%
% primzahlfunktion2.tex -- Primzahlfunktion, alternativer Vorschlag
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{pgfplots}
\usepackage{csvsimple}
\usetikzlibrary{arrows,intersections,math}
\begin{document}
\def\skala{1}
\begin{tikzpicture}[>=latex,thick,scale=\skala]

\def\dx{0.38}
\def\dy{0.5}

\foreach \x in {1,...,30}{
	\draw[color=gray!20] ({\x*\dx},0) -- ({\x*\dx},{10.5*\dy});
}
\foreach \y in {1,...,10}{
	\draw[color=gray!20] (0,{\y*\dy}) -- ({30.5*\dx},{\y*\dy});
}

\draw[->] (-0.1,0) -- ({30.8*\dx},0) coordinate[label={$x$}];
\draw[->] (0,-0.1) -- (0,{10.9*\dy}) coordinate[label={right:$\pi(x)$}];

\def\segment#1#2#3{
	%\draw[line width=0.1pt] ({#3*\dx},0) -- ({#3*\dx},{#2*\dy});
	\draw[color=blue,line width=1.4pt]
		({#1*\dx},{#2*\dy}) -- ({#3*\dx},{#2*\dy});
	\draw[color=blue,line width=0.3pt]
		({#3*\dx},{#2*\dy}) -- ({#3*\dx},{(#2+1)*\dy});
	\draw ({#3*\dx},-0.1) -- ({#3*\dx},0.1);
	\node at ({(#3)*\dx},-0.1) [below] {$#3\mathstrut$};
}

\foreach \y in {2,4,...,10}{
	\draw (-0.1,{\y*\dy}) -- (0.1,{\y*\dy});
	\node at (-0.1,{\y*\dy}) [left] {$\y\mathstrut$};
}

\begin{scope}
\clip (0,-0.5) rectangle ({30*\dx},{10.1*\dy});

\segment{0}{0}{2}
\segment{2}{1}{3}
\segment{3}{2}{5}
\segment{5}{3}{7}
\segment{7}{4}{11}
\segment{11}{5}{13}
\segment{13}{6}{17}
\segment{17}{7}{19}
\segment{19}{8}{23}
\segment{23}{9}{29}
\segment{29}{10}{31}
\end{scope}

\end{tikzpicture}
\end{document}