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\documentclass[border=10cm]{standalone}
\usepackage{pgf}
\newcount\ulami
\newcount\ulamj
\newcount\ulamlen
\newcount\ulamx
\newcount\ulamy
\newcount\ulamdx
\newcount\ulamdy
\ulami=1 %
\ulamj=0 %
\ulamlen=1 %
\ulamdx=-1 %
\ulamdy=1 %
\ulamx=0 %
\ulamy=0 %
\def\ulamplot#1{%
\advance\ulami by 1 %
\advance\ulamj by 1 %
\advance\ulamx by \the\ulamdx %
\advance\ulamy by \the\ulamdy %
\pgfpathmoveto{\pgfpoint{\the\ulamx cm}{\the\ulamy cm}}
\pgfmathparse{isprime(\the\ulami)}
\let\r=\pgfmathresult
\ifnum\r=1
\pgfpathcircle{\pgfpoint{\the\ulamx cm}{\the\ulamy cm}}{5pt}
\fi
\ifnum\ulamj=\the\ulamlen %
\advance\ulamlen by 1 %
\ulamj=0 %
\ifnum\ulamdx=1 %
\ulamdx=-1 %
\ulamdy=1 %
\else%
\ifnum\ulamdx=-1 %
\ulamdx=0 %
\ulamdy=-1 %
\else%
\ulamdx=1 %
\ulamdy=0 %
\fi
\fi
\fi
\ifnum#1>0 %
\advance#1 by -1 %
\ulamplot{#1}%
\fi
}
\begin{document}
\begin{pgfpicture}
\pgfmathsetmacro{\x}{cos(60)}
\pgfmathsetmacro{\y}{sin(60)}
\pgftransformcm{1}{0}{\x}{\y}{\pgfpointorigin}
\pgfpathmoveto{\pgfpointorigin}
\color{blue}
\newcount\ulamn
\ulamn=400
\ulamplot{\ulamn}
\pgfusepath{stroke,fill}
\end{pgfpicture}
\end{document}
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