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Doubly Recursive Factorization 59281

LaTeX

$\begin{array}{l} 59281 ~\text{is the}~ 5995^\text{th} ~\text{prime} \\[4pt] \mathrm{pi}(59281) = 5995 \end{array}$

$\begin{array}{rcl} 59281 & = & p_{5995} \\[4pt] 5995 & = & 5 \cdot 11 \cdot 109 \\[4pt] 5995 & = & p_{3} p_{5} p_{29} \\[4pt] 29 & = & p_{10} \\[4pt] 10 & = & p_{1} p_{3} \\[8pt] 59281 & = & p_{5995} \\ & = & p_{p_{3} p_{5} p_{29}} \\ & = & p_{p_{p_{2}} p_{p_{3}} p_{p_{10}}} \\ & = & p_{p_{p_{p_{1}}} p_{p_{p_{2}}} p_{p_{p_{1} p_{3}}}} \\ & = & p_{p_{p_{p_{1}}} p_{p_{p_{p_{1}}}} p_{p_{p_{1} p_{p_{2}}}}} \\ & = & p_{p_{p_{p_{1}}} p_{p_{p_{p_{1}}}} p_{p_{p_{1} p_{p_{p_{1}}}}}} \\ & = & p_{p_{p_{p}} p_{p_{p_{p}}} p_{p_{p p_{p_{p}}}}} \\[8pt] 59281 & = & p_{5995} \\[4pt] & = & p_{p_{p_{p}} p_{p_{p_{p}}} p_{p_{p p_{p_{p}}}}} \end{array}$