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Goldbach's Conjecture:     more books (25)

Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession by Apostolos Doxiadis, 2001-02-03 The Goldbach Conjecture (2nd Edition) Transtheoretic Foundations of Mathematics, Volume 1C: Goldbach Conjecture by H. Pogorzelski, 1997-12 Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis, 2001-03-05 Oncle Petros ou la conjecture de Goldbach by Apostolos Doxiadis, 2002-01-14 The Goldbach Conjecture and the Universe of Primes by Charles William Johnson, 2007-11-26 Uncle Petros and Goldbach's Conjecture : A Novel of Mathematical Obsession by Apostolos K. Doxiadis, 2000 Hilbert's Problems: Goldbach's Conjecture, Continuum Hypothesis, Consistency, Diophantine Set, Hilbert's Third Problem, Hilbert's Tenth Problem Uncle Petros and Goldbachs Conjecture - 2000 publication. by Apostolos Doxiadis, 2000 Conjectures About Prime Numbers: Goldbach's Conjecture, Twin Prime Conjecture, Goldbach's Weak Conjecture, Schinzel's Hypothesis H Goldbach Conjecture Uncle Petros and Goldbach's Conjecture.(Review): An article from: World Literature Today by Minas Savvas, 2000-06-22 Analytic Number Theory: Goldbach's Conjecture, Prime Number Theorem, Elliptic Curve, Elliptic Function, Brun's Constant Additive Number Theory: Goldbach's conjecture, Waring's problem, Goldbach's weak conjecture, Polite number, Schnirelmann density

lists with details

41. Goldbach's Conjecture
    Goldbach s Conjecture is one of the oldest unsolved problems in number theory Goldbach made two related conjectures about sums of primes, the strong  
    http://www.fact-index.com/g/go/goldbach_s_conjecture.html
    
    Extractions: Main Page See live article Alphabetical index Goldbach's Conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: (The same prime may be used twice.) The conjecture had been known to Descartes . The following statement is equivalent and is the one originally conjectured in a letter written by Goldbach to Euler in . The majority of mathematicians believe the conjecture to be 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. As a result of work by Vinogradov, every sufficiently large even number can be written as the sum of at most four primes. Vinogradov proved furthermore that almost all even numbers can be written as the sum of two primes (in the sense that the fraction of even numbers which can be so written tends towards 1). In

42. Goldbach's Conjecture
    Apr 11, 2000 A popular magazine announced a contest to solve Goldbach s Conjecture. Don t expect much enthusiasm from the mathematical community.  
    http://math.fau.edu/locke/Goldbach.htm
    
    Extractions: 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. Vinogradov (1937): There is an integer N such that any odd integer greater than N is the sum of three primes.

43. Goldbach's Conjecture@Everything2.com
    The conjecture that every even number may be expressed as the sum of 2 prime number s. This conjecture has yet to be prove d or disproved. The conjecture has been tested  
    http://www.everything2.com/title/Goldbach%27s conjecture

44. Goldbach Conjecture Verification
    Computational results up to 3.10^17 and graphics by Tomás Oliveira e Silva.  
    http://www.ieeta.pt/~tos/goldbach.html
    
    Extractions: Introduction News Results Top 50 ... [Up] 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

45. Goldbach Conjecture
    Maths What different approaches have been applied in attempts to mathematically prove and verify that Goldbach s bi.  
    http://www.slideshare.net/Anil1091/goldbach-conjecture-1822075

46. F. Conjectures (Math 413, Number Theory)
    Verifying Goldbach's Conjecture up to 4 x 10 14; Catalan's Conjecture. Conj The only consecutive prime powers are 8=2 3 and 9=3 2. Langevin and Tijdeman showed that any counterexamples must  
    http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html
    
    Extractions: F. Conjectures Number Theory, Math 413, Fall 1998 A collection of easily stated number theory conjectures which are still open. Each conjecture is stated along with a collection of accessible references. The Riemann Hypothesis Fermat Numbers Goldbach's Conjecture Catalan's Conjecture ... The Collatz Problem Def: Riemann's Zeta function, Z(s), is defined as the analytic extension of sum n infty n s Thm: Z( s )=prod i infty p i s , where p i is the i th prime. Thm: The only zeros of Z( s ) are at s s Conj: The only zeros of Z( s ) are at s =-2, -4, -6, ... and on the line Re( s Thm: The Riemann Conjecture is equivalent to the conjecture that for some constant c x )-li( x c sqrt( x )ln( x where pi( x ) is the prime counting function. Def: n is perfect if it is equal to the sum of its divisors (except itself). Examples are 6=1+2+3, 28, 496, 8128, ... Def: The n th Mersenne Number, M

47. Goldbach Conjecture
    File Format PDF/Adobe Acrobat Quick View  
    http://www.imsc.res.in/~sitabhra/meetings/school10/Balasubramanian_Chennai2010_s

48. Goldbach Summary
    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  
    http://www-history.mcs.st-and.ac.uk/Mathematicians/Goldbach.html
    
    Extractions: 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:

49. Goldbach's Conjecture
    2008/9 Schools Wikipedia Selection. Related subjects Mathematics. Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics.  
    http://schools-wikipedia.org/wp/g/Goldbach%27s_conjecture.htm

50. Goldbach's Conjecture
    The Conjecture All even numbers larger than 4 are the sum of two primes. For example 18 = 13 + 5, or 102 = 97 + 5.  
    http://conceptualmath.org/musings/goldbach.htm
    
    Extractions: The Conjecture : All even numbers larger than 4 are the sum of two primes. For example: 18 = 13 + 5, or 102 = 97 + 5. This conjecture is simple enough that a sixth grader can understand it or demonstrate examples, yet the worlds best mathematicians have not solved it in over 200 years. Math teachers : all too often we fail to demonstrate to students the value of making mistakes, and learning from false paths and divergent concepts. Sometimes what we learn along the way is more important than what we intended to discover at the beginning. Use this page to show what learning or new ideas might occur from studying arcane conjectures such as Goldbach's. The goal is either to prove Goldbach or to disprove Goldbach. There is one obvious way to disprove Goldbach, simply, find one exception to the rule. There is no obvious way to prove Goldbach, and other methods of disproving Goldbach are not so obvious. I studied Goldbach's Conjecture, but did not solve it. Neither has anyone else since Goldbach first proposed it. But here are some ideas I stumbled on in the process of studying it. Will any of these ideas help you solve it? Some Important Notes about Primes Critical Factors - The Largest Prime Needed to Test a Larger Number for Primality All composite numbers are multiples of numbers equal to or smaller than their square root. Example: All composite numbers smaller than 121 are multiples numbers smaller than 11, where 11 = sqrt(121). Since 4,6,8,9, and 10 are composite, we need only test 2,3,5, and 7. Thus, all numbers between 49 = 7^2 and 121 = 11^2 are either multiples 2,3,5, or 7, or they are prime. So we may consider 2,3,5, and 7 the

51. 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 number greater than 2 can be written  
    http://acm.uva.es/p/v5/543.html
    
    Extractions: 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 number greater than 2 can be written as the sum of three prime numbers. Goldbach cwas considering 1 as a primer number, a convention that is no longer followed. Later on, Euler re-expressed the conjecture as: Every even number greater than or equal to 4 can be expressed as the sum of two prime numbers. Anyway, your task is now to verify Goldbach's conjecture as expressed by Euler for all even numbers less than a million. 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 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

52. Goldbach Conjecture (mathematics) -- Britannica Online Encyclopedia
    Goldbach conjecture (mathematics), in number theory, assertion (here stated in modern terms) that every even counting number greater than 2 is equal to the  
    http://www.britannica.com/EBchecked/topic/237447/Goldbach-conjecture
    
    Extractions: document.write(''); Search Site: With all of these words With the exact phrase With any of these words Without these words Home My Britannica CREATE MY Goldbach con... NEW ARTICLE ... SAVE Table of Contents: Goldbach conjecture Article Article Related Articles Related Articles External Web sites External Web sites Citations ARTICLE from the Goldbach conjecture in number theory , assertion (here stated in modern terms) that every even counting number greater than 2 is equal to the sum of two prime numbers. The Russian mathematician Christian Goldbach first proposed this conjecture in a letter to the Swiss mathematician Leonhard Euler prime numbers Edward Waring Meditationes algebraicae (1770), which also contained

53. Goldbach's Conjecture On GetGlue
    Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states Expressing a given even number as a sum of two primes is  
    http://getglue.com/topics/p/goldbachs_conjecture
    
    Extractions: GetGlue Hi! This is a topic page on Glue! Glue is a free service connecting your friends and fans around entertainment you love. Check-in and rate things to discover new favorites, get stickers and win free stuff. Join now! takes 30 seconds You are thinking about this Just Now Feature this on your profile Check-in to your entertainment on iPhone, iPad, Android and more with GetGlue Apps Tooltip I like it More Goldbach's conjecture Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states: Expressing a given even number as a sum of two primes is called a Goldbach partition of the number. For example, In other words, the Goldbach conjecture states that every even number greater than or equal to four is a Goldbach... more Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states: Expressing a given even number as a sum of two primes is called a Goldbach partition of the number. For example, In other words, the Goldbach conjecture states that every even number greater than or equal to four is a Goldbach number, a number that can be expressed as the sum of two primes. Similar to things you like: Share Loading Suggestions

54. 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
    
    Extractions: 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.

55. Goldbach's Conjecture@Everything2.com
    The conjecture that every even number may be expressed as the sum of 2 prime number s. This conjecture has yet to be prove d or disproved. The conjecture has been tested  
    http://www.everything2.com/index.pl?node_id=450804

56. Goldbach S Conjecture On ECDSA Protocols
    File Format PDF/Adobe Acrobat Quick View  
    http://eprint.iacr.org/2003/076.ps

57. Andy Wardley: Goldbach Weave
    On Prime Numbers. Goldbach's conjecture relates to a branch of mathematics known as number theory which deals with prime numbers.  
    http://wardley.org/misc/goldbach.html

58. Springer Verlag Publishes 'Proof' Of Goldbach's Conjecture | The N-Category CafĂ
    Jun 30, 2009 Moreover, proofs of FLT and Goldbach s Conjecture (Ch.8, 9) are given, both using a residueand-carry method (with proper choice of  
    http://golem.ph.utexas.edu/category/2009/06/springer_verlag_publishes_proo.html

59. Answers.com - What Is Goldbach
    Math question What is Goldbach s conjecture? Goldbach s Conjecture is that every even number greater than two can be expressed as the sum of two prime  
    http://wiki.answers.com/Q/What_is_Goldbach's_conjecture

60. Proof Of Goldbach S Conjecture - 1 A PROOF OF GOLDBACH S
    File Format PDF/Adobe Acrobat Quick View  
    http://www.the-origin.org/goldbach.pdf

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