Sieve of Eratosthenes with tikz

eratosthenes.tex

\documentclass[tikz]{standalone}
\usepackage{tikz}

\begin{document}

\def\primes{2,3,5,7,11,13,17,19,23}
\def\revprimes{23,19,17,13,11,7,5,3,2}

\def\palette{{
 "0.00 0.00 1.00",
 "0.00 0.00 1.00",
 "0.00 0.00 1.00",
 "0.00 0.00 1.00",
 "0.00 0.00 1.00",
 "0.00 0.00 1.00",
 "0.00 0.00 1.00",
 "0.73 0.00 0.00",
 "1.00 0.98 0.00",
 "0.00 0.77 1.00"}}

\def\width{5}
\def\height{5}

\newcommand{\drawboundingbox}[3]{% anchor, fill
  \draw [thick, #3, fill=#2, fill opacity=0.2] (#1.north west) -- (#1.south west) -| (#1.north east) -- (#1.north west);
}

% for the ifnodedefined macro, full credit to: https://tex.stackexchange.com/questions/85528/checking-whether-or-not-a-node-has-been-previously-defined
\makeatletter
\long\def\ifnodedefined#1#2#3{%
  \@ifundefined{pgf@sh@ns@#1}{#3}{#2}%
}
\makeatother

\foreach \prime [count=\pp] in \primes{

  \pgfmathtruncatemacro{\firststep}{\prime}
  \pgfmathtruncatemacro{\secondstep}{\prime*\prime}
  \pgfmathtruncatemacro{\thirdstep}{\secondstep+\prime}
  \pgfmathtruncatemacro{\numgrid}{\width*\height}

  \foreach \step in {1, \firststep, \secondstep, \thirdstep, ..., \numgrid}{

    \begin{tikzpicture}

      % set canvas size
      \useasboundingbox (0pt,0pt) rectangle (230pt,230pt);

      % draw grid
      \pgfmathtruncatemacro{\gridwidth}{\width}
      \foreach \x [count=\xx] in {1, ..., \gridwidth} {

        \pgfmathtruncatemacro{\gridheight}{\height-1}
        \foreach \y [count=\yy] in {\gridheight, ..., 0} {

          \pgfmathtruncatemacro{\cell}{\width*\y+\x}  % draw location

          \ifnum\cell>1

            \foreach \iterprime [count=\x] in \revprimes {

              % define colour
              \pgfmathparse{\palette[\x]}
              \definecolor{fillcolour}{rgb}{\pgfmathresult};

              \ifnum\prime<\iterprime
              \else  % i.e. iterprime <= prime
                \pgfmathparse{Mod(\cell,\iterprime)==0?1:0}
                \ifnum\pgfmathresult>0
                  \ifnum\iterprime=\prime % current prime--wait for grid
                    \ifnum\cell>\step
                    \else % label <= step
                      \ifnum\cell<\secondstep % skip over multiples between prime and prime**2
                        \ifnum\cell>\firststep
                        \else
                      	\ifnum\cell=\firststep
			  \node[inner sep=8pt, text=black, font=\bfseries, minimum size=1.2cm] (n\xx\yy) at (\xx*1.5-0.5, \yy*1.5-0.5) {\cell};
                           \drawboundingbox{n\xx\yy}{fillcolour}{very thick}%{0.4}
                           \breakforeach
			\else
                          % draw
                          \node[inner sep=8pt, minimum size=1.2cm] (n\xx\yy) at (\xx*1.5-0.5, \yy*1.5-0.5) {\cell};
                          \drawboundingbox{n\xx\yy}{fillcolour}{semithick}%{0.2}
                          \breakforeach
                          \fi
                        \fi
                      \else
                        \node[inner sep=8pt, minimum size=1.2cm] (n\xx\yy) at (\xx*1.5-0.5, \yy*1.5-0.5) {\cell};
                        \drawboundingbox{n\xx\yy}{fillcolour}{semithick}%{0.2}
                        \breakforeach
                      \fi
                    \fi
                  \else
                    \pgfmathtruncatemacro{\iterfirststep}{\iterprime}
                    \pgfmathtruncatemacro{\itersecondstep}{\iterprime*\iterprime}
                    \ifnum\cell<\itersecondstep % skip over multiples between prime and prime**2
                      \ifnum\cell>\iterfirststep
                      \else
                      	\ifnum\cell=\iterfirststep
			  \node[inner sep=8pt, text=black, font=\bfseries, minimum size=1.2cm] (n\xx\yy) at (\xx*1.5-0.5, \yy*1.5-0.5) {\cell};
                           \drawboundingbox{n\xx\yy}{fillcolour}{very thick}%{0.4}
                           \breakforeach
			\else
                          % draw
                          \node[inner sep=8pt, minimum size=1.2cm] (n\xx\yy) at (\xx*1.5-0.5, \yy*1.5-0.5) {\cell};
                          \drawboundingbox{n\xx\yy}{fillcolour}{semithick}%{0.2}
                          \breakforeach
                          \fi
                      \fi
                    \else
                      \node[inner sep=8pt, minimum size=1.2cm] (n\xx\yy) at (\xx*1.5-0.5, \yy*1.5-0.5) {\cell};
                      \drawboundingbox{n\xx\yy}{fillcolour}{semithick}%{0.2}
                      \breakforeach
                      % draw
                    \fi
                  \fi
                \fi
              \fi
            }
            \ifnodedefined{n\xx\yy}{} {% if node not drawn by a prime
                \node[inner sep=8pt, minimum size=1.2cm] (char) at (\xx*1.5-0.5, \yy*1.5-0.5) {\cell};
                \drawboundingbox{char}{gray}{semithick}{0.2}
            }
          \fi
        }
      }

    % \xdef\primelist{Primes:}

    % \foreach \x in \primes{
    %   \ifnum\x>\prime
    %   \else
    %     \ifnum\x=\prime
    %       \ifnum\step>1
    %         \xdef\primelist{\primelist \ \ \x}
    %       \fi
    %     \else
    %       \xdef\primelist{\primelist \ \ \x}
    %     \fi
    %   \fi
    % }
    % \node[inner sep=8pt, anchor=west] (list) at (0.3, 9) {\Large\primelist};
    \end{tikzpicture}
  \ifnum\step=\firststep
    \ifnum\secondstep>\numgrid  % break if overstep grid size (larger primes)
            \breakforeach
    \fi
  \fi
  \ifnum\step=\secondstep
    \ifnum\thirdstep>\numgrid  % break if overstep grid size (larger primes)
            \breakforeach
    \fi
  \fi
  }
}

\end{document}