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I'm in a senior seminar class for my undergraduate degree and I am tasked with writing a short, 12 page paper on some subject I have not been taught before. I chose the twin prime conjecture. My original plan was to go through the history and proofs surrounding the conjecture; however, the chair of my department told me that proving all of this material would take too much time and learning for such a short paper. He then suggested that I discuss all of the work that has been done and just prove Viggo Brun's work. Currently my outline for the paper is as follows:

  • Basic Prime proofs
  • Introduction to seiving methods and the prime number theorem
  • Analysis of Viggo Brun's seiving method and proof
  • Proof of Merten's Theorems
  • Proof of Brun's theorem
  • Analysis of Hardy-Littlewood Conjecture
  • Analysis of Goldbach Conjecture
  • Analysis of Yitang Zhang's work
  • Analysis of the most recent results

I have done some research on these topics, but any nice links to material on any of these subjects would be great. Any information that I can add to this or any site detailing the connection between the twin prime conjecture, the Goldbach conjecture, or any other conjecture would also be greatly appreciated.

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Yitang Zhang's proof is at here

For sieving method and PNT, may be this would help

Terry Tao's blog has many nice articles on Goldbach's conjecture

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  • $\begingroup$ Thank you, I have been looking everywhere for Dr. Zhang's proof. Now I just need to read it, find the important parts, and write about it (: $\endgroup$ – Pareod Mar 16 '16 at 5:47
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It's a great outline but a lot for 12 pages. I suggest you focus on Brun and Zhang's theorems, which are directly related to twin primes, and maybe drop Goldbach, Hardy-Littlewood and Mertens.

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  • $\begingroup$ I'm just having trouble thinking of what I would write really. I need Merten's theorems to prove Brun's, and I can really only discuss Zhang's proof. Going through the proof would be too much to learn for this paper. $\endgroup$ – Pareod Mar 16 '16 at 6:06

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