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 e-prints
- Pub Date:
- July 2006
- DOI:
- 10.48550/arXiv.math/0607096
- arXiv:
- arXiv:math/0607096
- Bibcode:
- 2006math......7096H
- Keywords:
-
- Mathematics - Number Theory;
- 11A41;
- 11N05
- E-Print:
- This is a three pages unsuccessful (but maybe useful) challenge, for proving the old-famous conjecture, which asserts for every positive integer n, the interval (n^2,(n+1)^2) contains at least a prime