| 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. |
| American_Communications_Foundation_Newsource__Science_&_Technology Assists the commercial broadcast news media in its coverage of science and technology, which is often under-reported because of staffing and budgetary restraints. Enhances the coverage by providing re |
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| ANOVA_Science_Education Services public and private school districts and schools on the continental USA and in Hawaii through teacher and administrator seminars and workshops. |
| Asia_Link_program__MUMA_project A training project dedicated to improve the quality of higher education for heritage management in Asia and Europe. The project runs from March 2004 to August 2006. |
| Ask_Dr__Jekyl_and_Mr__Hyde Answers to a variety of science and technology questions, including questions you never thought to ask. |
| Athena NASA page features earth and space science resources for K-12 and teachers. Included are class exercises with data collecting and background information for each topic, as well as related links. |
| Attaining_Excellence_Through_TIMSS Resources for learning about and discussing the Third International Mathematics and Science Study, including related reports, data and commentaries. |
| BBC_Science_&_Nature Information about humans, animals, space, the planet Earth and various hot topics. Includes TV listings, Listen Again online radio, news reports, quizzes, picture galleries and games. |
| Berkshire_Biological_Supply_Company Online sale of living organisms for biology class, science fair projects, home teaching. |
| BETR_World_Science_and_Computer_Education Offering information on classes and camps for science and computer education in Maryland and Virginia. |
| Beyond_Discovery A series of articles that trace the origins of important recent technological and medical advances. Each story reveals the crucial role played by basic science. |
| Bill_Nye_the_Science_Guy Online science laboratory. Includes learning activities and show information. |
| Brainium A curriculum-based, online environment where teachers and students can share ideas, experiments and activities. |
| The_Bubblesphere All about soap bubbles. Bubble blowing, solutions, history, fun, Java games, bubble machines and trivia. |
| Candis_Mitchell\'s_Science_Teacher\'s_Site Designed to help educators search for internet material appropriate for their classrooms. |
| Cornell_Theory_Center_Math/Science_Gateway Links to resources in mathematics and science for educators and students in grades 9-12. |
| Cute_Science Learning materials for include coloring books, audio lectures, videos and workbooks. Subjects covered are math, science, and HTML. Includes product list and online order form. |
| Department_of_Energy_Science_Education_Programs Internship and fellowship opportunities for undergraduate students and teachers related to science, technology, engineering, and mathematics. |
| Did_You_Ever_Wonder? Each month a dozen questions are posed and answered by lab scientists on various topics on how things work in the natural world. |
| Dive_and_Discover__Expeditions_to_the_Seafloor An interactive distance learning web site designed to immerse your students in the exciting process of deep-sea research and exploration. |
| Dr__Carlson\'s_Science_Theater Video podcast of cool science demonstrations. |
| Dr__Fred\'s_Place Children's science author, Dr. Fred Bortz, including biographical information, list of books, FAQ's, and information about school visits. |
| Ed_Quest Includes guided links for students, lesson plans and references for teachers, as well as collaborative projects directed towards the middle school level. |
| Education_Links_-_Top_rated_educational_sites_ Collection of educational resources separated into categories such as astronomy, lesson plans, math, and webquests. |
| Educational_Resources_Catalog In addition to the catalog itself, links are provided to curriculum materials, professional development, software, visual and audiovisual classroom support, print material and online resources. |
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| The_ENC_Digital_Dozen Each month the Eisenhower National Clearinghouse selects a dozen useful math and science sites for teachers and students. Includes archives. |
| EOA_Scientific_Internet_Campus Find educational information and interactive multimedia resources in earth science,geology,oceanography,space science, astronomy, physical science, and remote sensing. |
| ERIC_Clearinghouse_for_Science,_Mathematics,_and_Environmental_Education Goal is to provide access to information for teaching and learning about science, mathematics, and the environment. |
| Every_Child_a_Scientist For those who want to take an active role in improving the science program in their schools. |
| Extreme_Science Science news and activities with an emphasis on extremes. |
| Field_Trips Includes virtual science tours on nature topics. Includes related educational resources. |
| FizzBang_Science Hands-on science books written by a high school teacher. Includes online shopping and sample experiments. |
| Frank_Potter\'s_Science_Gems Resources are sorted by category and grade level. |
| Free_Science_Worksheets Features over science labs for biology, chemistry, and physics, and numerous other printable note skeletons, graphic organizers, and worksheets. |
| Fun_With_Science A professional geophysicist maintains this collection of resources for classroom demonstrations and hands-on exercises about physics, earth science, earthquakes, math and fun illusions. Includes video |
| The_Gender_&_Science_Digital_Library_(GSDL) Aims to provide digital resources to help educators promote interest and engagement with STEM (science, technology, engineering and mathematics) topics for learners of all ages, particularly females. |
Be sure to note the scaling on the graph; there is a tremendous amount of vertical exaggeration. Each dark band in the graph represents a prime number: 3, 5, 7, 11, ... . This is a little bit confusing to understand, so lets look at a strictly increasing sequence of minimal values for n.The table below shows the minimal values for n < 1,000,000,000 (It took more than a month of 586 CPU time to create). The last column in the table is the ratio g(n) / n. The ratio is particularly interesting because is shows largest values of g(n) and we can see that it in almost every case is less than its predecessor. It therefore strictly bounds above the minimal Goldbach partition. Table of minimal Goldbach partition values for n < 1,000,000,000: n g(n) n - g(n) g(n) / n 6 3 3 0.500000000 12 5 7 0.416666667 30 7 23 0.233333333 98 19 79 0.193877551 220 23 197 0.104545455 308 31 277 0.100649351 556 47 509 0.084532374 992 73 919 0.073588710 2642 103 2539 0.038985617 5372 139 5233 0.025874907 7426 173 7253 0.023296526 43532 211 43321 0.004847009 54244 233 54011 0.004295406 63274 293 62981 0.004630654 113672 313 113359 0.002753536 128168 331 127837 0.002582548 194428 359 194069 0.001846442 194470 383 194087 0.001969455 413572 389 413183 0.000940586 503222 523 502699 0.001039303 1077422 601 1076821 0.000557813 3526958 727 3526231 0.000206127 3807404 751 3806653 0.000197247 10759922 829 10759093 0.000077045 24106882 929 24105953 0.000038537 27789878 997 27788881 0.000035876 37998938 1039 37997899 0.000027343 60119912 1093 60118819 0.000018180 113632822 1163 113631659 0.000010235 187852862 1321 187851541 0.000007032 335070838 1427 335069411 0.000004259 419911924 1583 419910341 0.000003770 721013438 1789 721011649 0.000002481Looking at the minimal Goldbach partition graphically for n < 1,000,000,000 we can observe an interesting relationship. For convenience and to aid in the interpretation, the X axis is log10(n), while the Y axis is g(n):
What the graph illustrates is what the data in the table assert, that the larger the number, the smaller the ratio between minimum g(n) and n. If this trend could be inviolably bounded below by some function, the conjecture would be proved. Looking at the Goldbach partition a different way, we can look at the number of distinct representations that exist for n. For example, as noted at the beginning of this discussion: 12 = 5 + 7 (1 distinct representation) 24 = 5 + 19 = 7 + 17 = 11 + 13 (3 distinct representations) 48 = 5 + 43 = 7 + 41 = 11 + 37 = 17 + 31 = 19 + 29 (5 distinct representations)The diagram that follows is sometimes called the "Goldbach Comet". It shows that generally the number of distinct representations increases with increasing n. If ever there was an n which had 0 distinct representations, the conjecture would be false. However, the graph, at least for n < 100,000, suggests the opposite. 
An asymptotic approach appears to provide a possible avenue for success in proving out the Goldbach Conjecture. This is the approach that I am taking in my analysis of this problem.