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# Logarithmic and absolute-value like properties of $\pi(x)$ with applications

• ##### Boris B. Benyaminov
08/2011;
Source: arXiv

ABSTRACT We derive properties of $\pi(x)$ reminiscent of those of the logarithm and
absolute value functions. Two of these properties are similar to the relations
defining the linearity of a function. Several applications of these properties
of $\pi(x)$ are also examined.

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• ##### Article: Several new relations for the $n^{th}$ prime number
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ABSTRACT: We arrive at some new relations for the prime number $P_n$, based on the logarithmic and absolute-value properties of the function $\pi(x)$.
08/2011;