This is going to be a question from Analytic Number Theory.One of the important problems in this area that led to the development of the circle method is the Goldbach problem:
Statement: Let $n\geq 4$ be even,then $n$ can be written as a sum of two primes.
Our instructor gave us a heuristic of how large the number of representations of $n$ as a sum of two primes can be.It is as follows:
Let $n$ be even,then the number of representations of $n$ as as sum of two primes should be about,
$\sum\limits_{n=n_1+n_2}\frac{1}{\log n_1}\frac{1}{\log n_2}\sim n/\log ^2n$
I think the expression on the LHS comes from some counting argument,but I am unable to figure out how the number comes.A little help will be helpful.