1. Goldbach's Conjecture Verification up to 4.10^14, with links, bibliography. Also computation of the number of Goldbachpartiti Category Science Math Open Problems Goldbach Conjecture......Verifying goldbach's conjecture up to 4 × 10 14. Diese Seite auf Deutsch Historiccomputations. In 1855, A. Desboves verified goldbach's conjecture up to 10000. http://www.informatik.uni-giessen.de/staff/richstein/res/g-en.html

Diese Seite auf Deutsch Introduction Historic computations Computational process Results ... 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'

2. 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. http://www.utm.edu/research/primes/notes/conjectures

Prime Conjectures and Open Questions (Another of the Prime Pages ' resources Home Search Site Largest Finding ... 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

3. Goldbach Conjecture -- From MathWorld Article from MathWorld.Category Science Math Open Problems Goldbach Conjecture...... never been proved and which any fool could have guessed. Faber and Faber offereda $1,000,000 prize to anyone who proved goldbach's conjecture between March 20 http://mathworld.wolfram.com/GoldbachConjecture.html

Foundations of Mathematics Mathematical Problems Prize Problems Foundations of Mathematics ... Prime Numbers Goldbach Conjecture Goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler states that every integer is the sum of three primes (Goldbach 1742; Dickson 1957, p. 421). As re-expressed by Euler an equivalent 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 ) such that for n a positive integer are sometimes called a Goldbach partition (Oliveira e Silva). According to Hardy (1999, p. 19), "It is comparatively easy to make clever guesses; indeed there are theorems, like 'Goldbach's Theorem', which have never been proved and which any fool could have guessed." Faber and Faber offered a $1,000,000 prize to anyone who proved Goldbach's conjecture between March 20, 2000 and March 20, 2002, but the prize went unclaimed and the conjecture remains open. Schnirelman (1939) proved that every even number can be written as the sum of not more than 300,000

4. Factoids > Goldbach's Conjecture goldbach's conjecture Every even number 4 is the sum of two odd primes. http://www-users.cs.york.ac.uk/~susan/cyc/g/goldbach.htm

Goldbach's conjecture Goldbach's conjecture primes 389,965,026,819,938 = 5,569 + 389,965,026,814,369 (and no decomposition with a smaller prime exists) Proof status g n p q n p q p q gives data on g n ), for n Goldbach's odd conjecture primes decompositions easily generated from the even decompositions, by systematically subtracting primes Proof status : Proved under the assumption of the truth of the generalized Riemann hypothesis; remains unproved unconditionally for only a finite (but yet not computationally coverable) set of numbers.

5. Goldbach's Conjecture A popular magazine announced a contest to solve goldbach's conjecture. Don't expect much enthusiasm from the mathematical community. Any even integer greater than 4 is the sum of two odd primes. 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. The last positive result I heard was many years ago: There is an integer N such that any odd integer greater than N is the sum of three primes. 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.

6. 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

Steven Finch's 'Favorite Mathematical Constants' website is temporarily unavailable. We hope to have this back online soon.

7. The Prime Glossary: Goldbach's Conjecture Locate a short biography on Goldbach, a description of his mathematical hypothesis, and various recommended resources. goldbach's conjecture. (another Prime Pages' Glossary entries) http://www.utm.edu/research/primes/glossary/GoldbachConjecture.html

Goldbach's conjecture (another Prime Pages ' Glossary entries) Glossary: Index Search Home Previous ... Mail Editor Prime Pages: Home Search Index 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

8. Goldbach's Conjecture And Factoring The Cryptographic Modulus Algebraic Factoring of the Cryptography Modulus and Proof of goldbach's conjecture http://findprimenumbers.coolissues.com/goldbach.htm

9. Goldbach's Conjecture - Wikipedia goldbach's conjecture. (Redirected goldbach's conjecture is one of the oldestunsolved problems in number theory and in all of mathematics. It http://www.wikipedia.org/wiki/Goldbachs_conjecture

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 Other languages: Deutsch Nederlands Goldbach's conjecture (Redirected from Goldbachs conjecture Goldbach's Conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It was first described in a letter written by Christian Goldbach to Leonhard Euler in 1742. It states: Every even number greater than 2 can be written as the sum of two primes (the same prime may be used twice). . The majority of mathematicians believe that the conjecture is true, mostly based on statistical considerations focusing on the probabilistic distribution of prime numbers : the bigger the even number, the more "likely" it becomes that it can be written as a sum of two primes. We know that every even number can be written as the sum of at most six primes, and in 1966, Chen showed that every sufficiently large even number can be written as the sum of a prime and a number with at most two prime factors. In order to generate publicity for one of his books, British publisher Tony Faber offered a $ 1,000,000 prize for a proof of the conjecture. The prize was offered in 2000 and was only to be paid for proofs submitted for publication before April 2002.

10. Talk:Goldbach's Conjecture - Wikipedia Talkgoldbach's conjecture. From Wikipedia, the free encyclopedia.I believe jpg). This seems to be Goldbach's weak conjecture. Are http://www.wikipedia.org/wiki/Talk:Goldbach's_conjecture

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 Talk:Goldbach's conjecture From Wikipedia, the free encyclopedia. I believe the statement given is that in the letter from Euler to Goldbach, the letter from Goldbach to Euler said "Es scheinet wenigstens, daß eine jede Zahl, die größer ist als 2, ein aggregatum trium numerorum primorum sey." (A scan of the letter is at, http://web.archive.org/web/20010622172850/http://www.informatik.uni-giessen.de/staff/richstein/ca/goldbach.jpg) This seems to be Goldbach's weak conjecture . Are you saying that the strong conjecture discussed in this article was not made by Goldbach, but by Euler? AxelBoldt 21:26 Nov 21, 2002 (UTC)

11. Goldbach's Conjecture. a topic from mathhistory-list. goldbach's conjecture. http://mathforum.com/epigone/math-history-list/praybluvang

a topic from math-history-list Goldbach's Conjecture. post a message on this topic post a message on a new topic 6 Feb 2000 Goldbach's Conjecture. , by R. E. Taylor 7 Feb 2000 Re: Goldbach's Conjecture. , by John Conway 7 Feb 2000 Re: Goldbach's Conjecture. , by Raul Nunes 8 Feb 2000 Re: Goldbach's Conjecture. , by David Mosher The Math Forum

12. Goldbach's Conjecture goldbach's conjecture. This conjecture claims that every even integerbigger equal to 4 is expressible as the sum of two prime numbers. http://db.uwaterloo.ca/~alopez-o/math-faq/node62.html

Next: Twin primes conjecture Up: Unsolved Problems Previous: Collatz Problem Goldbach's conjecture This conjecture claims that every even integer bigger equal to 4 is expressible as the sum of two prime numbers. It has been tested for all values up to by Sinisalo. Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

13. Mf15: Uncle Petros And Goldbach's Conjecture / Apostolos Doxiadis MATHEMATICAL a list compiled by Alex Kasman. Title Uncle Petrosand goldbach's conjecture Author Apostolos Doxiadis Year 1992. http://math.cofc.edu/faculty/kasman/MATHFICT/mf15.html

a list compiled by Alex Kasman Title: Uncle Petros and Goldbach's Conjecture Author: Apostolos Doxiadis Year: 1992 This novel, recently (2000) translated from Greek, follows the attempts of fictional mathematician Petros Papachristos to prove Goldbach's Conjecture (that every even number greater than two is the sum of two primes) and the frustrations of his nephew to whom he presents the problem as an elementary test of his mathematical skills. Real mathematicians (Hardy, Ramanujan, Turing, Littlewood, Caratheodory and Godel) appear in fictionalized form in this story as well. We have on the word of Sir Michael Atiyah that "[This book] is brilliantly written a mathematical detective story of great charm-and it certainly succeeds in capturing much of the spirit of mathematical research." (What more could you ask for?) "This novel offers an excellent dramatic account of the search for truth and obsession with mathematical certainty, which mathematics itself (!) tells us is unattainable. The fictional Uncle Petros finds out from Alan Turing that `truth is not always provable'." (Contributed by Vassilis Kyrtatas) "In my opinion, this is a grave misrepresentation of mathematicians. There is also a serious mathematical mistake underlying one of the main `events' in the book: Uncle Petros wants to talk to Godel to know whether it is decidable whether a particular problem ([Goldbach Conjecture], in his case) is provable or not. Unfortunately, as should be clear to any mathematically inclined person, if we can prove that [Goldbach] is undecidable, then it must be true (since, if it is false, a counterexample exists, which is a valid counterproof). Hence we can never prove that such a proposition is undecidable. Literarywise, I was not so impressed, either. Overall I found the book to be a quick, but unsatisfying read." (Contributed by Gordon Pace

14. Flak Magazine Review Of Uncle Petros Goldbach's Conjecture, 05 Books Uncle Petros goldbach's conjecture. by Apostolos Doxiadis. BloomsburyUSA. Uncle Petros goldbach's conjecture is a riveting debut. http://flakmag.com/books/goldbach.html

Section Links Book Archives Book Submissions Guidelines Search Flak Powered by Google Recently in Books Of Paradise and Power by Robert Kagan Cad by Rick Marin Field Guide to Stains by Virginia Friedman, Melissa Wagner, and Nancy Armstrong Fat Land by Greg Critser Speer: The Final Verdict by Joachim Fest Snowball's Chance by John Reed Confessions of a Dangerous Mind by Chuck Barris Get Your War On by David Rees Why Orwell Matters by Christopher Hitchens The Punch by John Feinstein More Books: The Book Archives Mailing List Sign up for Flak's monthly e-mail updates: Subscribe Unsubscribe About Flak About Flak Emails to Flak Submissions Rec Reading Books: by Apostolos Doxiadis Bloomsbury USA "One of life's failures." That is the casual dismissal Doxiadis' narrator receives when he asks his father about his reclusive uncle Petros Papachristos, who seems to spend all of his spare time gardening at his home in Ekali, a hamlet on the outskirts of Athens. (The novel is translated from Greek and was published in Greece in 1992.) Naturally, the narrator becomes curious, deciding to find out for himself the information his father fails to provide. Fortunately for us, he takes his reader along, as he pokes around the reclusive Petros's house and craftily reroutes and intercepts his uncle's mail.

15. Goldbach's Conjecture Anyway, your task is now to verify goldbach's conjecture for all even numbersless than a million. Input. You should take input from file P003In.txt. http://csku.edu.pk/quickP/goldbach's_conjecture.htm

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 two odd prime numbers. For example: = 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 for all even numbers less than a million. Input You should take input from file P003In.txt The input file will contain one or more test cases. Each test case consists of one even integer n with n Input will be terminated by a value of for n Download sample input file P003In.txt from here 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 n , choose the pair where the difference b a is maximized.

16. Goldbach's Conjecture (II) goldbach's conjecture (II). goldbach's conjecture For any even numbern greater than or equal to 4, there exists at least one pair http://www2.math.bas.bg/~keleved/vallad/06/686.html

17. Fiction > Reviews > Apostolos Doxiadis 1988; The Three Little Men. 1997; (Uncle Petros and goldbach's conjecture.2000). Apostolos Doxiadis. Uncle Petros and goldbach's conjecture. Faber. 2000. http://www-users.cs.york.ac.uk/~susan/bib/fiction/d/doxiadis.htm

Apostolos Doxiadis Novels/collections Search Web for Apostolos Doxiadis Google search Alta Vista search Novels/Collections A Parallel Life Macabetas The Three Little Men Uncle Petros and Goldbach's Conjecture Novels/Collections : reviews Apostolos Doxiadis. Uncle Petros and Goldbach's Conjecture . Faber. 2000 Review: Goldbach's Conjecture

18. Goldbach's Conjecture A Probability Approach to Goldbach’s Conjecture. Fat C. Lam. INTRODUCTION. Today,nearly three centuries later, Goldbach’s conjecture is yet unproven. http://depts.gallaudet.edu/mathcs/papers/goldbach.htm

A Probability Approach to Goldbach’s Conjecture Fat C. Lam INTRODUCTION. In a letter dated June 7, 1742 to Swiss mathematician Leonard Euler, Christian Goldbach suggested that every odd number is the sum of three primes. Euler took it a step further by stating that every even number (greater than 2) is the sum of two primes. Today, nearly three centuries later, Goldbach’s conjecture is yet unproven. Some progress has been made but the conjecture is still far from being proved. In 1937, Goldbach’s original suggestion that every odd number is the sum of three primes was proved by Russian mathematician Ivan Vinogradov. But a proof of the conjecture which today bears Goldbach’s name is still elusive. In 1996, Chinese mathematician Jing-Run Chen proved a theorem that every even number is the sum of a prime and an ‘almost prime,’ which is sort of close to the Goldbach Conjecture (GC). (A number is almost prime if is has at most two factors.) EXAMPLES Examples of Goldbach’s Conjecture: For each even integer c, there may be more than one distinct representation of c. For instance

19. Editorial Reviews: Uncle Petros And Goldbach's Conjecture Reviews of Uncle Petros and goldbach's conjecture by Apostolos DoxiadisFrom Kirkus Reviews An intellectual thriller that manages http://www.maths.ex.ac.uk/~mwatkins/zeta/doxiadis.htm

Reviews of Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis From Kirkus Reviews Oliver Sacks 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.

20. Read This: Uncle Petros And Goldbach's Conjecture Read This! The MAA Online book review column review of Uncle Petrosand goldbach's conjecture, by Apostolos Doxiadis. Read This! 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, Gödel, and Turing also make cameo appearances in the novel.)

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