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where the top row of numbers are the prime numbers. This also appears to converge on an integral coefficient Laurent series \begin{equation}  g(x)=\frac{2}{x}-\frac{6}{x^3}+\frac{48}{x^5}-\frac{594}{x^7}+\frac{B}{x^9}\cdots  \end{equation}  where $B>1100$. $B>10100$. If a factor of $2$ is removed we have the sequence $1,3,24,297,\cdots$ which has a single match on OEIS with sequence A258301. We see the next term in that sequence $5260$, is approximately half the suggested value of $B$, which was not yet converged.  That would give a conjecture for a very interesting relationship that \begin{equation}  \K_{i=1}^\infty \frac{p_i}{x} = \frac{2}{x} - \frac{6}{x^3} + \frac{48}{x^5} -\frac{594}{x^7} + \frac{10520}{x^9} -\cdots   \end{equation}