Inspired by a recent discussion on the wonders of , I started thinking about how easy it would be to generate prime numbers in . 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.