On some over primesArticle

• 1 Institut für Mathematik

It will be shown that, for any $\delta > 0$,

$${\sum_{p\leq n}}^* \; \frac{\log p}{p} = \frac{1}{2} \log n + O\Big((\log n)^{\frac{5}{6}+\delta}\Big),$$ where (*) restricts the summation to those primes $p$, which satisfy $n = kp+r$ for some integers $k$ and $r$, $p/2 < r < p$. This result is connected with questionsconcerning prime divisors of binomial coefficients.

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