This might be a simple question. But Can any one give me an asymptotic bound for $\sum_{p \leq x}{p \log p}$, where $p$ is a prime number
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Well, it's definitely $O(p^2\log(p))$, but there are probably stronger bounds. – Isaac Browne Dec 01 '17 at 07:08
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can it be written as $\Pi_{p\leq x}{\log p}^{p}$ – Math123 Dec 01 '17 at 07:16
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No, it cannot, it can, however, be written as $\log \Pi_{p\leq x}p^{p}$, which is probably what you meant to write? – Isaac Browne Dec 01 '17 at 07:19
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It's equivalent to $\log\left( \prod_p p^p \right)$ – Zubzub Dec 01 '17 at 07:19
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@ Isaac, YES, it was a typo from my side – Math123 Dec 01 '17 at 07:23