Hi everyone

This is my first post... I do mathematics from home... ie., not attached with any institution... I have deduced some results...

$\lim \inf_{n\to\infty} \frac{d_n}{\log p_n} = 0$

and, for constants $A,B$

$\lim_{n\to\infty} \log p_n - \sum_{i=1}^{n-1} \frac{d_i}{p_{i+1}} = A$

$\lim_{n\to\infty} \log p_n - \sum_{i=1}^{n-1} \frac{d_i}{p_{i}} = B$

Where, $p_n$ is the nth prime... $d_n = p_{n+1} - p_n$

My question is: Do you think these results are good ?