Consider again,
since the distance between two consecutive primes is roughly \(log(n)\) and the ratio of this distance to \(n\) is asymptotically zero by the Prime Number Theorem, the distance between the last prime and next prime as illustrated is also very narrow. And by
Bertrand–Chebyshev Theorem a prime exist between \(n\) and \(2n\). We have,
the space below the last prime \(\gt n\), is full of prime numbers. So, as \(n\rightarrow\infty\), it is easier to find \(p+q=2n\), although not necessarily certain.
The point is as \(n\rightarrow\infty\), Goldbach's Conjecture is easier to satisfy.
