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Title: Math/Number Theory/Open Problems/Goldbach Conjecture - Mathematical Mysteries A brief popular article with an applet generating solutions.
Proof_of_the_Twin_Primes_Conjecture Goldbach's Conjecture proves and extends the Twin Primes Conjecture as probable.

A_Simple_Solution_to_the_Goldbach_Conjecture A heuristic approach by Piers Newberry.

The_Stepladder_Proof_of_The_Goldbach_Conjecture A proposed proof offered for criticism.

XGC An eXtension of the Goldbach Conjecture. Mathematica code.

Advanced_Placement_Digital_Library_for_Biology,_Physics_and_Chemistry An NSF funded Rice University Digital Library project that hosts free reviewed online resources, linked to the content outline, for AP and Pre-AP teachers and students of biology, physics and chemistr

All_Science_Den_com Articles about assorted topics, such as molecular biology, physics. Some include Flash animations to help explain concepts.


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Mathematical mysteries: the Goldbach conjectureclick here for the plus home page about Plus support Plus Plus sponsors subscribe to Plus terms of use search plus with google home latest issue news careers library podcasts browse Plus © 1997-2004, Millennium Mathematics Project, University of Cambridge. Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Support Plus icon Make a difference to the future of Plus Issue 2May 1997Contents 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 Editorial 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 All the latest newsSubscribe to ourfree newsletterSubscribe to the Plus podcast:+iTunesSubscribe to our RSS feed:AddThis Feed Buttonsubscribe to our RSS feedGet your own copy of all the Plus posters! May 1997 Regulars

Mathematical mysteries: the Goldbach conjecture

addthis_pub = 'plusmathsorg'; Prime numbers provide a rich source of speculative mathematicalideas. Some of the mystical atmosphere that surrounds them can betraced back to Pythagoras and his followers who formed secretbrotherhoods in Greece, during the 5th Century BC. The Pythagoreansbelieved that numbers had spiritual properties. The discovery that somenumbers such as the square root of 2 cannot be expressed exactly as theratio of two whole numbers was so shocking to Pythagoras and hisfollowers that they hushed up the proof!Today, prime numbers are fascinating but they are also of commercialimportance, since the best commercial and military ciphers depend ontheir properties. (See "Discovering new primes" in Issue 1 - it is yet to be proved that there areinfinitely many Mersenne primes.)Here is another unproved conjecture about prime numbers. It iscalled the Goldbach conjecture and may be stated as follows: Definition of GFor example: 8 = 3 + 5. Both 3 and 5 are prime numbers.20 = 13 + 7 = 17 + 3.42 = 23 + 19 = 29 + 13 = 31 + 11 = 37 + 5.Notice that there can be more than one Goldbach pair. The conjecturesays only that there is at least one, and has nothing to say aboutwhether there may be more.You can explore the Goldbach conjecture yourself with this Goldbachcalculator. Simply enter an even integer, n, greater than 4 andthe calculator will find all the Goldbach pairs.Historical NoteChristian Goldbach (1690-1764) was a Prussian amateur mathematicianand historian who lived in St Petersburg and Moscow. He made hisconjecture in a letter to Leonhard Euler, who at first treated theletter with some disdain, regarding the result as trivial. Goldbach'sconjecture, however, remains unproved to this day.Further readingFor an entertaining and revealing introduction to this problem, seeDouglas R Hofstadter's book "Gödel, Escher, Bach" (Penguin Books1979, ISBN 0 14 00 5579 7), especially the section "Aria with DiverseVariations" following chapter XII. Download PDF version | Printer friendly version Return to article contact copyright info sponsors privacy info mmpnrichmotivate Plus is part of the family of activities in the MillenniumMathematics Project, which also includes the NRICH and MOTIVATE sites. var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www.");document.write(unescape("%3Cscript src="http://pass.maths.org/issue2/xfile//" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E"));try {var pageTracker = _gat._getTracker("UA-791317-2");pageTracker._trackPageview();} catch(err) {}
 

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