1. Goldbach's Conjecture - Wikipedia, The Free Encyclopedia Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states Every even integer greater than 2 is a Goldbach number, a http://en.wikipedia.org/wiki/Goldbach's_conjecture

Goldbach's conjecture From Wikipedia, the free encyclopedia Jump to: navigation search Goldbach's conjecture is one of the oldest unsolved problems 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 Contents Origins Verified results Heuristic justification Rigorous results ... edit 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.

2. Goldbach's Conjecture Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. http://pandapedia.com/wiki/Goldbach's_conjecture

3. Answers.com - What Is Goldbach's Conjecture Goldbach's Conjecture is that every even number greater than two can be expressed as the sum of two prime numbers. For example, 4 = 2 + 2, 6 = 3 + 3, 8 = 5 + 3, 10 = 7 + 3, 12 http://wiki.answers.com/Q/What_is_Goldbach's_conjecture

4. Goldbach’s Conjecture Summary And Analysis Summary | BookRags.com Goldbach’s conjecture summary with 7 pages of lesson plans, quotes, chapter summaries, analysis, encyclopedia entries, essays, research information, and more. http://www.bookrags.com/Goldbach's_conjecture

5. Goldbach's Conjecture: Facts, Discussion Forum, And Encyclopedia Article This article lists some unsolved problems in mathematics. See individual articles for details and sources. Millennium Prize Problems Of the seven Millennium Prize Problems http://www.absoluteastronomy.com/topics/Goldbach's_conjecture

Home Discussion Topics Dictionary ... Login Goldbach's conjecture Goldbach's conjecture Topic Home Discussion Overview Goldbach's conjecture is one of the oldest unsolved problem Unsolved problems in mathematics This article lists some unsolved problems in mathematics. See individual articles for details and sources.- Millennium Prize Problems :Of the seven Millennium Prize Problems set by the Clay Mathematics Institute, the six yet to be solved are:* P versus NP... s in number theory Number theory Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study.... and in all of mathematics Mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.... . It states: Every even Even and odd numbers In mathematics, the parity of an object states whether it is even or odd.This concept begins with integers. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without remainder; an odd number is an integer that is not evenly divisible by 2... integer Integer The integers are formed by the natural numbers including together with the negatives of the non-zero natural numbers...

6. Goldbach's Conjecture - Wikinfo In other words, the Goldbach conjecture states that every even number greater than or equal to four is a Goldbach number, a number that can be expressed as the sum of two http://www.wikinfo.org/index.php/Goldbach's_conjecture

Goldbach's conjecture From Wikinfo Jump to: navigation search Search for "Goldbach%27s_conjecture" on Wikipedia Wikimedia Commons Wiktionary Wikiquote ... Older NY Times For criticism see Criticism of Goldbach's_conjecture Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: Every even integer greater than 2 can be written 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, In other words, the Goldbach conjecture states that every even number greater than or equal to four is a Goldbach number , a number that can be expressed as the sum of two primes. See also Levy's conjecture File:GoldbachConjecture.gif An illustration of Goldbach's conjecture. Contents Origins Verified results Heuristic justification Rigorous results ... External links Origins On 7 June , the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII) in which he proposed the following conjecture: Every integer greater than 2 can be written as the sum of three primes.

7. Goldbach's Conjecture - Simple English Wikipedia, The Free Encyclopedia Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states Every even integer greater than 2 can be written as the sum http://simple.wikipedia.org/wiki/Goldbach's_conjecture

Goldbach's conjecture From Wikipedia, the free encyclopedia Jump to: navigation search Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: Every even integer greater than 2 can be written as the sum of two primes change Origins On 7 June , the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII) in which he proposed the following conjecture Every integer greater than 2 can be written as the sum of three primes. He considered 1 to be a prime number , a convention subsequently abandoned. A modern version of Goldbach's original conjecture is: Every integer greater than 5 can be written as the sum of three primes. Euler, becoming interested in the problem, answered by noting that this conjecture would follow from a stronger version, Every even integer greater than 2 can be written as the sum of two primes, adding that he regarded this a fully certain theorem ein ganz gewisses Theorema "), in spite of his being unable to prove it. change Other websites Goldbach's conjecture , part of Chris Caldwell's Prime Pages.

8. Bambooweb: Goldbach´s Conjecture In mathematics, Goldbach s conjecture is one of the oldest unsolved problems in number theory and in all of mathematics http://bambooweb.com/articles/g/o/Goldbach's_conjecture.html

Goldbach's conjecture In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: Every even number greater than 2 can be written as the sum of two primes . (The same prime may be used twice.) For example, etc. Top Origins In 1742, the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler in which he proposed the following conjecture: Every number greater than 5 can be written as the sum of three primes. Euler, becoming interested in the problem, answered with a stronger version of the conjecture: Every even number greater than 2 can be written as the sum of two primes. 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. Top Results Goldbach's conjecture has been researched by many number theorists. The majority of mathematicians believe the (strong) conjecture to be true, mostly based on statistical considerations focusing on the

9. Goldbach's Conjecture - Discussion And Encyclopedia Article. Who Is Goldbach's C Goldbach's conjecture. Discussion about Goldbach's conjecture. Ecyclopedia or dictionary article about Goldbach's conjecture. http://www.knowledgerush.com/kr/encyclopedia/Goldbach's_conjecture/

10. Goldbach's Conjecture In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states Every even number greater than 2 can be written as http://www.mywiseowl.com/articles/Goldbach's_conjecture

Goldbach's conjecture In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: Every even number greater than 2 can be written as the sum of two primes . (The same prime may be used twice.) For example, etc. Origins In 1742, the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler in which he proposed the following conjecture: Every odd number greater than 5 can be written as the sum of three primes. Euler, becoming interested in the problem, answered with a stronger version of the conjecture: Every even number greater than 2 can be written as the sum of two primes. 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. Heuristic justification The majority of mathematicians believe the conjecture (in both the weak and strong forms) to be true, at least for

11. Goldbach's Conjecture - On Opentopia, Find Out More About Goldbach's Conjecture Origins. In 1742, the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler in which he proposed the following conjecture Every integer greater than 2 can be http://encycl.opentopia.com/term/Goldbach's_conjecture

About Opentopia Opentopia Directory Encyclopedia ... Tools Goldbach's conjecture Encyclopedia G GO GOL : Goldbach's conjecture In mathematics, 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 can be written as the sum of two (not necessarily distinct) primes For example, etc. Contents 1 Origins 2 Heuristic justification 3 Rigorous results 4 Trivia ... 8 References Origins In , the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler link Every integer greater than 2 can be written as the sum of three primes. He considered 1 to be a prime number , a convention subsequently abandoned. So today, Goldbach's original conjecture would be written: Every integer greater than 5 can be written as the sum of three primes. Euler, becoming interested in the problem, answered with an equivalent version of the conjecture: Every even number greater than 2 can be written as the sum of two primes, adding that he regarded this a fully certain theorem (" ein ganz gewisses Theorema "), in spite of his being unable to prove it.

12. Goldbach's Conjecture - Encyclopedia Article - Citizendium This is a draft article, under development and not meant to be cited; you can help to improve it. These unapproved articles are subject to a disclaimer. http://en.citizendium.org:8080/wiki/Goldbach's_conjecture

Goldbach's conjecture From Citizendium, the Citizens' Compendium Jump to: navigation search addthis_pub = 'citizendium'; addthis_logo = ''; addthis_logo_color = ''; addthis_logo_background = ''; addthis_brand = 'Citizendium'; addthis_options = ''; addthis_offset_top = ''; addthis_offset_left = ''; Main Article Talk Related Articles Bibliography External Links This is a draft article , under development and not meant to be cited; you can help to improve it. These unapproved articles are subject to edit intro Goldbach's conjecture is an unsolved problem in number theory . Simply put, it states that: Every even number greater than 2 can be expressed as a sum of two (possibly equal) prime numbers The conjecture was first posed (as far as is known) by Christian Goldbach in a letter to Leonhard Euler . The conjecture is still unsolved, though important partial progress has been made towards resolving it. The Goldbach conjecture is characteristic of number theory problems, that are often simple to state, but amazingly difficult to solve. Other problems of this kind are the twin primes conjecture (still unsolved)

13. Goldbach Conjecture -- From Wolfram MathWorld Oct 11, 2010 Goldbach s original conjecture (sometimes called the ternary Goldbach conjecture), written in a June 7, 1742 letter to Euler, http://mathworld.wolfram.com/GoldbachConjecture.html

14. Goldbach Conjecture Research May 24, 2004 Information on research on proving the Goldbach Conjecture that any even number can be represented as the sum of two prime numbers. http://www.petrospec-technologies.com/Herkommer/goldbach.htm

Goldbach Conjecture Research by Mark Herkommer May 24, 2004 The Conjecture... This conjecture dates from 1742 and was discovered in correspondence between Goldbach and Euler. It falls under the general heading of partitioning problems in additive number theory. Goldbach made the conjecture that every odd number > 6 is equal to the sum of three primes. Euler replied that Goldbach's conjecture was equivalent to the statement that every even number > 4 is equal to the sum of two primes. Because proving the second implies the first, but not the converse, most attention has been focused on the second representation. The smallest numbers can be verified easily by hand: Of course all the examples in the world do not a proof make. Research On The Conjecture... As a partitioning problem it is worth noting that as the numbers get larger the number of representations grows as well: This would suggest that the likelihood of finding that exceptional even number that is not the sum of two primes diminishes as one searches in ever larger even numbers. Euler was convinced that Goldbach's conjecture was true but was unable to find any proof (Ore, 1948). The first conjecture has been proved for sufficiently large odd numbers by Hardy and Littlewood (1923) using an "asymptotic" proof. They proved that there exists an n0 such that every odd number n > n0 is the sum of three primes. In 1937 the Russian mathematician Vingradov (1937, 1954) again proved the first conjecture for a sufficiently large, (but indeterminate) odd numbers using analytic methods. Calculations of n0 suggest a value of 3^3^15, a number having 6,846,169 digits (Ribenboim, 1988, 1995a).

15. Goldbach's Conjecture Project Dec 26, 2009 What is the Goldbach s weak conjecture? The Goldbach s weak conjecture states that every odd number greater than 7 can be expressed as the http://goldbach.pl/

About Goldbach's Conjecture Project What is the Goldbach's weak conjecture? The Goldbach's weak conjecture states that every odd number greater than 7 can be expressed as the sum of three odd primes. Liu Ming-Chit and Wang Tian-Ze proved that for numbers greater than 2·10 Goldbach's weak conjencture is true, so checking every number under this figure is perfect for using Distributing Computing architecture like BOINC. And this would make the weak Goldbach conjecture effectively proved. Read More Join Goldbach's Conjecture Project Read our rules and policies This project uses BOINC. If you're already running BOINC, select Attach to Project. If not, download BOINC When prompted, enter http://goldbach.pl If you're running a command-line or pre-5.0 version of BOINC, create an account first. If you have any problems, get help here Returning participants Your account - view stats, modify preferences Teams - create or join a team Server Status Certificate Applications Project Results ... Binary release / source code Community Profiles User search Message boards Questions and Answers ... Make a donation The current time on the servers of the project: Time Zone: UTC+0:00 Time is synchronized using the Network Time Protocol with the atomic clocks and servers STRATUM-1.

16. Goldbach's Conjecture: Definition From Answers.com The unestablished conjecture that every even number except the number 2 is the sum of two primes. http://www.answers.com/topic/goldbach-s-conjecture

17. Goldbach's Conjecture There is another Goldbach Conjecture, that every odd number greater than 5 is the sum of three primes. This is known as the Weak Goldbach Conjecture. http://www.jimloy.com/number/goldbach.htm

Return to my Mathematics pages Go to my home page Goldbach's Conjecture The modern version of Goldbach's Conjecture (called Goldbach's Strong Conjecture) is this: Every even number greater than 2 is the sum of two primes. Let's try a few: The conjecture is looking safe so far. Not only is each even number the sum of two primes, but the number of pairs of primes tends to increase. This trend seems to continue. But no one has ever proved that this goes on forever. All of the even number up to 400,000,000,000 have been tested, so far, with no exceptions found. Mathematicians have achieved some results in their efforts to prove (or disprove) this conjecture. In 1966, J. R. Chen showed that every sufficiently large even number is either the sum of two primes or of a prime and a near prime. A near prime is a number that is the product of two primes, like 91=7x13 or 4=2x2. No one knows just how large "sufficiently large" is. There is another Goldbach Conjecture, that every odd number greater than 5 is the sum of three primes. This is known as the Weak Goldbach Conjecture. This too has not been proved or disproved. It has been shown that if there are exceptions, then there are only a finite number of exceptions. A slightly different form of these conjectures was originally posed by Christian Goldbach, in 1742. Incidentally, if either Goldbach Conjecture is ever proven, then that would also prove that there are infinitely many primes. But we already knew that. See

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

hosted by the Harvey Mudd College Math Department Francis Su The Math Fun Facts App is now in the App Store Subscribe to our RSS feed or Any Easy Medium Advanced The Math Fun Facts App! List All List Recent List Popular ... Francis Edward Su From the Fun Fact files, here is a Fun Fact at the Easy level: Goldbach's Conjecture Here's a famous unsolved problem: is every even number greater than 2 the sum of 2 primes The Goldbach conjecture , dating from 1742, says that the answer is yes. Some simple examples: What is known so far: Schnirelmann(1930): There is some N such that every number from some point onwards can be written as the sum of at most N primes. Vinogradov(1937): Every odd number from some point onwards can be written as the sum of 3 primes. Chen(1966): Every sufficiently large even integer is the sum of a prime and an "almost prime" (a number with at most 2 prime factors). See the reference for more details. Presentation Suggestions: Have students suggest answers for the first few even numbers. The Math Behind the Fact: This conjecture has been numerically verified for all even numbers up to several million. But that doesn't make it true for all N... see

19. Goldbach’s Conjecture « Programming Praxis Programming Praxis. A collection of etudes, updated weekly, for the education and enjoyment of the savvy programmer http://programmingpraxis.com/2010/03/02/goldbachs-conjecture/

Programming Praxis A collection of etudes, updated weekly, for the education and enjoyment of the savvy programmer Home About HOWTO: Posting Source Code Language Resources ... Miscellaneous Exercises Chronological Reverse Permuted Themes ... Contact March 2, 2010 Your task is to write a function that finds the two primes that add to a given even number greater than two. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below. Pages: 1 Posted by programmingpraxis Filed in Exercises said March 2, 2010 at 10:26 AM Remco Niemeijer said March 2, 2010 at 10:27 AM My Haskell solution (see http://bonsaicode.wordpress.com/2010/03/02/programming-praxis-goldbach%E2%80%99s-conjecture/ for a version with comments): Jason said March 3, 2010 at 3:08 AM said March 3, 2010 at 3:26 AM Jason said March 3, 2010 at 12:36 PM Dave said March 5, 2010 at 3:10 PM public static class Goldbach public static void GetGoldbachPrimes(int value, out int prime1, out int prime2) throw new ArgumentException("value must be even number greater than 2", "value");

20. Goldbach S Conjecture - Wikipedia, The Free Encyclopedia Goldbach s conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states Every even integer greater than 2 is a http://en.wikipedia.org/wiki/Goldbach's_conjecture

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