21. Goldbach's Conjecture Goldbach also studied infinite sums, the theory of curves and the theory of equations.goldbach's conjecture. Examples of goldbach's conjecture 100= 3 + 97. http://www.andrews.edu/~calkins/math/biograph/199899/biogoldb.htm

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. Examples of Goldbach's Conjecture: Links to find interesting facts about Goldbach and his Conjecture: History of Goldbach's Conjecture More information on Goldbach's Conjecture A short summary with examples This project was presented by students Risa Zander and Kaleena Katz in 1998.

22. Biography Of Goldbach goldbach's conjecture. Christian Goldbach's first conjecture is that every evennumber 4 is a sum of two primes. Examples of goldbach's conjecture http://www.andrews.edu/~calkins/math/biograph/biogoldb.htm

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.

23. Goldbach's Conjecture a topic from sci.math.research goldbach's conjecture. post a messageon this topic post a message on a new topic 30 Apr 1995 Goldbach's http://mathforum.org/epigone/sci.math.research/keldspolstoo

a topic from sci.math.research Goldbach's Conjecture post a message on this topic post a message on a new topic 30 Apr 1995 Goldbach's Conjecture , by robert katz 13 Jan 2003 Goldbach's conjecture , by Dale R Worley 13 Jan 2003 Re: Goldbach's conjecture , by Jim Nastos 14 Jan 2003 Re: Goldbach's conjecture , by John Baez 14 Jan 2003 Re: Goldbach's conjecture , by tchow@lsa.umich.edu 14 Jan 2003 Re: Goldbach's conjecture , by tchow@lsa.umich.edu 14 Jan 2003 Re: Goldbach's conjecture , by Victor S. Miller 20 Jan 2003 The proof of Goldbach's Conjecture , by José 3 Feb 2003 Re: Goldbach's conjecture , by Xiao-Song Lin The Math Forum

24. Re: The Proof Of Goldbach's Conjecture a topic from sci.math.research Re The proof of goldbach's conjecture.post a message on this topic post a message on a new topic http://mathforum.org/epigone/sci.math.research/skoihoaproo

a topic from sci.math.research Re: The proof of Goldbach's Conjecture post a message on this topic post a message on a new topic 23 Jan 2003 Re: The proof of Goldbach's Conjecture , by Gino Prosapio 26 Jan 2003 Re: The proof of Goldbach's Conjecture , by Steve Gray 27 Jan 2003 Re: The proof of Goldbach's Conjecture , by Jakob Jonsson The Math Forum

25. Mudd Math Fun Facts: Goldbach's Conjecture Easy level goldbach's conjecture. Here's a famous unsolved problemis every even number greater than 2 the sum of 2 primes? The http://www.math.hmc.edu/funfacts/ffiles/10002.5.shtml

hosted by the Harvey Mudd College Math Department Francis Su Any Easy Medium Advanced Search Tips List All Fun Facts Fun Facts Home About Math Fun Facts ... Other Fun Facts Features 887365 Fun Facts viewed since 20 July 1999. 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

26. Goldbach's Sequence And Goldbach's Conjecture Goldbach's Sequence And goldbach's conjecture by Huen YK CAHRC, PO.Box 1003, Singapore911101 http//web.singnet.com.sg/~activweb/ Related URLsites http//web http://web.singnet.com.sg/~huens/paper43.htm

Goldbach's Sequence And Goldbach's Conjecture by Huen Y.K. CAHRC, P.O.Box 1003, Singapore 911101 http://web.singnet.com.sg/~activweb/ Related URL-sites: http://web.singnet.com.sg/~huens/ email: huens@mbox3.singnet.com.sg (A short communication - 1st released: 18/12/97) Abstract 1. Introduction A very efficient way of weeding out unnecessary tests for noncontiguities in Goldbach's sequences, i.e. Goldbach(z), is to test only the high ends of Prime(z). This comes from a theorem on the contiguity of Odd(z)^2 in which it was proved that if the second largest odd integer is removed from Odd(z) before squaring, the resultant even integer sequence is never contiguous [11]. Since Prime(z) is a subset of Odd(z), we know that if Odd(z)^2 is not conitiguous then Prime(z)^2 of the same integer range will not be contiguous. This method is used here to extend the range of search for noncontiguous Goldbach(z) above 10^9. The method is determinstic on noncontiguities only. To determine contiguities, we still need to perform the full contiguity tests. 2. The Original Global Contiguity Tests

27. (2) Brief History Of Goldbach's Conjecture (2). Brief History of goldbach's conjecture. goldbach's conjecture. Then, in 1728,he went to Moscow as tutor to Tsar Peter II. goldbach's conjecture states http://web.singnet.com.sg/~huens/gbpage02.htm

2). Brief History of Goldbach's Conjecture Goldbach's Conjecture In 1725 Goldbach became professor of mathematics and historian at St. Peterburg. Then, in 1728, he went to Moscow as tutor to Tsar Peter II. Goldbach's Conjecture states: Every even positive integer greater than 3 is the sum of two (not necessarily distinct) primes. Go back to Homepage.

28. Indxbuls TheOrigin Foundation's Proof of goldbach's conjecture . Likewise RemainsUnchallenged. See the Proof of goldbach's conjecture in pdf format. http://www.the-origin.org/indxbuls.htm

Other Bulletins of The-Origin Foundation, Inc The-Origin Foundation's Recently Published Concise and Direct Proof of "Fermat's Last Theorem" (in Only 3 Pages of Simple Algebra) Remains Not Successfully Challenged What does this have to do with The Origin and Its Meaning ? The point is the importance of understanding the mechanism of things, the "why" not just the "what". This proof was developed in less than 10 hours of intermittent effort spread over several weeks. It was successful because, from the beginning, it was a search for why the theorem is true what effects operating cause it to be so. That attitude is essential for success in physics and philosophy. It is not enough to understand what happens. It is not enough to say "It is a physical law." One must understand the mechanisms that cause it to happen. The failure to have that attitude is why 20th Century physics has so many unresolved and by-passed problems. And, the solutions to those problems have been found in The Origin and Its Meaning because the quest there has always been to understand the underlying mechanisms involved.

29. Goldbach's Conjecture goldbach's conjecture. © Copyright 2000, Jim Loy. The modern version ofgoldbach's conjecture (called Goldbach's Strong Conjecture) is this 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

30. Conjecture 1. Goldbach's Conjecture Conjecture 1. goldbach's conjecture. In a letter of 1742 to Euler, Goldbach expressedthe belief that ‘Every integer N 5 is the sum of three primes’. http://www.primepuzzles.net/conjectures/conj_001.htm

Conjectures Conjecture 1. Goldbach's Conjecture "In a letter of 1742 to Euler, Goldbach expressed the belief that ‘ . Euler replied that this is easily seen to be equivalent to the following statement (Ref. 1, p. 291) Then as we can see the original idea was from Goldbach but the simplification and limitation of it came from Euler. By the above reasons the original statement of the Goldbach’s conjecture now is known as "the odd Goldbach conjecture". Samuli Larvala send today (11/08/98) the following interesting information about the status of the work done over this conejcture: " Matti Sinisalo has checked the conjecture up to 4*10^11. His paper was published in Math.Comp. "M.K. Sinisalo, Checking the Goldbach conjecture up to 4*10^11, Math. Comp. 61 (1993)". J-M. Deshouillers and Herman te Riele have recently checked it up to 10^14. They published a preview paper on their work when they had reached 10^13. This paper can be found at: ftp://ftp.cwi.nl/pub/herman/Goldbach/gold13.ps

31. The Structure Of The 3x + 1 Function Papers by Peter Schorer describing several new approaches.Category Science Math Number Theory Open Problems Collatz Problem...... Back to the top. About Peter Schorer's Note describing a possibleapproach to proving goldbach's conjecture Peter Schorer's Note http://www.occampress.com/

Welcome to Occam Press! Information about Occam Press and about this web site. Peter Schorer's papers on the 3 x + 1 Problem (aka the Syracuse Problem) Peter Schorer's paper, "Is There a 'Simple' Solution to Fermat's Last Theorem?". Peter Schorer's Note describing a possible approach to proving Goldbach's Conjecture. Peter Schorer's paper describing an attempt to prove the validity of Occam's Razor in a program testing context Peter Schorer's collection of notes, "Thoughts, Questions, and Projects," primarily concerned with mathematics and computer science, but also containing material on physics and economics. William Curtis's book, How to Improve Your Math Grades , which sets forth a radical new organization of mathematical subjects aimed at improving the speed of problem solving. Information about Occam Press: Occam Press is a small publisher located in Berkeley, CA. It was created to provide an outlet for independent scholars, including mathematicians and computer scientists working outside the university. We will be placing entire works on this web site. Interested persons will be able to buy printed copies directly from us. However, until the works have been placed on the web site, we offer brief descriptions of each. Interested persons may obtain sample pages, and more information, by e-mailing or calling us, or by sending us surface mail.

32. Goldbach Conjecture Research Information on research and computations on the Goldbach Conjecture. By Mark Herkommer.Category Science Math Open Problems Goldbach Conjecture...... A Proof That goldbach's conjecture Is True 34 = 3 + 31. 28 = 5 + 23. 18= 5 + 13. 8 = 3 + 5. 2. Another Proof That goldbach's conjecture Is True http://www.flash.net/~mherk/goldbach.htm

Goldbach Conjecture Research by Mark Herkommer June 23, 2002 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).

33. Goldbach's Conjecture goldbach's conjecture. In Anyway, your task is now to verify Goldbach'sconjecture for all even numbers less than a million. Input. The http://www.en.oit.edu.tw/web/軟體競賽/datas/Lv_1/543/543.htm

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 two odd 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 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 n , choose the pair where the difference b a is maximized.

34. In Quest Of Information About Goldbach's Conjecture Moledet, 17.VI.2000 In quest of information about goldbach's conjecture.Aroused by an essay in NY Times of end April 2000 I was http://www.private.org.il/goldbach.html

Moledet, 17.VI.2000 In quest of information about Goldbach's conjecture Aroused by an essay in N.Y. Times of end April 2000 I was inspired to the following arrangement : Put in a horizontal row the odd primes in their natural order, the same in a vertical column and put at the points of intersection of coordinates the sum of the two primes concerned. In the main diagonal we will find the double of every prime in natural order, dividing between two mirrored parts; say, in the lower, left part, we find all the possible sums, and we count their appearances according to order. The total of all splittings up to some limit is equal to the area concerned, and therefore the average of representations of every even sum will grow indefinitely as the number of primes, specially here from i to , but naturally there are fluctuations between local maxima and local minima. In the domain under examination (up to 560) these fluctuations stay between twice and half the average about x1.6 and x0.6; statistically there is no tendency for the minimum to be , contrary to Goldbach's conjecture.

35. For "provers" Of Goldbach's Conjecture For provers of goldbach's conjecture. Does your proof of Goldbach'sconjecture includes some heuristic like the number of prime http://www.asdf.org/~fatphil/math/goldbach.html

For "provers" of Goldbach's Conjecture Does your proof of Goldbach's conjecture includes some heuristic like : the number of prime pairs summing to each even number increases as the even number target increases so it'll never be zero? If so, then please analyse the behaviour of the following function using the same approach, and tell me if it ever equals zero: f(n)=n!*(n-2)^2*(n-7686)^2*(n-47474748489367)^2*(n-64367436784367867634673466)^2*(n-34867678456784576763546546785468754687568754678546786)^2

36. Mathematical Mysteries: The Goldbach Conjecture A brief popular article with an applet generating solutions.Category Science Math Open Problems Goldbach Conjecture...... with some disdain, regarding the result as trivial. goldbach's conjecture,however, remains unproved to this day. Further reading. http://plus.maths.org/issue2/xfile/

PRIME NRICH PLUS Current Issue ... Subject index Issue 22: Jan 03 Issue 21: Sep 02 Issue 20: May 02 Issue 19: Mar 02 Issue 18: Jan 02 Issue 17: Nov 01 Issue 16: Sep 01 Issue 15: Jun 01 Issue 14: Mar 01 Issue 13: Jan 01 Issue 12: Sep 00 Issue 11: Jun 00 Issue 10: Jan 00 Issue 9: Sep 99 Issue 8: May 99 Issue 7: Jan 99 Issue 6: Sep 98 Issue 5: May 98 Issue 4: Jan 98 Issue 3: Sep 97 Issue 2: May 97 Issue 1: Jan 97 Mathematical mysteries: the Goldbach conjecture 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.)

37. Gold For Goldbach In Issue 2 of Plus, we introduced you to goldbach's conjecture, the speculationby mathematician Christian Goldbach in a 1742 letter to Leonhard Euler that http://plus.maths.org/issue11/news/Goldbach/

PRIME NRICH PLUS Current Issue ... Subject index Issue 22: Jan 03 Issue 21: Sep 02 Issue 20: May 02 Issue 19: Mar 02 Issue 18: Jan 02 Issue 17: Nov 01 Issue 16: Sep 01 Issue 15: Jun 01 Issue 14: Mar 01 Issue 13: Jan 01 Issue 12: Sep 00 Issue 11: Jun 00 Issue 10: Jan 00 Issue 9: Sep 99 Issue 8: May 99 Issue 7: Jan 99 Issue 6: Sep 98 Issue 5: May 98 Issue 4: Jan 98 Issue 3: Sep 97 Issue 2: May 97 Issue 1: Jan 97 Gold for Goldbach 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 n > 5 is the sum of three primes". It was Euler who pointed out that this is easily seen to be equivalent to the statement that "Every even integer is the sum of two primes", the standard description of "Goldbach's Conjecture".

38. Apostolos Doxiadis. Uncle Petros And Goldbach's Conjecture http://www.lesekost.de/HHL154.htm

Apostolos Doxiadis. Uncle Petros and Goldbach's Conjecture Nachdem ich von Simon Singhs Fermat's Enigma der Goldbachschen Vermutung Empfehlenswert. Bei Amazon nachschauen durch Klick aufs Bild Onkel Petros und die Goldbachsche Vermutung Uncle Petros and Goldbach's Conjecture

39. Apostolos Doxiadis brilliant and foolhardy enough to stake everything on solving a problem that hasdefied all attempts at proof for nearly three centuries goldbach's conjecture http://www.apostolosdoxiadis.com/petros-about.htm

Apostolos Doxiadis Home Biography Works News News checkdata('1','8'); Upcoming project: "Logicomix: the story of logic" >> checkdata('0','5'); Lecture: "Narrative as a form of knowledge" >> checkdata('0','4'); Lecture: "Mathemathics, a human adventure" >> Sign Up Contact Info

40. Apostolos Doxiadis Home, RULES OF THE goldbach's conjecture CHALLENGE (15.3.00) NO PURCHASENECESSARY. Terms and Conditions. goldbach's conjecture was http://www.apostolosdoxiadis.com/rules.htm

Apostolos Doxiadis Home Biography Works News News checkdata('1','8'); Upcoming project: "Logicomix: the story of logic" >> checkdata('0','5'); Lecture: "Narrative as a form of knowledge" >> checkdata('0','4'); Lecture: "Mathemathics, a human adventure" >> Sign Up Contact Info

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