I'm interested in number theory, and everyone seems to be saying that "It's all about the Riemann hypothesis (RH)". I started to agree with this, but my question is:
- Why then doesn't RH imply the (asymptotic) Goldbach conjecture?
By "asymptotic" here I mean that any $n\in\mathbb N$ big enough can be written as $p+q$, with $p,q$ primes. I already asked some experts, and they told me that "RH is rather about the distribution of primes".
But look at this table, http://en.wikipedia.org/wiki/File:Goldbach-1000000.png (number of ways to write an even number n as the sum of two primes, 4 ≤ n ≤ 1,000,000) isn't that saying that the asymptotic Goldbach conjecture is also about the distribution of primes? I don't understand.
Any help would be very welcome.