# Generating primes in LaTeX

Inspired by a recent discussion on the wonders of $\LaTeX$, I started thinking about how easy it would be to generate prime numbers in $\LaTeX$. Well, unsurprisingly, it was presented as an example by Knuth using trial division in The TeXbook (download) in 1984:

\documentclass{article}

\newif\ifprime \newif\ifunknown % boolean variables
\newcount\n \newcount\p \newcount\d \newcount\a % integer variables
\def\primes#1{2,~3% assume that #1 is at least 3
\n=#1 \advance\n by-2 % n more to go
\p=5 % odd primes starting with p
\loop\ifnum\n>0 \printifprime\advance\p by2 \repeat}
\def\printp{, % we will invoke \printp if p is prime
\ifnum\n=1 and~\fi % ‘and’ precedes the last value
\number\p \advance\n by -1 }
\def\printifprime{\testprimality \ifprime\printp\fi}
\def\testprimality{{\d=3 \global\primetrue
\loop\trialdivision \ifunknown\advance\d by2 \repeat}}
\def\trialdivision{\a=\p \divide\a by\d
\ifnum\a>\d \unknowntrue\else\unknownfalse\fi
\multiply\a by\d
\ifnum\a=\p \global\primefalse\unknownfalse\fi}

\begin{document}

% usage
The first 100 prime numbers are:~\primes{100}

\end{document}


You can also do it by sieving; check out the examples in my GitHub repo.

## One thought

1. Tom says:

Also some good examples here.

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