121. Mathematical Mysteries: The Goldbach Conjecture | Plus.maths.org A brief popular article with an applet generating solutions. http://pass.maths.org/issue2/xfile/

Skip to Navigation about Plus support Plus Plus sponsors ... subscribe to Plus Search this site: Mathematical mysteries: the Goldbach conjecture Issue 2 Submitted by plusadmin on April 30, 1997 in Goldbach calculator Goldbach Conjecture Mathematical mysteries primes May 1997 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.) Here is another unproved conjecture about prime numbers. It is called the Goldbach conjecture and may be stated as follows:

122. The Hodge Conjecture A description of the conjecture by Deligne (PDF) and details of the prize offered for its resolution. http://www.claymath.org/prizeproblems/hodge.htm

123. MathWorld News: Draft Proof Of Catalan's Conjecture Circulated News brief announcing the break through that provides a history and description of the equation. http://mathworld.wolfram.com/news/2002-05-05/catalan/

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Headline News Draft Proof of Catalan's Conjecture Circulated By Eric W. Weisstein May 5, 2002Today, in an email sent to the NMBRTHRY mailing list, number theorist Alf van der Poorten confirmed that an apparent proof of the long-outstanding Catalan's conjecture has been circulated to a group of mathematicians by number theorist Preda Mihailescu. The conjecture in question was made by Belgian mathematician in 1844, and it states that 8 and 9 (2 and 3 ) are the only consecutive powers excluding and 1. In other words, Catalan conjectured that is the only nontrivial solution to the so-called Catalan's Diophantine problem x p y q three consecutive powers existed (Ribenboim 1996), Catalan's conjecture itself has stubbornly refused attack for more than a century and a half. The first groundbreaking result was that of Robert Tijdeman (1976), who showed that there can be at most a finite number of exceptions should the conjecture not hold. This led to considerable computational efforts, and in 1999, Maurice Mignotte showed that if a nontrivial solution exists, then 10 p and 10 q (Peterson 2000).

124. Goldbach Conjecture Verification Computational results up to 3.10^17 and graphics by Tom s Oliveira e Silva. http://www.ieeta.pt/~tos/goldbach.html

Goldbach conjecture verification Introduction News Results Top 50 ... [Up] Introduction The Goldbach conjecture is one of the oldest unsolved problems in number theory [1, problem C1] . In its modern form, it states that every even number larger than two can be expressed as a sum of two prime numbers. Let n be an even number larger than two, and let n=p+q , with p and q prime numbers, , be a Goldbach partition of n . Let r(n) be the number of Goldbach partitions of n . The number of ways of writing n as a sum of two prime numbers, when the order of the two primes is important, is thus R(n)=2r(n) when n/2 is not a prime and is R(n)=2r(n)-1 when n/2 is a prime. The Goldbach conjecture states that , or, equivalently, that , for every even n larger than two. In their famous memoir [2, conjecture A] , Hardy and Littlewood conjectured that when n tends to infinity, R(n) tends asymptotically to (i.e., the ratio of the two functions tends to one) n p-1 N2(n) = 2 C PRODUCT - , twin (log n)(log n-2) p odd prime p-2 divisor of n where p(p-2) C = PRODUCT - = twin p odd prime (p-1)^2 is the twin primes constant. In

125. Proof Of The Goldbach Conjecture By Kerry M. Evans This article by Kerry M. Evans attempts to show that the proposition is correct as a consequence of Wilson s Theorem. http://goldbach.yolasite.com/

Proof of the Goldbach Conjecture by Kerry M. Evans Dedicated in dear memory of my Father Dr. Roy L. Evans Nearly two-hundred, seventy years have lapsed since Christian Goldbach proposed (in 1742) that every positive even Integer, not 2, can be expressed as the sum of two primes. This manuscript shows that the proposition is correct as a consequence of Wilson’s Theorem. Little effort will be required to understand the proof as it is not complicated. Many attempts have been made to solve the problem over the years. So the author must acknowledge that it is only by a stroke of good fortune that this “discovery,” as simply and straightforwardly as it presents itself, is the result only of astute observation. The method of proof is simple once the preliminary groundwork is presented. SECTION I The first section is begun with the statement of a version of Wilson’s Theorem. As the method rests nearly entirely on the development of this theorem, there must be little doubt as to its’ few limitations. Wilson’s Theorem has been known for a long time.

126. Celebrity Gossip By Derek Hail — Celebrity Gossip, Celebrity Pictures, And Hot Discussion of rumors and conjecture, with a humorous twist to the lives of celebrities, movie reviews, and fashion. http://www.derekhail.com

ggv2id = "derekhai"; Celebrity Gossip by Derek Hail Celebrity Gossip, Celebrity Pictures, and Hot Girls with a humorous twist. October 28, 2010 My last Emmanuelle Chriqui picture from the Sharp magazine photoshoot ( sigh Then check out these luscious links: Moejackson Celebslam The Blemish Yeeeah ... Rihanna Does Marie Claire October 28, 2010 Rihanna brought her girls out (kinda) for Marie Claire . Could be better, could be worse. Once you get over that damn Ronald McDonald hair of hers, at least. What the HELL is she (or her hair stylist) thinking Rather than imitate Lady Gaga, maybe you should copy Madonna and do a coffee table book posing nude. some imitation I could get behind! Candice Swanepoel is Hot October 28, 2010 This chick is simply physically gifted. Blessed. And we are all grateful. Now if Candice could just hook up with Playboy October 27, 2010 Miranda Kerr is wasted in Glamour Check out these luscious links: Moejackson Celebslam shut The Blemish Yeeeah CityRag Hollywoodtuna ... Melissa Sata Steams Up Maxim October 27, 2010 Oh, yeah, baby! Meet Melissa Sata. As you can see, she has done one hell of a steamy photo spread with

127. MYSTERIES: FACT, FICTION AND CONJECTURE Provides accounts of many of the world s greatest mysteries. http://www.factfictionandconjecture.ca

MYSTERIES: FACT, FICTION AND CONJECTURE A RATIONAL LOOK AT THE INTRIGUING, MYSTERIOUS AND UNKNOWN FROM POLITICAL ASSASSINATIONS, SECRET SOCIETIES AND GIANT CRYPTIDS TO CLOSE ENCOUNTERS, ALIEN ABDUCTIONS AND THE SEARCH FOR EXTRATERRESTRIAL LIFE, THE FACT, THE FICTION AND THE CONJECTURE. ENTER TITLE PAGE TABLE OF CONTENTS SITE MAP

128. CONjecture 2011 Annual science fiction and fantasy convention with an emphasis on literary programming and events. Held in San Diego. http://www.conjecture.org

129. Broue's Abelian Defect Group Conjecture A record of which groups and blocks have been proved to satisfy the conjecture, maintained by Jeremy Rickard. http://www.maths.bris.ac.uk/~majcr/adgc/adgc.html

The main purpose of these pages is to keep an up-to-date record of which groups and blocks have been proved to satisfy the conjecture. This is very much a first draft, and I would very much appreciate any corrections and additions. You can email me at In particular, I would be grateful for New results. Notification of any errors, broken links, etc. on these pages. Missing references, especially to preprints. URLs where preprints can be found. Suggestions of how these pages can be made more useful, or improved in any other way. In compiling the bibliographies, I made extensive use of MathSciNet to collect references in BibTeX format, and of to create the web pages. Jeremy Rickard. What methods have been used to verify it? Which cases are known to be true? Bibliography: Published papers, etc. Preprints, etc. , with some links to online versions.

130. Beal An elementary proof of Beal s Conjecture given the proof of Fermat s Last Theorem. http://beal.yolasite.com/

Home Beal ON THE FULL BEAL CONJECTURE The purpose here is to confirm Beal’s Conjecture, specifically as a consequence of Fermat’s Last Theorem (FLT) and a defining transform, T used to generalize the problem, all in context with conditions necessary to uniquely describe the values of all supposed solutions. Consider the sum of a and b which is now unspecified: a + b a and b can be “cross-defined,” (one in terms of the other) by the transform T: a to b m b to a n with m and n greater than 2 subject to the specification p q T a b b m + a n p q which is the general representation of Beal’s Conjecture when equivalence on the right is negated. T may reapplied such that it does nothing to change the conditions on a and b. Reapplying T: T a + b = T( b m + a n b mn a mn p q The latter is possible only when a = b = 2 (see: http://fermat.yolasite.com ), in which case, 2 mn mn mn+1 Now let m n p q and further, Then m-n m-n p q n again see: http://fermat.yolasite.com Otherwise, 2 r r r+1 which is factorable to 1 z z = 2 where a = b = 1 while p q is reduced to 2. In all other cases a , b and p are factorable such that the general representation fails to hold.

131. The Prime Glossary: Catalan's Problem Entry in the Prime Glossary with description, brief history and references. http://primes.utm.edu/glossary/page.php?sort=CatalansProblem

132. A New Extreme ABC-example Explanation of an example with quality 1.920859, found by Benne de Weger and Niklas Broberg. http://deweger.xs4all.nl/oud/broberg.txt

A new extreme abc-example ========================= For coprime integers a, b, c such that a + b = c the well known "abc-conjecture" says that H(a,b,c)

133. [math/0312309] The Collatz 3n+1 Conjecture Is Unprovable A paper by Craig Alan Feinstein arguing that the Collatz Conjecture cannot be formally proved. http://arxiv.org/abs/math.GM/0312309

arXiv.org math Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PDF PostScript Other formats Current browse context: math new recent NASA ADS Bookmark what is this? Mathematics > General Mathematics Title: The Collatz 3n+1 Conjecture is Unprovable Authors: Craig Alan Feinstein (Submitted on 16 Dec 2003 ( ), last revised 4 May 2006 (this version, v16)) Abstract: In this paper, we show that any proof of the Collatz 3n+1 Conjecture must have an infinite number of lines; therefore, no formal proof is possible. We also give an informal argument that the Riemann Hypothesis is also unprovable. Comments: 3 pages. Modified the proof of Theorem 2 Subjects: General Mathematics (math.GM) MSC classes: Cite as: arXiv:math/0312309v16 [math.GM] Submission history From: Craig Alan Feinstein [ view email Tue, 16 Dec 2003 16:45:16 GMT (5kb) Fri, 9 Jan 2004 18:27:15 GMT (5kb) Wed, 14 Jan 2004 16:40:51 GMT (5kb) Thu, 15 Jan 2004 20:59:17 GMT (5kb) Tue, 20 Jan 2004 18:36:16 GMT (5kb) Fri, 23 Jan 2004 00:36:42 GMT (5kb)

134. Goldbach Summary Biography, with links to other Goldbach resources. http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Goldbach.html

Christian Goldbach Christian Goldbach was a Prussian mathematician best known for the conjecture he made in a letter to Euler that every even integer > 2 is a sum of two primes. Full MacTutor biography [Version for printing] List of References (14 books/articles) Mathematicians born in the same country Show birthplace location Other Web sites Encyclopaedia Britannica The Prime Pages (Goldbach's conjecture) J Richstein including Goldbach's letter to Euler Linda Hall Library (Star Atlas) Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR � August 2006 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Goldbach.html

135. Clay Mathematics Institute A Clay Mathematics Institute Prize problem, with description by Andrew Wiles PDF and lecture by Fernando Rodriguez-Villegas .ram. http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/

Clay Mathematics Institute Dedicated to increasing and disseminating mathematical knowledge HOME ABOUT CMI PROGRAMS AWARDS ... PUBLICATIONS Birch and Swinnerton-Dyer Conjecture Mathematicians have always been fascinated by the problem of describing all solutions in whole numbers x,y,z to algebraic equations like x + y = z The Millennium Problems Lecture by Fernando Rodriguez-Villegas at University of Texas (video) Return to top Contact Search Clay Mathematics Institute

136. Novikov Conjecture Home Page An archive of developments concerning the Novikov Conjecture and related problems in Algebraic Topology, General Topology, Geometry, Algebra, and Analysis. Maintained by Jonathan Rosenberg. http://www.math.umd.edu/users/jmr/NC.html

Novikov Conjecture Home Page The intended function of this home page is to keep you up-to-date on the latest developments concerning the Novikov Conjecture and related problems in topology, geometry, algebra, and analysis. Further contributions of all sorts are welcome. Please send them to Jonathan Rosenberg at jmr@math.umd.edu Bibliography on the Novikov Conjecture and related topics: This bibliography is based on the one in "A history and survey of the Novikov Conjecture" by Steve Ferry, Andrew Ranicki, and Jonathan Rosenberg. The original version appeared in volume 1 of "Novikov Conjectures, Index Theorems and Rigidity" (listed below under books) but we will try to update it regularly. To view the dvi file (approx. 80kb), click here . For a tar'ed dvi file (better suited for downloading), click here Some recent books: "Novikov Conjectures, Index Theorems and Rigidity," co-edited by Steve Ferry, Andrew Ranicki, and Jonathan Rosenberg, London Math. Soc. Lecture Notes, vols. 226 and 227 (approx. 380 pages each), Cambridge Univ. Press,

137. Goldbach's Conjecture And Factoring The Cryptographic Modulus Algebraic Factoring of the Cryptography Modulus and Proof of Goldbach s Conjecture http://www.coolissues.com/mathematics/Goldbach/goldbach.htm

ALGEBRAIC FACTORING OF THE CRYPTOGRAPHY MODULUS AND PROOF OF GOLDBACH'S CONJECTURE James Constant math@coolissues.com Solving an Algebraic Quadratic Equation Factors the Cryptographic Modulus p=ab of Prime Numbers a and b and Proves Goldbach's Conjecture Introduction In the RSA cryptographic system a user chooses a pair of prime numbers a and b so large that factoring the product (modulus) p=ab is beyond all projected computing capabilities. As of 1984, the consensus was that a and b need to be about 75 decimal digits in size, and so p was roughly a 150-digit number. Since the largest hard numbers that could then be factored were 80 digits or less in size, and since the difficulty of factoring grows exponentially with the size of the number, 150 digits appeared cryptosecure for the foreseeable future. In 1996, a 130 digit number was factored and cryptographers talked about 100 digit prime numbers and 200 digit moduli. Today, some suggest 1024 and 2048 digit moduli. Goldbach's conjecture (GC) suggests that every even number greater than is the sum s of two prime numbers a and b , i.e.

138. Losing The Dressing Room Blog covering football news and conjecture. http://ltdr.blogspot.com/

Losing The Dressing Room Football (soccer) conjecture, blatherings, stuff and nonsense Friday, January 22, 2010 Summer is icumen in The World Is Watching - a World Cup 2010 blog posted by Simon at 8:42 PM 19 comments Wednesday, January 06, 2010 Don't know if anybody still reads this but... who'd like to be involved in this year's World Cup group blog? It's going to start, hopefully, on 3rd March, 100 days before the first game, and during the tournament your regular interaction will of course be especially required. Any good names for it would also be welcome. This is what we got up to in 2006 posted by Simon at 5:12 PM 2 comments Sunday, March 01, 2009 HTV's video editing team takes the weekend off The boys attempting to leg up home players with two scarves tied together as they run out is particularly special. And not one of those parachutists lands properly. Highly recommended reading: Broken TV covers The Big Match Replayed posted by Simon at 10:39 PM 58 comments Let's talk about you As you can tell, what with Sweeping The Nation, other online ventures and trailing in a distant third 'life', we haven't been updating Losing The Dressing Room a lot recently. We're loathe to just abandon it, so... do you want to join in? We're looking for co-maintaners for this blog to help us keep its mix of informed comment, uninformed whimsy and YouTube embeds that only really amuse us ticking over. (And, with a World Cup next year, also looking ahead to taking part in another seperate tournament spectacular) Email address is up there on the right. No time wasters.

139. BLDGBLOG Los Angeles-based writer Geoff Manaugh provides architectural news and conjecture, heavily illustrated. http://bldgblog.blogspot.com/

140. The N! Conjecture Offers outline of the problem, bibliography, and math tables. Resources assembled by Fran ois Bergeron. http://bergeron.math.uqam.ca/conjecture_fact.html

Harmonic Polynomials for the Symmetric Group and Macdonald Symmetric Polynomials (See also A. Garsia's n! homepage , and M. Zabrocki's page on Macdonald Polynomials go down to a brief Outline of these subjects go down to Publications from various sources concerning these subjects go down to some Tables of values for various objects Outline For more information on the Garsia-Haiman conjecture (also known as the n! conjecture) stating that the bigraded Frobenius characteristic of the modules mentioned above is closely related to Macdonald polynomials The study of similar questions for diagonal harmonics is linked to the study of the nabla operator , which can be used to define a (q,t)-analog of the Catalan polynomials Also available, tables of small values of the bigraded Frobenius characteristic of the modules mentioned above, as well as some of Macdonald q,t-Kostka coefficients appearing as coefficients of Macdonald polynomials when expanded in the Schur polynomial basis. Publications Summaries of some of the manuscripts (PostScript 71K) J. Alfano, A basis for the Y2 subspace of Diagonal Harmonics , PHD. Thesis UCSD 1994.

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