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However this is a statement of the obvious! It implies consitency with what was done so far.  Further diagonal were found, the key being the polynomial in $k$ in the index of the prime number inside the $\pi$ function the next terms int in  the series was were  found to be \begin{equation} +\delta^i_{j+3}\sum_{k=1}^j P_{k+3}\pi(P_{k(k+1)(k+2)/6})  \end{equation}