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lines changed Original file line number Diff line number Diff line change 1+ +++
2+ title = " Willan’s Formula"
3+ description = " An exact prime formula which is however quite insane and fairly useless."
4+ extra.typesetters = [ " typst" , " sile" , " xelatex" ]
5+ +++
6+
7+ 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.
Original file line number Diff line number Diff line change 1+ \begin[papersize=a7,landscape=true]{document}
2+ \nofolios
3+ \neverindent
4+ \use[module=packages.math]
5+
6+ \begin[mode=display]{math}
7+ \def{floor}{\lfloor #1 \rfloor}
8+ 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}}}
9+ \end{math}
10+
11+ \end{document}
12+
Original file line number Diff line number Diff line change 1+ # set page (
2+ paper : " a7" ,
3+ flipped : true ,
4+ )
5+
6+ $
7+ p_n = 1 + sum _( i=1) ^( 2^n) floor ((n / ( sum _( j=1) ^i floor (cos ^2(pi ((j - 1)! + 1) / j))) )^( 1/n) )
8+ $
Original file line number Diff line number Diff line change 1+ \documentclass {article }
2+ \usepackage [paperheight=74mm,paperwidth=105mm,margin=4mm ]{geometry }
3+ \pagenumbering {gobble}
4+ \usepackage {unicode-math }
5+ \begin {document }
6+
7+ $$
8+ p_n = 1 + \sum _{i=1}^{2^n} \left \lfloor \left (\frac {n}{\sum _{j=1}^i \left\lfloor \cos ^2\left (\pi \frac {(j-1)! + 1}{j}\right ) \right\rfloor }\right )^{\frac {1}{n}} \right \rfloor
9+ $$
10+
11+ \end {document }
12+
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