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1. Prime Conjectures And Open Question
Another page about Prime Numbers and related topics. goldbach's conjecture Every even n 2 is the sum of two primes primesthis is now know as goldbach's conjecture. Schnizel showed that
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

2. Goldbach's Conjecture - Wikipedia, The Free Encyclopedia
In mathematics, goldbach's conjecture is one of the oldest unsolved problems in number theory and in all Results. goldbach's conjecture has been researched by many number theorists
http://en.wikipedia.org/wiki/Goldbachs_conjecture

Extractions: In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: For example, Table of contents 1 Origins 2 Results 3 Trivia 4 External links ... edit 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. edit 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

3. Goldbach's Conjecture
Verifying goldbach's conjecture up to 4 × 1014 In 1855, A. Desboves verified goldbach's conjecture up to 10000
http://www.informatik.uni-giessen.de/staff/richstein/ca/Goldbach.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'

4. Dichotomy's Purgatory: (Golf) GoldBach's Conjecture
( Golf) goldbach's conjecture. 200308-19 843PM. There was a Perl golf contest floating about concerning goldbach's conjecture, which basically states
http://www.alpha-geek.com/2003/08/19/golf_goldbachs_conjecture.html

Extractions: Bertrand Russell Clarity of thought is never enough... Navigation Main One-liners Bob's Quick Guide to the Apostrophe (via this comment on The apostrophe is the modern day Shibboleth ). I'd, also like to point out: "Look at all those clowns; look it's the clowns' car" and "That's Joe Jones's From How many jellybeans will that take? , "each person can get 12 'jellybeans' of work done per week." I call it "mental manna." I only get allotted a certain amount each day. CJAN is still making steady progress . This is good news for the Java community. After it is up and running, the first thing they need to do is get an apt-get -like interface for it a la CPAN.pm For those of you who have never heard of Mk Linux DR3 UNIX history (via Jeremy Zawodny's linkblog Crash Testing: MINI Cooper vs Ford F150 "[In 2034] I'll own a computer that runs at 3 PHz CPU speed, has a petabyte of memory, half an exabyte of harddisk-equivalent storage, and connects to the Internet with a bandwidth of a quarter terabit per second," Thirty Years With Computers (via Scripting News i pour the tiny This is not the first time I have somehow ended up stumbling across interconnected , and each time I encounter it, I somehow feel as if I have read something. No fucking clue as to what it was that I read, but I am relatively sure I optically interpreted a series of symbols that encoded some type of information.

5. 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 even number greater than 4 can be. written as the sum of
http://acm.uva.es/p/v5/543.html

Extractions: Anyway, your task is now to verify Goldbach's conjecture for all even numbers less than a million. 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 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 n , choose the pair where the difference b a is maximized. If there is no such pair, print a line saying ``

6. Several Proofs Of The Twin Primes Conjecture
goldbach's conjecture proves and extends the Twin Primes Conjecture as probable.
http://www.coolissues.com/mathematics/Tprimes/tprimes.htm

Extractions: SEVERAL PROOFS OF THE TWIN PRIMES AND GOLDBACH CONJECTURES James Constant math@coolissues.com Proof of Goldbach's Conjecture, the Prime Number Theorem, and Euclid's Logic Provide Proofs of the Twin Primes Conjecture. Proof of the Twin Primes Conjecture Provides Proof of Goldbach's Conjecture Theorem There are infinitely many twin primes. Proof of the Twin Primes Conjecture Using Proofs of Goldbach's Conjecture or Using the Prime Number Theorem The twin primes conjecture (TPC) suggests that there is an infinite number of primes a and b with a difference , i.e., a - b = 2. Goldbach's conjecture (GC) suggests that every even number greater than is the sum s of two prime numbers a and b , i.e., a + b = s where s is even GC is proved by the author herein below and elsewhere For prime numbers a,b,c a - b = (a + c) - (b + c) even integer and thus, generally, a - b = 2k k = integer and since a + b is an even number a + b = 2n Now, using (2) and (3) results in a = n + k and b = n - k which say that for every single value of k primes a and b are separated by an interval and occur as numbers n + k and n - k . Suppose that n ,n ,n , . . . ,n

7. Mathematical Constants
A summary of some recent progress towards goldbach's conjecture with references to the literature.
http://pauillac.inria.fr/algo/bsolve/constant/hrdyltl/goldbach.html

Extractions: My website is smaller than it once was. Please visit again, however, since new materials will continue to appear occasionally. It's best to look ahead to the future and not to dwell on the past. * My book Mathematical Constants is now available for online purchase from Cambridge University Press (in the United Kingdom and in North America ). It is far more encompassing and detailed than my website ever was. It is also lovingly edited and beautifully produced - many thanks to Cambridge! - please support us in our publishing venture. Thank you. (If you wish, see the front cover and some reviews Here are errata and addenda to the book (last updated 5/25/2004), as well sample essays from the book about integer compositions optimal stopping and Reuleaux triangles . Here also are recent supplementary materials, organized by topic: Number Theory and Combinatorics Inequalities and Approximation Real and Complex Analysis Probability and Stochastic Processes

8. Goldbach's Conjecture And Factoring The Cryptographic Modulus
Algebraic Factoring of the Cryptography Modulus and Proof of goldbach's conjecture

9. 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.' Come explore a new goldbach's conjecture. ( another Prime Pages' Glossary entries Goldbach's comet the numbers related to goldbach's conjecture " J. Recreational Math
http://www.utm.edu/research/primes/glossary/GoldbachConjecture.html

Extractions: (another Prime Pages ' Glossary entries) Glossary: Prime Pages: 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

10. Goldbach's Conjecture
Verification up to 4.10^14, with links, bibliography. Also computation of the number of Goldbachpartitions of all even numbers up to 5.10^8.
http://www.informatik.uni-giessen.de/staff/richstein/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'

11. Mathematical Mysteries: The Goldbach Conjecture
He made his conjecture in a letter to Leonhard Euler, who at first treated the letter with some the result as trivial. goldbach's conjecture, however, remains unproved to this day
http://pass.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 ... poster! 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!

12. Goldbach's Conjecture - Wikipedia, The Free Encyclopedia
In mathematics, goldbach's conjecture is one of the oldest unsolved problems in number theory and in c primes". According to this, goldbach's conjecture is the special case where
http://www.wikipedia.org/wiki/Goldbach's_conjecture

Extractions: In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: For example, Table of contents 1 Origins 2 Results 3 Trivia 4 External links ... edit 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. edit 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

13. Read This: Uncle Petros And Goldbach's Conjecture
Read This! The MAA Online book review column review of Uncle Petros and goldbach's conjecture, by Apostolos Doxiadis Who's spoken to you about goldbach's conjecture?" he asked quietly.
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.)

14. Goldbach's Conjecture - Encyclopedia Article About Goldbach's Conjecture. Free A
encyclopedia article about Goldbach s conjecture. Goldbach s conjecture in Free online English dictionary, thesaurus and encyclopedia. Goldbach s conjecture.
http://encyclopedia.thefreedictionary.com/Goldbach's conjecture

Extractions: Dictionaries: General Computing Medical Legal Encyclopedia Word: Word Starts with Ends with Definition In mathematics, Goldbach's conjecture is one of the oldest unsolved problem This article describes currently unsolved problems in mathematics The seven Millennium Prize Problems set by the Clay Mathematics Institute are: Other still-unsolved problems: Click the link for more information. s in number theory Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers and contains many open problems that are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arose naturally from the study of integers. Number theory may be subdivided into several fields according to the methods used and the questions investigated. See for example the list of number theory topics.

15. Goldbach Conjecture From MathWorld
Goldbach conjecture from MathWorld goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler, states "at least it seems that
http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/GoldbachConjecture

16. Goldbach's Conjecture
http://www.worldhistory.com/wiki/G/Goldbach's-conjecture.htm

Extractions: World History (home) Encyclopedia Index Localities Companies Surnames ... This Week in History Goldbach's conjecture in the news 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 number greater than 2 can be written as the sum of two primes . (The same prime may be used twice.) For example, :etc. 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. 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

17. Goldbach Conjecture -- From MathWorld
Goldbach conjecture. Goldbach s original conjecture (sometimes called the ternary Goldbach conjecture), written in a June 7, 1742
http://mathworld.wolfram.com/GoldbachConjecture.html

Extractions: Goldbach Conjecture Goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler states "at least it seems that every number that is greater than 2 is the sum of three primes " (Goldbach 1742; Dickson 1957, p. 421). Note that here Goldbach considered the number 1 to be a prime, a convention that is no longer followed. As re-expressed by Euler an equivalent form of this conjecture (called the "strong" or "binary" Goldbach conjecture) asserts that all positive even integers can be expressed as the sum of two primes . Two primes ( p, q

18. Goldbach's Conjecture - Wikipedia, The Free Encyclopedia
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
http://en.wikipedia.org/wiki/Goldbach's_conjecture

Extractions: In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: For example, Table of contents 1 Origins 2 Results 3 Trivia 4 External links ... edit 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. edit 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

19. Goldbach's Conjecture
Goldbach s conjecture. The conjecture All even numbers larger than 4 are the sum of two primes. I studied Goldbach s conjecture, but did not solve it.