61. Factoids > Goldbach's Conjecture Goldbach s conjecture Every even number 4 is the sum of two odd primes. Goldbach s odd conjecture Every odd number = 9 is the sum of three odd 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.

62. SS > Fiction Reviews > Apostolos Doxiadis Novels/Collections. A Parallel Life. 1985; Macabetas. 1988; The Three LittleMen. 1997; Uncle Petros and Goldbach s conjecture. 2000 http://www-users.cs.york.ac.uk/~susan/bib/fiction/d/doxiadis.htm

home fiction reviews 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: Uncle Petros is dismissed as a failure by his family. His nephew is curious to find out why, and as he investigates, he discovers something remarkable: Petros was once a mathematical genius bent on proving Goldbach's Conjecture ? What happened to make him end up a virtual hermit? This is a lovely story, with some great twists along the way. The middle third is structured like a rather chatty mathematical biography indeed at least one of the incidents is lifted straight from a story by Hardy (acknowledged in a tongue-in-cheek footnote). It's about the marvelous beauty of mathematics, about what are suitable goals in life, about what constitutes failure, and about the courage of achievement. Rating: 3 worth reading reviewed 9 May 2004

63. Apostolos Doxiadis Apostolos Doxiadis. Uncle Petros and Goldbach s conjecture Uncle Petros andGoldbach’s conjecture (2000) tells the tale of brilliant mathematician http://www.apostolosdoxiadis.com/page/default.asp?id=48&la=1

64. Apostolos Doxiadis the publishers of Uncle Petros and Goldbach s conjecture, a novel by Goldbach s conjecture is easy to verify for small numbers 24=19+5 and 72=19+53. http://www.apostolosdoxiadis.com/page/default.asp?id=147&la=1

65. Sonderbooks Book Review Of Uncle Petros And Goldbach's Conjecture ****Uncle Petros and Goldbach s conjecture. by Apostolis Doxiadis. Reviewed January20, 2004. Bloomsbury, New York, 2000. First published in Greece in 1992. http://www.sonderbooks.com/Fiction/unclepetros.html

Book Reviews by Sondra Eklund Home Buy from Amazon.com Rate this Book Sonderbooks 70 ... Fiction Literary Previous Book Next Book Young Adult Fiction Children's Nonfiction ... View Bulletin Board I don't review books I don't like! *****= An all-time favorite **** = Outstanding *** = Above average ** = Enjoyable * = Good, with reservations Uncle Petros and Goldbach's Conjecture by Apostolis Doxiadis Reviewed January 20, 2004. Bloomsbury, New York, 2000. First published in Greece in 1992. 209 pages. Sonderbooks Stand-out 2004,

66. Goldbach Weave Goldbach s conjecture relates to a branch of mathematics known as number theorywhich Goldbach s original conjecture (known as the ternary Goldbach http://www.andywardley.com/misc/goldbach.html

Goldbach Weave http://wardley.org/misc/goldbach.html Miscellaneous Commmercial Email Home ... Killing Music wardley.org web Goldbach Weave Prime Numbers Goldbach's conjecture relates to a branch of mathematics known as number theory which deals with prime numbers . A prime number is a number that cannot be divided by any other number except 1 and the number itself. 13 is a prime number, for example, because it can only be divided by 1 (to get 13) or by 13 (to get 1). 15 is not a prime number, being divisible by both 3 and 5. Note that when we talk about numbers here we really mean whole numbers (known as integers or natural numbers). Of course it is possible to divide any number by any other number, but we're only interested in results that don't leave any fractions. For example, you can divide 15 by 6, for example, but you end up with 2.5 (2 ). That's clearly not an integer so it doesn't interest us here. Goldbach's original conjecture (known as the "ternary" Goldbach conjecture) was stated in a letter he wrote to Euler in 1742: Every number that is greater than 2 is the sum of three primes Christian Goldbach In this case he was treating the number 1 as a prime number but we no longer follow that convention today. Euler re-stated it in the more familiar form now known as the "binary" or "strong" Goldbach conjecture:

67. Goldbach Conjecture twoprime version of Goldbach s conjecture before either Goldbach or Euler did . Paul Erdös said, It is better that the conjecture be named after http://www.daviddarling.info/encyclopedia/G/Goldbach_conjecture.html

Return to The Worlds of David Darling INDEX LATEST NEWS ARCHIVE ... Z 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, .... In fact René Descartes knew about the two-prime version of Goldbach's conjecture before either Goldbach or Euler did. So, is it misnamed? Paul Erdös said, "It is better that the conjecture be named after Goldbach because, mathematically speaking, Descartes was infinitely rich and Goldbach was very poor." In any event, there is a much more important question, namely, is the conjecture true? The general assumption is that it is, but

68. FOM: Understanding Con(ZFC) And Goldbach's Conjecture Using Neil s example of Goldbach s conjecture, we understand GC in the strongsense if for no other reason than that we can straightforwardly verify it for http://www.cs.nyu.edu/pipermail/fom/1998-September/002074.html

FOM: understanding Con(ZFC) and Goldbach's conjecture Stephen G Simpson simpson at math.psu.edu Mon Sep 7 21:06:46 EDT 1998 Previous message: FOM: Complexity theory Next message: FOM: goading Harvey Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: FOM: Complexity theory Next message: FOM: goading Harvey Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

69. Articles - Goldbach's Conjecture He considered 1 to be a prime number, a convention subsequently abandoned.So today, Goldbach s original conjecture would be written http://www.1-electric.com/articles/Goldbach_conjecture

Home Electric Scooters Wheelchairs Lifts Origins In , 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 written as the sum of three primes. He considered 1 to be a prime number 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. The former conjecture is today known as the "ternary" Goldbach conjecture, the latter as the "strong" Goldbach conjecture. The conjecture that all odd numbers greater than 9 are the sum of three odd primes is called the "weak" Goldbach conjecture. 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 sufficiently large integers, mostly based on statistical considerations focusing on the

70. American Scientist Online - Me & Isaac Newton , Uncle Petros And Goldbach's Conj Uncle Petros and Goldbach s conjecture (Bloomsbury USA, $19.95), by ApostolosDoxiadis, is fiction that is bound to appeal to scientists and engineers. http://www.americanscientist.org/template/AssetDetail/assetid/23898

Home Current Issue Archives Bookshelf ... Subscribe In This Section Reviewed in This Issue Book Reviews by Issue New Books Received Publishers' Directory ... Virtual Bookshelf Archive Site Search Advanced Search Visitor Login Username Password Help with login Forgot your password? Change your username see list of all reviews from this issue: November-December 2000 Uncle Petros and Goldbach's Conjecture , and more . . . click for full image and caption I n , a First Look Pictures film by Michael Apted (director of the acclaimed Seven-Up series), seven scientists reflect on their lives and work and on the role of science in society: Gertrude Elion, pharmaceutical chemist (pictured); Ashok Gadgil, environmental physicist; Michio Kaku, theoretical physicist; Maja Mataric, computer scientist; Steven Pinker, cognitive scientist; Karol Sikora, professor of cancer medicine; and Patricia Wright, primatologist and conservationist. Hearing them speak about their aspirations and inspirations from childhood on, their hopes and achievements, is surprisingly moving. Highlights include Elion's description of the satisfaction of saving children's lives; Gadgil's infectious delight in finding a simple, inexpensive way to disinfect water in developing countries; Kaku?s figure skating ("When things go wrong, I get on the ice and all of the problems just melt away. . . . It's just me and Isaac Newton"); and the turns in Wright's unusual career path, from her impulsive purchase of an owl monkey in a pet shop to her role in founding Madagascar?s Ranomafana National Park with her MacArthur Fellowship money. The film opens November 3.

71. Vedic Ganita Goldbach s conjecture. Dr. SKKapoor has authored a book Goldbach Theorem inwhich proof of Goldbach s conjecture has been published as Proof of Goldbach http://www.vedicganita.org/goldbatch.htm

Why Vedic Mathematics? Glimpses of Vedic Mathematics Ganita Sutras Multidimension of Time and Space In Manasara ... Scriptures Formats Goldbach's Conjecture: Its Proof Vedic Mathematics Answer Transcendental Basis of Vedic Literature Published Books About the Scholar Feedback Goldbach's Conjecture Dr. S.K.Kapoor has authored a book "Goldbach Theorem" in which proof of Goldbach's conjecture has been published as "Proof of Goldbach Theorem". Subsequently Step 2A has been added. This proof inclusive of Step 2A is published as an Article in Issue No. 10 (July 2000) of Vedic Mathematics Newsletter Precisely the conjecture is that every even greater than 2 can be written as a pair of sum of primes. It is part of the famous letter (June 7, 1942) of Christian Goldbach (1690-1764) to great Swiss mathematician Leonhard Euler. Since then this conjecture has remained a brain teaser and unsolved problem of the order of Fermat's Last Theorem and Riemann Hypothesis. The book "Goldbach Theorem" has four chapters. The proof except Step 2A has been settled in Chapter 1 of the book. All what is presumed as background is only the mature comprehension of the whole numbers. As every even number by definition admits two parts, therefore, it is this property of evens which has come very handy to express even E as M+M. With this the maximum possible pairs with numbers to E have been formed putting a restriction that some of the numbers of the pairs should always be equal to E. The pairs are designated as duplexes. Then the recursive subsets of the source set of maximum number of duplexes of given even number E are constructed and the subset of duplexes with both numbers of the duplexes being primes is reached at. The cardinality of this set is computed as

72. Uncle Petros And Goldbach's Conjecture Read a good book? Tell the rest of the world about it. Either that or have a goslating it, on einekleine s book review pages. http://homepage.mac.com/wbaltyn/books/unclepetros.html

Uncle Petros and Goldbach's Conjecture This book is, much to my surprise, is a great little novel which deserves to become a mini-classic for those who are interested in the ideas and history behind science or mathematics but pretty much innumerate. This recommendation makes it sound dry, but rest assured that this tale of a lifetime's obsession and its effect on the relationship between an uncle and his 'most favoured nephew' is far from boring. On the contrary, former maths prodigy Apostolos Doxiadis manages to infuse his fourth novel, the story of reclusive mathematical genius Uncle Petros, with all the idealistic passion and none of the off-putting incomprehensibility of the subject. Goldbach's Conjecture is an idea first postulated two hundred and fifty years ago, that any even number is the sum of two primes. Despite its deceptive simplicity, it remains unverified to this day. As a tie-in to the publication of this book, Faber have offered $1 million to anyone who proves it within two years. But don't go rushing off for your calculators just yet - given the history of the problem, you're more likely to be crushed to death by a rogue blancmange than get the prize. It's a great publicity stunt and a cunning move on Faber's part: they know their money is safe. Let's hope they use the increased sales of the book to donate some money to the Home for Frustrated Mathematicians. But to return to the book: Uncle Petros is the black sheep of the Papachristos family, which is what attracts his insatiably curious nephew, the unnamed hero of the story, towards him. Having been warned off having anything to do with Petros, our lovable young scamp naturally enough finds out all he can about his reclusive relative, and discovers that far from being the 'failure' the rest of the family brands him, he is - or was - a world-class mathematician wrestling with one of the most famous problems in the field. This inspires the nephew to become a mathematician himself, despite Petros's discouragement, until in desperation, trying to save his nephew from the same fate, Petros is persuaded to narrate his own tragic tale of hope, despair and Number Theory. Doxiadis's achievement is to convey the drama and pathos of Petros's quest for the proof of one of the great unproven theories of mathematics, without losing the attention of innumerate (and innumerable) readers.

73. Problem 1564 * Goldbach S Conjecture Anyway, your task is now to verify Goldbach s conjecture for all even If thereis no such pair, print a line saying ``Goldbach s conjecture is wrong. http://acm.scu.edu.cn/soj/problem.do?problem=1564

74. Historia Matematica Mailing List Archive: Re: [HM] Goldbach's C Subject Re HM Goldbach s conjecture From Michele Emmer (M.Emmer@iol.it)Date Sat Mar 18 2000 042546 EST. Next message Emili Bifet Re HM http://sunsite.utk.edu/math_archives/.http/hypermail/historia/mar00/0087.html

Re: [HM] Goldbach's Conjecture Subject: Re: [HM] Goldbach's Conjecture From: Michele Emmer ( M.Emmer@iol.it Date: Sat Mar 18 2000 - 04:25:46 EST Next message: Emili Bifet: "Re: [HM] L'Hopital, Pythagoras, Ptolemy and Hilbert" Previous message: John Conway: "Re: [HM] Caratheodory Biography" In reply to: James A. Landau: "[HM] Goldbach's Conjecture" Next in thread: Julio Gonzalez Cabillon: "Re: [HM] Goldbach's Conjecture" Reply: Michele Emmer: "Re: [HM] Goldbach's Conjecture" Reply: Julio Gonzalez Cabillon: "Re: [HM] Goldbach's Conjecture" Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... http://www.royalsoc.ac.uk Your reference is to a journal called "Times", or is it "The Times"? I am interested in having a copy of the original article. Michele Emmer emmer@mat.uniroma1.it Next message: Emili Bifet: "Re: [HM] L'Hopital, Pythagoras, Ptolemy and Hilbert" Previous message: John Conway: "Re: [HM] Caratheodory Biography" In reply to: James A. Landau: "[HM] Goldbach's Conjecture" Next in thread: Julio Gonzalez Cabillon: "Re: [HM] Goldbach's Conjecture" Reply: Michele Emmer: "Re: [HM] Goldbach's Conjecture" Reply: Julio Gonzalez Cabillon: "Re: [HM] Goldbach's Conjecture" Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] This archive was generated by hypermail 2b28 Sat Mar 18 2000 - 10:43:41 EST

75. Historia Matematica Mailing List Archive: [HM] Goldbach's Conje Subject HM Goldbach s conjecture From James A. Landau (JJJRLandau@aol.com)Date Thu Mar 16 2000 102659 EST. Next message John Conway Re HM http://sunsite.utk.edu/math_archives/.http/hypermail/historia/mar00/0085.html

[HM] Goldbach's Conjecture Subject: [HM] Goldbach's Conjecture From: James A. Landau ( JJJRLandau@aol.com Date: Thu Mar 16 2000 - 10:26:59 EST Next message: John Conway: "Re: [HM] Caratheodory Biography" Previous message: M.Carmen Hernandez Martin: "Re: [HM] Kant and non-Euclidean geometry" Next in thread: Michele Emmer: "Re: [HM] Goldbach's Conjecture" Reply: Michele Emmer: "Re: [HM] Goldbach's Conjecture" Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] From the Web site of the Royal Society ( http://www.royalsoc.ac.uk dated 16 March 2000: Faber, the publisher, has offered to pay a million US dollars to the first person who can conclusively prove Golbach's Conjecture that every even number greater than two can be expressed as the sum of two primes. Article mentions several FFRS, including Professor Alan Baker [FRS] and Professor Andrew Wiles [FRS]. Times 2, pp.6-7, 1 1/2p. Back in 1982 Worldwide Computer Services announced a US $25,000 prize for a proof of the Twin Prime Conjecture "there are an infinite number of twin prime pairs". The original offer expired in 1985 and I have no idea whether

76. Biography Of Xxxxx Christian Goldbach s first conjecture is that every even number 4 is a sum of Although it has not been proved Goldbach s conjecture has been verified up http://home.uchicago.edu/~matt1/biogoldb.html

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. The most important facts to remember should be blue-boxed exactly as below. 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. The most important facts to remember should be blue-boxed exactly as below.

77. A Proof Of "Goldbach's Conjecture" Title A Proof of Goldbach s conjecture Authors Ellman, Roger Journal Goldbach s conjecture proven by analysis of how all combinations of the odd http://adsabs.harvard.edu/abs/2000math......5185E

Smithsonian/NASA ADS arXiv e-prints Abstract Service Find Similar Abstracts (with default settings below arXiv e-print (arXiv:math/0005185) Also-Read Articles Translate Abstract Title: A Proof of "Goldbach's Conjecture" Authors: Ellman, Roger Journal: eprint arXiv:math/0005185 Publication Date: Origin: ARXIV Keywords: General Mathematics Comment: 8 pages, change is non-material editing Bibliographic Code: Abstract "Goldbach's Conjecture" proven by analysis of how all combinations of the odd primes, summed in pairs, generates all of the even numbers. Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Keywords (in text query field) Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy/Planetary Instrumentation Physics/Geophysics arXiv e-prints Smithsonian/NASA ADS Homepage ADS Sitemap Query Form Preferences ... FAQ

78. Holtzbrinck Academic Marketing Uncle Petros and Goldbach s conjecture is certain to shatter your preconceptions .. . It is a novel about life choices. At every point, it revolves around http://www.holtzbrinckpublishers.com/academic/Book/BookDisplay.asp?BookKey=38075

79. Goldbach Conjecture - Definition Of Goldbach Conjecture In Encyclopedia In mathematics, Goldbach s conjecture is one of the oldest unsolved problems innumber theory and in all of mathematics. It statesEvery even number greater http://encyclopedia.laborlawtalk.com/Goldbach_conjecture

Add to Favorites General Encyclopedia Legal ... Law forum Search Word: Visit our Law forums Labor Law Accidents Law Bankruptcy Law Business Law ... Tax Law 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. Contents showTocToggle("show","hide") 1 Origins 2 Heuristic justification 3 Rigorous results 4 Trivia ... 7 References 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

80. Upload - Goldbach's Conjecture Upload Goldbach s conjecture. The Type field is used to differentiate betweenyou best solution (Normal), solutions found after the contest has ended http://terje.perlgolf.org/wsp/pgas/score.pl?func=show&template=upload&hole=41&se

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