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\section{Consequences}  If we can find the relationship of the $\chi_{p_n}$ functions, then we can state the following \begin{equation}  p_n=\lim_{x\to0}\frac{d}{dz}\frac{\sum_{k=0}^{\varphi(p_{n-1}\#)}\chi_{p_n}(k)z^k}{1-z-z^{\varphi(p_{n-1}\#)}+z^{\varphi(p_{n-1}\#)+1}} p_n=\lim_{z\to0}\frac{d}{dz}\left[\frac{\sum_{k=0}^{\varphi(p_{n-1}\#)}\chi_{p_n}(k)z^k}{1-z-z^{\varphi(p_{n-1}\#)}+z^{\varphi(p_{n-1}\#)+1}}\right]  \end{equation}