In general I wonder how can anything be proved about prime numbers (other than the fact that they are infinitely many), because they seem to appear quite randomly.
EDIT: I will accept if the inferential distance is simply too large. I am just hoping that maybe it isn’t.
Presumably you mean explaining the proofs? Unfortunately the proof of Dirichlet’s theorem is quite difficult starting from a high-school background, and I don’t even know the proof of Green-Tao. I can try to say something about how one could go about proving nontrivial facts about prime numbers, though; for example, various special cases of Dirichlet’s theorem are much easier to prove.
Thanks; I am not really interested in the theorem per se, but in the tools that are useful for proving it. I guess the special cases use quite different tools, which is what makes them much easier.
In general, I would like to read about things that are not high-school knowledge, but that have a short inferential distance from the high-school knowledge. But I don’t have a strong preference for anything specifically here; mostly because I don’t even know what’s there.
I don’t know if it is possible, but could you explain Dirichlet’s theorem on arithmetic progressions and Green–Tao theorem to someone with, uhm, good knowledge of high-school math, but not much beyond that?
In general I wonder how can anything be proved about prime numbers (other than the fact that they are infinitely many), because they seem to appear quite randomly.
EDIT: I will accept if the inferential distance is simply too large. I am just hoping that maybe it isn’t.
Presumably you mean explaining the proofs? Unfortunately the proof of Dirichlet’s theorem is quite difficult starting from a high-school background, and I don’t even know the proof of Green-Tao. I can try to say something about how one could go about proving nontrivial facts about prime numbers, though; for example, various special cases of Dirichlet’s theorem are much easier to prove.
Thanks; I am not really interested in the theorem per se, but in the tools that are useful for proving it. I guess the special cases use quite different tools, which is what makes them much easier.
In general, I would like to read about things that are not high-school knowledge, but that have a short inferential distance from the high-school knowledge. But I don’t have a strong preference for anything specifically here; mostly because I don’t even know what’s there.