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% Copyright 2003--2007 by Till Tantau
% Copyright 2010 by Vedran Mileti\'c
% Copyright 2015 by Vedran Mileti\'c, Joseph Wright
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Free Documentation License.
%
% See the file doc/licenses/LICENSE for more details.
\beamertemplatesolidbackgroundcolor{black!5}
\beamertemplatetransparentcovered
\title{There Is No Largest Prime Number}
\subtitle{With an introduction to a new proof technique}
\author[Euklid]{Euklid of Alexandria}
\institute[Univ. Alexandria]{Department of Mathematics\\ University of Alexandria}
\date[ISPN '80]{27th International Symposium on Prime Numbers, --280}
\begin{document}
\begin{frame}
\titlepage
\tableofcontents
\end{frame}
\section{Results}
\subsection{Proof of the Main Theorem}
\begin{frame}<1>
\frametitle{There Is No Largest Prime Number}
\framesubtitle{The proof uses \textit{reductio ad absurdum}.}
\begin{theorem}
There is no largest prime number.
\end{theorem}
\begin{proof}
\begin{enumerate}
% The strange way of typesetting math is to minimize font usage
% in order to keep the file sizes of the examples small.
\item<1-| alert@1> Suppose $p$ were the largest prime number.
\item<2-> Let $q$ be the product of the first $p$ numbers.
\item<3-> Then $q$\;+\,$1$ is not divisible by any of them.
\item<1-> Thus $q$\;+\,$1$ is also prime and greater than $p$.\qedhere
\end{enumerate}
\end{proof}
\end{frame}
\end{document}
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