References of Goldbach's Conjecture?

Question

If one want to read the proof of Jingrun Chen's theorem called '$1+2$' of Goldbach's Conjecture, then before that he/she should read which books about number theory?

Answer 1

You'll want to look for books on "sieve theory". It's pretty slow reading, due in part to a lot of notation (and partially because sieve results tend to be proved in great generality, so that they are broadly useful).

Three well-known books on sieve theory are one by Halberstam and Richert (Sieve Methods), one by Cojocaru and Murty (An Introduction to Sieve Methods and Their Applications), and one by Friedlander and Iwaniec (Opera de Cribro, which despite the title really is in English).

Answer 2

Chapter 10 in Melvyn B. Nathanson's book "Additive Number Theory" is about Chen's Theorem. I feel that the structure of the proof is pretty clear, even though I am still trying to understand the details.

Answer 3

Although the references mentioned by Greg martin and Adam do contain a full derivation of Chen's theorem, I personally do not recommend them if you want an systematic investigation into Goldbach's conjecture.

I would recommend Yuan Wang's The Goldbach Conjecture, a collection of significant research paper focusing on the conjecture (the representation of large odd integers as sum of 3 primes, the "a+b" problem including Chen's original paper). By navigating through this collection, one can obtain a better understanding on the historical progress to this problem.

In addition, because early researchers construct sieves from concrete problems, reading this collection allows you to better understand the motivation behind abstract sieves constructed in Halberstam & Richert's Sieve Methods and Nathanson's Additive Number Theory I: Classical bases.