Counting primes in the interval (n^2,(n+1)^2)
| dc.creator | Hassani, Mehdi | |
| dc.date | 2006-07-04 | |
| dc.date.accessioned | 2026-07-07T07:18:00Z | |
| dc.date.available | 2026-07-07T07:18:00Z | |
| dc.description | In this note, we show that there are many infinity positive integer values of $n$ in which, the following inequality holds $$ \left\lfloor{1/2}(\frac{(n+1)^2}{\log(n+1)}-\frac{n^2}{\log n})-\frac{\log^2 n}{\log\log n}\right\rfloor\leqπ\big((n+1)^2\big)-π(n^2). $$ | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/0607096 | |
| dc.identifier | http://arxiv.org/abs/math/0607096 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114148 | |
| dc.subject | Number Theory | |
| dc.subject | 11A41, 11N05 | |
| dc.title | Counting primes in the interval (n^2,(n+1)^2) | |
| dc.type | text |