Example: Ulam spiral

% Ulam spiral
% Author: Alain Matthes (http://altermundus.fr/)

\documentclass[]{article}
\usepackage{ifthen,fullpage}
\usepackage{tikz}
\newcounter{cmpt}
\newcounter{next}
\newcounter{end}
\makeatletter
\newcounter{prim@a}
\newcounter{prim@n}
\newcounter{prim@d}
\newcounter{prim@b}
\newboolean{reponse}

\newcommand*\primality[1]
{\setboolean{reponse}{true}
 \setcounter{prim@n}{#1}
 \ifthenelse{\value{prim@n}=0}% n = 0
   {\setboolean{reponse}{false}}
   {\ifthenelse{\value{prim@n}=1}% n =1
     {\setboolean{reponse}{false}}%
     {\ifthenelse{\value{prim@n}=2}{}% n = 2
       {\ifthenelse{\value{prim@n}=3}{}% n = 3
         {\ifthenelse{\isodd{\value{prim@n}}}% n > 3 parité ?
            {\setcounter{prim@a}{#1}
             \setcounter{prim@d}{3} % n impair on continue
            \whiledo{\value{prim@a}>\value{prim@d}}% deb whiledo
              {\setcounter{prim@a}{\value{prim@n}/\value{prim@d}}
               \setcounter{prim@b}{\value{prim@a}*\value{prim@d}}
               \ifthenelse{\value{prim@b}=\value{prim@n}}%
                 {\setboolean{reponse}{false}
                  \setcounter{prim@d}{\value{prim@a}}}%
                 {\addtocounter{prim@d}{2}%
                 }%
              }% end whiledo
           }
           {\setboolean{reponse}{false}}% n est pair
         }%
       }%
     }%
   }
}%end macro
\makeatother

\newcommand*\ballcolor{%
    \stepcounter{cmpt}
    \primality{\value{cmpt}}
    \ifthenelse{\boolean{reponse}}%
        { \colorlet{colornb}{blue!50}}%
        { \colorlet{colornb}{red!30}}%
}

\newcommand*{\ulam}[2]{%
    \setcounter{cmpt}{#1}
    \addtocounter{cmpt}{-1}
    \setcounter{next}{0}
    \setcounter{end}{#2}

    \ballcolor
    \node(place) at (0,0)  {$\mathbf\thecmpt$};

    \whiledo{\value{cmpt}<\value{end}}%
    {
            \foreach \i in {0,...,\thenext}
            {\ballcolor
            \node[above of=place] (place) {$\mathbf\thecmpt$};
        }

        \foreach \i in {0,...,\thenext}
        {
            \ballcolor
            \node[right of=place] (place) {$\mathbf\thecmpt$};
        }
        \stepcounter{next}

        \foreach \i in {0,...,\thenext}
        {
            \ballcolor
            \node[below of=place] (place) {$\mathbf\thecmpt$};
        }

        \foreach \i in {0,...,\thenext}
        {
            \ballcolor
            \node[left of=place] (place) {$\mathbf\thecmpt$};
        }
        \stepcounter{next}
    }
    \addtocounter{next}{-1}
    \foreach \i in {0,...,\thenext}
    {
        \ballcolor
        \node[above of=place] (place) {$\mathbf\thecmpt$};}
}
\begin{document}

\begin{center}
  \begin{tikzpicture}
  \tikzstyle{every node}=[draw,%
                          rectangle,%
                          shade,%
                          minimum size  = 1.6cm,%
                          ball color    = colornb,%
                          node distance = 1.6cm]

  \ulam{41}{113}

  \end{tikzpicture}
\end{center}
\end{document}