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

Main Page See live article Alphabetical index Goldbach's conjecture 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.) 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 Every number greater than 5 can be written as the sum of three primes. . 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

Goldbach's Conjecture 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. Chen and Wang (1989): e e Liu and Wang (2002): e Why aren't mathematician's thrilled? Over the years, many of us have received purported proofs of famous conjectures or recently proven theorems. Examples The four colour theorem: The shortest accepted proofs so far (Haken and Appel, Seymour) have 500 or more cases. No mathematican expects that somebody will find a two-page solution in the near future. Fermat's last theorem: Andrew Wiles solved this (with a little help on one piece) after a seven-year effort. The proof is several hundred pages long. Again, no short proof is expected. Angle trisection, duplication of the cube, squaring the circle: These cannot be done with ruler and compass. It is extremely hard to convince a non-mathematician of this. However, the proof is understandable to students in undergraduate mathematics programs. If I left out your favorite problem, you don't need to contact me.

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

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

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

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 The Riemann Hypothesis 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. Refs: Unsolved Problems Elementary Number Theory http://www.utm.edu/research/primes/notes/rh.html (notes in Chris Caldwell's Prime Pages) http://match.stanford.edu/rh/ (Dan Bump's notes) 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

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

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

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. 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

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. 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 as expressed by Euler 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

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

document.write(''); Search Site: Advanced Search With all of these words With the exact phrase With any of these words Without these words Home SHOP BROWSE BLOG ... HELP Username: Password: Remember me Forgot your password? Help Email " is the e-mail address you used when you registered. Password " is case sensitive. If you need additional assistance, please contact customer support Enter the e-mail address you used when enrolling for Britannica Premium Service and we will e-mail your password to you. Goldbach-conjecture My Britannica CREATE MY Goldbach con... NEW ARTICLE ... SAVE Goldbach conjecture Table of Contents: Goldbach conjecture Article Article Related Articles Related Articles External Web sites External Web sites Citations Article Related Articles 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

GetGlue Login 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 Visits Likes Check-ins Just Checked-in You are thinking about this Just Now Obsessed? Feature this on your profile Apps Check-in to your entertainment on iPhone, iPad, Android and more with GetGlue Apps Get the Latest News Blog Twitter Tooltip I like it More Goldbach's conjecture 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 Facebook Twitter Tell Friends Recent ... Top Rated People Who Liked This geoff Adataghost Adam Ritchie Matthew Conroy ... tayoulevy 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

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

Page 3     41-60 of 90    Back | 1  | 2  | 3  | 4  | 5  | Next 20