Sieve of Eratosthenes

By popular demand, here is the Sieve of Eratosthenes written in Plain TeX.

\newcount\cm\cm100
\newcount\ci
\newcount\cj
\def\prime{prime}
\def\composite{composite}
\def\set#1#2{\global\expandafter\let\csname s\number#1\endcsname#2}
\def\get#1{\csname s\number#1\endcsname}
\def\doprime{%
        \set\ci\prime
        \cj\ci
        \loop
                \advance\cj\ci
                \ifnum\cj<\cm
                        \set\cj\composite
        \repeat
}
\ci2
\loop\ifnum\ci<\cm
        \expandafter\ifx\csname s\number\ci\endcsname\relax
                \begingroup
                \doprime
                \endgroup
        \fi
        \advance\ci1
\repeat
% Print them
\ci2
\loop\ifnum\ci<\cm
        \number\ci: \get\ci\endgraf
        \advance\ci1
\repeat
\bye

Replacing \begingroup with \let\outerbody\body and \endgroup with \let\body\outerbody, you can test even more numbers due to the difference in hash space and save space. Of course, you can test twice as many if you don't bother testing the even numbers.

\newcount\cm\cm300000
\newcount\ci
\newcount\cj
\def\prime{prime}
\def\composite{composite}
\def\set#1#2{\global\expandafter\let\csname s\number#1\endcsname#2}
\def\get#1{\csname s\number#1\endcsname}
\def\doprime{%
        \set\ci\prime
        \cj\ci
        \loop
                \advance\cj\ci
                \advance\cj\ci
                \ifnum\cj<\cm
                        \ifodd\cj
                                \set\cj\composite
                        \fi
        \repeat
}
\set2\prime
\ci3
\loop\ifnum\ci<\cm
        \expandafter\ifx\csname s\number\ci\endcsname\relax
                \let\outerbody\body
                \doprime
                \let\body\outerbody
        \fi
        \advance\ci2
\repeat
% Print them
2: \prime\par
\ci3
\loop\ifnum\ci<\cm
        \number\ci: \ifodd\ci\get\ci\else\composite\fi\endgraf
        \advance\ci1
\repeat
\bye

Hendrik Vogt pointed out that Knuth wrote a different prime computing function in TeX that appears in The TeXbook on page 218. Thanks!