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.

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