So, I've understood the proof of
A*x/logx < pi(x) < B*x/logx for (A,B) = (0.5,2), but how can I make this difference smaller? Does any one know the methods used by him and further by J.J. Sylvester?
I'd like references in english for I found some papers in french, but could figure out anything.
Ps: pi(x) is the prime counting function