Add Willian's formula samples

content/willans.md

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++++
+title = "Willan’s Formula"
+description = "An exact prime formula which is however quite insane and fairly useless."
+extra.typesetters = [ "typst", "sile", "xelatex" ]
++++
+
+Willan's formula for the nth prime circa 1964; a.k.a. an exact prime formula which is quite insane and fairly useless but a nice typesetting stress test.

data/willans/sile.sil

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+\begin[papersize=a7,landscape=true]{document}
+\nofolios
+\neverindent
+\use[module=packages.math]
+
+\begin[mode=display]{math}
+	\def{floor}{\lfloor #1 \rfloor}
+	p_n = 1 + \sum_{i=1}^{2^n} \floor{(\frac{n}{\sum_{j=1}^i \floor{\cos^2(\pi \frac{(j-1)! + 1}{j})}})^{\frac{1}{n}}}
+\end{math}
+
+\end{document}
+

data/willans/typst.typ

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+#set page(
+  paper: "a7",
+  flipped: true,
+)
+
+$
+p_n = 1 + sum_(i=1)^(2^n) floor((n / (sum_(j=1)^i floor(cos^2(pi ((j - 1)! + 1) / j))))^(1/n))
+$

data/willans/xelatex.tex

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+\documentclass{article}
+\usepackage[paperheight=74mm,paperwidth=105mm,margin=4mm]{geometry}
+\pagenumbering{gobble}
+\usepackage{unicode-math}
+\begin{document}
+
+$$
+p_n = 1 + \sum_{i=1}^{2^n} \left\lfloor \left(\frac{n}{\sum_{j=1}^i \left\lfloor \cos^2\left(\pi \frac{(j-1)! + 1}{j}\right) \right\rfloor}\right)^{\frac{1}{n}} \right\rfloor
+$$
+
+\end{document}
+