Matematické Fórum

\documentclass{article}
\RequirePackage{ifthen,fullpage}
\RequirePackage{tikz}
\newcounter{cmpt}
\newcounter{next}
\newcounter{end}
\makeatletter
\newcounter{prim@r}
\newcounter{prim@a}
\newcounter{prim@n}
\newcounter{prim@d}
\newcounter{prim@b}
\newboolean{tkzaIsAPrim}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
% test if #1 is a prim number result set boolean :tkzaIsAPrim
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*\primality[1]{%
\setboolean{tkzaIsAPrim}{true}%
\setcounter{prim@a}{#1}%
   \ifthenelse{#1 = 0}{%
     \setboolean{tkzaIsAPrim}{false}}{%
     \ifthenelse{#1 = 1}{%
       \setboolean{tkzaIsAPrim}{false}}{%
       \ifthenelse{#1 = 2}{}{%
          \ifthenelse{#1 = 3}{}{%
             \ifthenelse{\isodd{#1}}{%
               \setcounter{prim@d}{3}%
               \whiledo{\value{prim@a} > \value{prim@d}}{%
                  \pgfmathsetcounter{prim@r}{mod(\theprim@a,\theprim@d)}%
                  \ifthenelse{\value{prim@r} = 0}{%
                    \setboolean{tkzaIsAPrim}{false}%
                    \setcounter{prim@d}{\theprim@a}}{%
                    \pgfmathaddtocounter{prim@d}{2}
                   }%
               }% fin du whiledo
               }{%
               \setboolean{tkzaIsAPrim}{false}%
             }%
            }%
          }%
        }%
     }%
}%
\makeatother

\newcommand*\ballcolor{%
\stepcounter{cmpt}
\primality{\value{cmpt}}
\ifthenelse{\boolean{tkzaIsAPrim}}{%
\colorlet{colornb}{blue!50}}{%
\colorlet{colornb}{orange!60}}%
}

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

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

\whiledo{\value{cmpt}<\value{end}}%
{
\foreach \i in {0,...,\thenext} 
{\ballcolor
\node[above of=place] (place) {};
}
\foreach \i in {0,...,\thenext} 
{\ballcolor
\node[right of=place] (place) {};
}
\stepcounter{next}
\foreach \i in {0,...,\thenext} 
{\ballcolor
\node[below of=place] (place) {};
}
\foreach \i in {0,...,\thenext} 
{\ballcolor
\node[left of=place] (place) {};
}
\stepcounter{next}
}
\addtocounter{next}{-1}
\foreach \i in {0,...,\thenext} 
{\ballcolor
\node[above of=place] (place) {};}
}
\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}