Twin Prime Related Material

Question

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.

Answer 1

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

Answer 2

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.