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.


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

  • $\begingroup$ 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

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.

  • $\begingroup$ 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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