Counting primes in the interval (n^2,(n+1)^2)
Abstract
In this note, we show that there are many infinity positive integer values of $n$ in which, the following inequality holds $$ \left\lfloor{1/2}(\frac{(n+1)^2}{\log(n+1)}\frac{n^2}{\log n})\frac{\log^2 n}{\log\log n}\right\rfloor\leq\pi\big((n+1)^2\big)\pi(n^2). $$
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2006
 DOI:
 10.48550/arXiv.math/0607096
 arXiv:
 arXiv:math/0607096
 Bibcode:
 2006math......7096H
 Keywords:

 Mathematics  Number Theory;
 11A41;
 11N05
 EPrint:
 This is a three pages unsuccessful (but maybe useful) challenge, for proving the oldfamous conjecture, which asserts for every positive integer n, the interval (n^2,(n+1)^2) contains at least a prime