries) Glossary: Index Search Home Previous ... Mail Editor Prime Pages: Home Search Index FAQ Top 5000: Primes Provers Curios 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 imply Every integer n greater than five is the sum of three primes. There is little doubt that both results are 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

25. The Prime Glossary: Goldbach's Conjecture Welcome to the Prime Glossary a collection of definitions, information and facts all related to prime numbers. This pages contains the entry titled 'Goldbach's conjecture.' http://primes.utm.edu/glossary/page.php?sort=GoldbachConjecture

26. Goldbach's Conjecture | Define Goldbach's Conjecture At Dictionary.com World English Dictionary Goldbach's conjecture (ˈɡəʊldˌbɑːxs) — n the conjecture that every even number greater than two is the sum of two prime numbers named after http://dictionary.reference.com/browse/goldbach's conjecture?qsrc=2446

27. Mathematical Mysteries: The Goldbach Conjecture | Plus.maths.org May 1, 1997 A brief popular article with an applet generating solutions. http://plus.maths.org/issue2/xfile/

Skip to Navigation about Plus support Plus Plus sponsors ... subscribe to Plus Search this site: Mathematical mysteries: the Goldbach conjecture Issue 2 Submitted by plusadmin on April 30, 1997 in Goldbach calculator Goldbach Conjecture Mathematical mysteries primes May 1997 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 " Discovering new primes " in Issue 1 - it is yet to be proved that there are infinitely many Mersenne primes.) Here is another unproved conjecture about prime numbers. It is called the Goldbach conjecture and may be stated as follows:

28. Prime Conjectures And Open Question 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 http://primes.utm.edu/notes/conjectures/

Prime Conjectures and Open Questions (Another of the Prime Pages ' resources) Our book " Prime Curios! The Dictionary of Prime Number Trivia " is now available on CreateSpace Amazon Home Search Site ... 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 known 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 integer 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

29. Goldbach�s Conjecture Goldbach’s conjecture . This is a simple text site to provide access to the research that I have done on Goldbach’s Conjecture, while an undergraduate. http://www-zeus.desy.de/~brownson/data/Goldbach.html

Goldbach�s conjecture This is a simple text site to provide access to the research that I have done on Goldbach�s Conjecture, while an undergraduate. Goldbach�s Conjecture: Any integer 6 or greater can be written as the sum of three primes. Modern form of Goldbach�s Conjecture Any even integer 4 or greater can be written as the sum of two primes. This is an eight page account of my findings. Paper Here is a program that I wrote in c++ to verify the Modern form of Goldbach�s Conjecture. Range test program Here is a program to list the primes that are less than a number, or p (n) for those who are familiar with it. Prime number lister program Here is a paper outlining a statistical approach to Goldbach�s Conjecture. It can be used to show the chance that Goldbach�s Conjecture is a random occurrence. It shows that the most likely candidates to violate this Conjecture are the smaller integers. Probability Here is a proof showing that the two forms of Goldbach�s conjecture are equivalent. Proof Here is a famous proof written by Euler that there are an infinite number of primes. Euler

30. Goldbach Conjecture In its original form, now known as the weak Goldbach conjecture, it was put forward by the Prussian amateur mathematician and historian Christian Goldbach http://www.daviddarling.info/encyclopedia/G/Goldbach_conjecture.html

PRIME NUMBERS A B C ... CONTACT entire Web this site Goldbach conjecture One of the oldest and easiest-to-understand hypotheses in mathematics that remains unproven. In its original form, now known as the weak Goldbach conjecture , it was put forward by the Prussian amateur mathematician and historian Christian Goldbach (1690-1764) in a letter dated Jun. 7, 1742, to Leonhard Euler . In this guise it says that every whole number greater than 5 is the sum of three prime numbers . Euler restated this, in an equivalent form, as what is now called the strong Goldbach conjecture or, simply, the Goldbach conjecture: every even number greater than 2 is the sum of two primes. Thus, 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 3 + 7, ..., 100 = 53 + 47, ... Descartes knew about the two-prime version of Goldbach's conjecture before either Goldbach or Euler did. So, is it misnamed? Paul Erd�s Uncle Petros and Goldbach's Conjecture by the Greek mathematician and author Apostolos Doxiadis, went unclaimed.

31. Goldbach's Conjecture Information, Goldbach's Conjecture Reference Articles - Fi Information and research on Goldbach's conjecture on FindTarget Reference online encyclopedia. Find articles and information resources on Goldbach's conjecture. http://reference.findtarget.com/search/Goldbach's conjecture/

reference Home Shopping Articles Local ... Reference Search for Goldbach's conjecture Sponsored Links Goldbach's conjecture Low Prices on Millions of Books. Free Shipping on Qualified Orders! www.Amazon.com/books conjecture Find conjecture s at Great Prices. www.Pronto.com Goldbach's conjecture is one of the oldest unsolved problem s in number theory and in all of mathematics . It states: Every even integer greater than 2 is a Goldbach number , a number that can be expressed as the sum of two primes The number of ways an even number can be represented as the sum of two primes Expressing a given even number as a sum of two primes is called a Goldbach partition of the number. For example, 10 = 7 + 3 or 5 + 5 14 = 3 + 11 or 7 + 7 Origins On 7 June, 1742, the German mathematician Christian Goldbach of originally Brandenburg-Prussia wrote a letter to Leonhard Euler (letter XLIII) in which he proposed the following conjecture: Every integer which can be written as the sum of two primes, can also be written as the sum of as many primes as one wishes, until all terms are units. He then proposed a second conjecture in the margin of his letter: Every integer greater than 2 can be written as the sum of three primes.

32. Goldbach's Conjecture In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture http://uva.onlinejudge.org/external/5/543.html

Goldbach's Conjecture In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture: Every number greater than 2 can be written as the sum of three prime numbers. Goldbach cwas considering 1 as a primer number, a convention that is no longer followed. Later on, Euler re-expressed the conjecture as: Every even number greater than or equal to 4 can be expressed as the sum of two prime numbers. For example: 8 = 3 + 5. Both 3 and 5 are odd prime numbers. Today it is still unproven whether the conjecture is right. (Oh wait, I have the proof of course, but it is too long to write it on the margin of this page.) Anyway, your task is now to verify Goldbach's conjecture as expressed by Euler for all even numbers less than a million. Input The input file will contain one or more test cases. Each test case consists of one even integer n with Input will be terminated by a value of for n Output For each test case, print one line of the form n a b , where a and b are odd primes. Numbers and operators should be separated by exactly one blank like in the sample output below. If there is more than one pair of odd primes adding up to

33. Goldbach's Conjecture A popular magazine announced a contest to solve Goldbach's Conjecture. Don't expect much enthusiasm from the mathematical community. http://www.math.fau.edu/locke/Goldbach.htm

Goldbach's Conjecture A popular magazine announced a contest to solve Goldbach's Conjecture . Don't expect much enthusiasm from the mathematical community. Goldbach's Conjecture . Any even integer greater than 4 is the sum of two odd primes. Vinogradov (1937): There is an integer N such that any odd integer greater than N is the sum of three primes. Chen and Wang (1989): e e Liu and Wang (2002): e Why aren't mathematician's thrilled? Over the years, many of us have received purported proofs of famous conjectures or recently proven theorems. Examples The four colour theorem: The shortest accepted proofs so far (Haken and Appel, Seymour) have 500 or more cases. No mathematican expects that somebody will find a two-page solution in the near future. Fermat's last theorem: Andrew Wiles solved this (with a little help on one piece) after a seven-year effort. The proof is several hundred pages long. Again, no short proof is expected. Angle trisection, duplication of the cube, squaring the circle: These cannot be done with ruler and compass. It is extremely hard to convince a non-mathematician of this. However, the proof is understandable to students in undergraduate mathematics programs. If I left out your favorite problem, you don't need to contact me.

34. Goldbach's Conjecture I have been tasked with writing a program that allows a user to input a lower bound and an upper bound so the program can show that every even number http://cboard.cprogramming.com/c-programming/94753-goldbachs-conjecture.html

35. Goldbach& - Encyclopedia Article - Citizendium Feb 15, 2010 Goldbach s conjecture is an unsolved problem in number theory. The Goldbach conjecture is characteristic of number theory problems, http://en.citizendium.org/wiki/Goldbach's_conjecture

Citizendium is governed by a Charter with Representatives From Citizendium, the Citizens' Compendium Jump to: navigation search There is currently no text in this page. You can search for this page title in other pages or log in to begin an article for this page. If you don't have a log in, we welcome you to request a contributor account Retrieved from " http://en.citizendium.org/wiki/Goldbach%26 Views Page Discussion Personal tools Log in Search Read Welcome to Citizendium Live Articles Random Page Recent Changes Dive In! Register Quick Start Start Article Article Mechanics ... General Help Communicate Workgroups Mailing Lists Forums Blog About Us About FAQ Fundamentals Personnel ... Donate Toolbox What links here Upload file Special pages Printable version ... About Citizendium

36. Goldbach's Conjecture - ( 1742 ), Unsolved Problems In Number Theory Christian Goldbach (1690 – 1764) was born in K nigsberg. His conjecture states that every even integer greater than http://science.jrank.org/pages/21851/Goldbach's-conjecture.html

37. Goldbach's Conjecture Christian Goldbach was born in March 1690 in K nigsberg, Prussia (now Kaliningrad, Russia), and died in 1764 in Moscow, Russia. When he was 35 Goldbach became a professor of http://www.mathsisgoodforyou.com/conjecturestheorems/goldbachs.htm

Goldbach's Conjecture home courses topics theorems ... timeline Christian Goldbach was born in March 1690 in K�nigsberg , Prussia (now Kaliningrad, Russia), and died in 1764 in Moscow, Russia. When he was 35 Goldbach became a professor of mathematics and a historian at St. Petersburg . He went to Moscow in 1728 to be a tutor to Tsar Peter II. Goldbach knew many mathematicians around Europe. In 1742 he wrote to Euler conjecturing that every even integer greater than 2 can be represented as a sum of 2 primes. n = p + p This conjecture has not yet been proved or disproved. This conjecture is equivalent to saying that every integer greater than 5 is the sum of three primes. Copy of Goldbach's letter to Euler in which he conjectures, dated 7 th July 1742. Euler responded to Goldbach saying that "There is little doubt that this result is true... that every even number is a sum of two primes, I consider [this] an entirely certain theorem in spite of that I am not able to demonstrate it." Ivan Matveevich Vinogradov was another Russian mathematician (1891-1983) who showed that if we look at 'sufficiently' large odd integers, we deduce that they can be written as the sum of at most three primes. From this follows that every sufficiently large integer (not necessarily odd) is the sum of at most four primes. One result of Vinogradov's work is that we take that Goldbach's Conjecture holds true for almost all even integers.

38. Read This: Uncle Petros And Goldbach's Conjecture Apr 1, 2010 Read This! The MAA Online book review column review of Uncle Petros and Goldbach s Conjecture, by Apostolos Doxiadis. http://www.maa.org/reviews/petros.html

Read This! The MAA Online book review column Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis Reviewed by Keith Devlin 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, G�del, and Turing also make cameo appearances in the novel.)

39. Mathematical Mysteries: The Goldbach Conjecture | Plus.maths.org Goldbach's conjecture, however, remains unproved to this day. Further reading. For an entertaining and revealing introduction to this problem, see Douglas R Hofstadter's book G del http://plus.maths.org/issue2/xfile/index.html

Skip to Navigation about Plus support Plus Plus sponsors ... subscribe to Plus Search this site: Mathematical mysteries: the Goldbach conjecture Issue 2 Submitted by plusadmin on April 30, 1997 in Goldbach calculator Goldbach Conjecture Mathematical mysteries primes May 1997 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 " Discovering new primes " in Issue 1 - it is yet to be proved that there are infinitely many Mersenne primes.) Here is another unproved conjecture about prime numbers. It is called the Goldbach conjecture and may be stated as follows:

40. PlanetMath: Goldbach's Conjecture The conjecture states that every even integer $n 2$ is expressible as the sum of two This is version 7 of Goldbach s conjecture, born on 200201-24, http://planetmath.org/encyclopedia/GoldbachsConjecture.html

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclopædia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About 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 a 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. "Goldbach's conjecture" is owned by drini full author list owner history view preamble ... get metadata View style: jsMath HTML HTML with images page images TeX source See Also: prime Attachments: Goldbach representations for even (Example) by PrimeFan Log in to rate this entry.

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