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Topic: Goldbach problem

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	Goldbach biography
		Goldbach was recording secretary for the opening ceremony of the Academy which was held on 27 December 1725, and continued to act in this role until January 1728.
		Goldbach was appointed to the position and he moved to Moscow when Peter moved the court there in January 1728.
		Goldbach's problem, however, was that as well as being heavily involved with the administration of the Academy, he was also rising to more responsible roles in the government of Russia.
	www-history.mcs.st-andrews.ac.uk /Biographies/Goldbach.html (1758 words)

	Encyclopedia: Goldbach problem (Site not responding. Last check: 2007-10-23)
		In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics.
		The former conjecture is known today as the "weak" Goldbach conjecture, the latter as the "strong" Goldbach conjecture.
		The strong Goldbach conjecture is in fact very similar to the twin prime conjecture, and the two conjectures are believed to be of roughly comparable difficulty.
	www.nationmaster.com /encyclopedia/Goldbach-problem (1343 words)

	Goldbach's conjecture (Site not responding. Last check: 2007-10-23)
		In mathematics, Goldbach's conjecture is one of the oldest unsolved problemss in number theory and in all of mathematics.
		The majority of mathematicians believe the (strong) 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.
		H.A. Pogorzelski circulated a proof of the Goldbach conjecture in 1977, but this work is not generally accepted in mathematical circles.
	www.sciencedaily.com /encyclopedia/goldbach_s_conjecture (699 words)

	Goldbach problem. Who is Goldbach problem? What is Goldbach problem? Where is Goldbach problem? Definition of Goldbach ...
		Goldbach's Conjecture is one of the oldest unsolved problem in number theory and in all of mathematics.
		In 1982 Doug Lenat's Automated Mathematician independently rediscovered Goldbach's Conjecture in one of the earliest demonstrations that Artificial Intelligences were capable of scientific discovery.
		Goldbach made two related conjectures about sums of primes, the 'strong' Goldbach conjecture and the 'weak' Goldbach conjecture.
	knowledgerush.com /kr/encyclopedia/Goldbach_problem (407 words)

	Goldbach problem Definition / Goldbach problem Research (Site not responding. Last check: 2007-10-23)
		In mathematics, Goldbach's conjecture is one of the oldest unsolved problemsThis article describes some currently unsolved problems in mathematics.
		Goldbach problem is the question of whether the set of primes has an additive.
		Goldbach problem is the question of whether the set of primes has an additive decomposition in the following sense.
	www.elresearch.com /Goldbach_problem (493 words)

	Prime Conjectures and Open Question
		Goldbach wrote a letter to Euler in 1742 suggesting that every integer n > 5 is the sum of three primes.
		Ramaré95] (Goldbach's conjecture suggests two) and in 1966 Chen proved every sufficiently large even integers is the sum of a prime plus a number with no more than two prime factors (a P
		Goldbach conjecture also showed that every even number is the difference between a prime and a P
	primes.utm.edu /notes/conjectures (580 words)

	Goldbach's conjecture (Site not responding. Last check: 2007-10-23)
		Goldbach wrote a letter to Euler dated June 7, 1742 suggesting (roughly) that every even integer is the sum of two integers p and q where each of p and q are either one or odd primes.
		Goldbach's conjecture: Every even integer n greater than two is the sum of two primes.
		Progress has been made on this problem, but slowly--it may be quite awhile before the work is complete.
	library.thinkquest.org /C006364/ENGLISH/problem/goldbach.htm (358 words)

	Goldbach's conjecture - Enpsychlopedia (Site not responding. Last check: 2007-10-23)
		The former conjecture is today known as the "ternary" Goldbach conjecture, the latter as the "strong" Goldbach conjecture.
		Because it is easily understood by laymen, Goldbach's conjecture is a popular target for pseudomathematicians who attempt to prove it, sometimes even disprove it, using only high-school-level mathematics.
		It is possible that problems like Goldbach's conjecture may yield to simple methods, but given the amount of professional attention given to these problems, it is unlikely that the first solution will be easy to find.
	www.grohol.com /psypsych/Goldbach_problem (1569 words)

	Springer Online Reference Works
		One of the well-known problems in number theory: To give a proof that every odd integer equal to or larger than 7 can be written as the sum of three prime numbers.
		Euler replied by pointing out that in order to solve this problem it is sufficient to prove that every even number
		In [a1] a concise proof can be found of Vinogradov's result on the ternary Goldbach problem.
	eom.springer.de /g/g044550.htm (368 words)

	Goldbach Conjecture Research
		Goldbach made the conjecture that every odd number > 6 is equal to the sum of three primes.
		The Goldbach partition shall be denoted by the representation n = p + q, where p and q are prime.
		The smallest prime in the Goldbach partition is indicated by partition function g(n).
	www.petrospec-technologies.com /Herkommer/goldbach.htm (1445 words)

	Search Results for problem*
		Open problems and unresolved difficulties are carefully noted, and the reader is never left in doubt as to whether he is presented with a mathematical theorem or with a conjecture based on physical experience.
		This marriage caused problems for Sofia and, throughout its fifteen years, it was a source of intermittent sorrow, exasperation and tension and her concentration was broken by her frequent quarrels and misunderstandings with her husband.
		Important problems in the linear theory of the equilibrium of beams of isotropic elastic material have usually been approached by the so-called semi-inverse method, whereby a system of stresses or displacements is guessed and subsequently verified.
	www-groups.dcs.st-and.ac.uk /history/Search/historysearch.cgi?SUGGESTION=problem*&CONTEXT=1 (17725 words)

	Prime Conjectures and Open Question
		Goldbach wrote a letter to Euler in 1742 suggesting that every integer n > 5 is the sum of three primes.
		Ramaré95] (Goldbach's conjecture suggests two) and in 1966 Chen proved every sufficiently large even integers is the sum of a prime plus a number with no more than two prime factors (a P
		Goldbach conjecture also showed that every even number is the difference between a prime and a P
	www.utm.edu /research/primes/notes/conjectures (566 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		Unsolved Problem 13: (Rational Distances to the Vertices of a Square) Is there a point in the plane that is at a rational distance from each of the four corners of a unit square?
		Unsolved Problem 28: (Expressing 3 as the Sum of Three Cubes) The number 3 can be written as 1^3+1^3+1^3 and also as 4^3+4^3+(-5)^3.
		Unsolved Problem 29: (Fitting One Triangle Inside Another) Let triangles A and B have edge lengths a1, a2, a3, and b1, b2, b3, respectively.
	lifc.univ-fcomte.fr /~dedu/math/unsolvedPbs.txt (1899 words)

	Goldbach's conjecture biography .ms (Site not responding. Last check: 2007-10-23)
		Chen Jingrun showed in 1966 using the methods of sieve theory that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes)—e.g., 100 = 23 + 7·11.
		Viktar Karpau (Victor Karpov), a mathematician from Belarus, allegedly found a proof of Goldbach's conjecture which was published in September 2004.
		It shares this fate with the four-color theorem and Fermat's Last Theorem, both of which also have easily stated problems and enormously difficult solutions, making them common targets for mathematical cranks.
	www.biography.ms /Goldbach_problem.html (1350 words)

	Spring 2003 - Problem 2 (Site not responding. Last check: 2007-10-23)
		The Goldbach conjecture states that any positive even number greater than or equal to 4 can be expressed as the sum of two prime numbers.
		For purposes of this problem, 1 is not considered a prime number, but 2 is considered a prime number.
		Note, answers to this problem are not necessarily unique and the order of the primes does not matter.
	www.nmt.edu /~acm/old/problems/goldbach.html (301 words)

	Open Questions: Number Theory
		Goldbach's conjecture says that every integer larger than 2 can be expressed (perhaps in many ways) as a sum of two primes.
		To be sure, this problem sounds rather specialized, but it's still rather surprising to imagine that only one set of numbers meeting the stated conditions can exist.
		Now that Fermat's problem has been solved, one might wonder whether there are any interesting generalizations to consider, or in fact any other problems in the area of Diophantine equations that are similarly important and challenging.
	www.openquestions.com /oq-ma001.htm (3870 words)

	Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis (Site not responding. Last check: 2007-10-23)
		This is probably what lies at the heart of Goldbach's Conjecture: he speculated that the bigger the even number, the more likely it would be that he was correct, since the number of chances would multiply.
		For Goldbach, this meant that he could quite happily make his conjecture, because the chances of his being proved wrong were so small, (probably smaller than the chance of someone winning the lottery and being killed by a meteorite on the same night!).
		The one big problem with Goldbach's Conjecture is that there seems to be no magic formula with which to prove it, with the only way forward seeming to be to check every even number in existence, to see if Goldbach is right.
	www.authortrek.com /uncle_petros.html (1924 words)

	Goldbach's Conjecture
		The goal is either to prove Goldbach or to disprove Goldbach.
		Goldbach's conjecture has two boundaries that set limits on how masking may occur.
		The first condition is the symmetry of the masking pattern around 1/2 G. The second condition occurs from where zero pairs with G through the critical region.
	www.geocities.com /CapeCanaveral/Launchpad/5577/musings/goldbach.htm (2149 words)

	Cardiff University School of Mathematics Home Page (Site not responding. Last check: 2007-10-23)
		Sieve methods were created to attack the well-known Goldbach and twin-prime problems.
		Goldbach problem in strong form: is every reasonably large even number a sum of two prime numbers?
		It turns out that there are excellent reasons why sieve methods alone cannot solve these problems, but they give partial information on these and many other problems where the `deeper' methods of analytic number theory, such as exponential sums will not work.
	www.cf.ac.uk /maths/numbertheory/sieves.html (174 words)

	Goldbach conjecture verification (Site not responding. Last check: 2007-10-23)
		The Goldbach conjecture is one of the oldest unsolved problems in number theory [1, problem C1].
		In order to verify the Goldbach conjecture for a given n, it is sufficient to find one of its Goldbach partitions.
		Besides the expected near exponential decay of D(x;p), it is interesting to observe that there exists a distinct difference of behavior in the values of this function when p is a multiple of three plus one (white dots) and when it is not (yellow dots).
	www.ieeta.pt /~tos/goldbach.html (1153 words)

	Goldbach (Site not responding. Last check: 2007-10-23)
		In 1725 Christian Goldbach became professor of mathematics and historian at St Petersburg.
		Goldbach also conjectured that every odd number is the sum of three primes.
		Goldbach also studied infinite sums, the theory of curves and the theory of equations.
	www-groups.dcs.st-andrews.ac.uk /~history/Mathematicians/Goldbach.html (147 words)

	[No title]
		In this well-written expository paper, the author surveys the history of prime number theory with an emphasis on the twin prime problem; in particular, there is a short biography with a photo of Viggo Brun, a pioneer in the study of this problem.
		The topics covered are: sums of polygonal numbers; elementary results on Waring's problem, including Hilbert's work; the Hardy-Littlewood method; estimates for primes; Brun's theorem on twin primes; the Selberg sieve; Shnirelman's theorem on the Goldbach problem; Vinogradov's 3 primes theorem; the linear sieve; and Chen's theorem.
		The reader is left in the dark regarding both the variety and type of problem being studied, and the depth and sophistication of the tools being used in modern number theory.
	www.math.niu.edu /~rusin/known-math/99/twins (2106 words)

	Primesbehaviour
		In 1742, a Prussian mathematician called Christian Goldbach felt interested about the relation between prime numbers (all those numbers that only can be divided by themselves and 1 –all the others are called composite numbers-) and even numbers.
		In a letter written to the great mathematician Leonard Euler, he proposed a problem that has been called ‘Goldbach Conjecture’, which says that any even number can be expressed as the addition of two prime numbers.
		The problem now is that in the figure we see all the combinations, and we only need those composed for 2 prime numbers: we look for GC’s.
	eureka.ya.com /angelgalicia30/Primesbehaviour.htm (1596 words)

	Publications of R. C. Vaughan
		On Waring's problem for cubes, J. für die reine und angewandte Mathematik, 365(1986), 122-170.
		On Waring's problem for smaller exponents II, Mathematika, 33(1986), 6-22.
		A generalised divisor problem, J. für die reine und angewandte Mathematik, 537(2001), 151-163.
	www.math.psu.edu /rvaughan/rcvpubs.html (1137 words)

	[No title]
		In addition, we have verified the Goldbach conjecture for all of the even numbers in the intervals $[10\sp {5i},10\sp {5i}+10\sp 8]$, for $i=3,4,\cdots,20$ and $[10\sp {10i},10\sp {10i}+10\sp 9]$, for $i=20,21,\cdots,30$.
		This implies that the odd Goldbach hypothesis is a consequence of GRH.
		Subject: Re: Goldbach conjecture Date: Tue, 19 Sep 2000 11:31:21 +0200 Newsgroups: sci.math freelancefabulous@my-deja.com wrote: > Actually it is pretty clear that the twin primes > is a corollary of GC.
	www.math.niu.edu /~rusin/known-math/00_incoming/goldbach (1233 words)

	riemann (Site not responding. Last check: 2007-10-23)
		The Riemann Hypothesis is currently the most famous unsolved problem in mathematics.
		Like the Goldbach Conjecture (all positive even integers greater than two can be expressed as the sum of two primes), it seems true, but is very hard to prove.
		May 4 2002 -- The first ten billion zeroes are on the critical line, 1/2.
	www.mathpuzzle.com /riemann.html (309 words)

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