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% Copyright 2010 by Vedran Mileti\'c
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% $Header: /Users/joseph/Documents/LaTeX/beamer/doc/themeexamples/beamerthemeexample.tex,v 5a25f58600c3 2010/04/27 12:17:50 rivanvx $
\documentclass{beamer}
\ifx\themename\undefined
\def\themename{default}
\fi
\usetheme{\themename}
\beamertemplatetransparentcovered
\usepackage{times}
\usepackage[T1]{fontenc}
\title{There Is No Largest Prime Number}
\subtitle{With an introduction to a new proof technique}
\author{Euklid of Alexandria}
\institute{Department of Mathematics\\ University of Alexandria}
\date{Symposium on Prime Number, --280}
\begin{document}
\begin{frame}
\titlepage
\end{frame}
\begin{frame}
\frametitle{Outline}
\tableofcontents
\end{frame}
\section{Results}
\subsection{Proof of the Main Theorem}
\begin{frame}<1>
\frametitle{Proof That There Is No Largest Prime Number}
\framesubtitle{A proof using \textit{reductio ad absurdum}.}
\begin{theorem}
There is no largest prime number.
\end{theorem}
\begin{proof}
\begin{enumerate}
\item<1-> Suppose $p$ were the largest prime number.
\item<2-> Let $q := 1 + \prod_{i=1}^p i = 1+p!$.
\item<3-> Then $q$ is not divisible by any $p' \in \{1,\dots,p\}$.
\item<1-> Thus $q>p$ is also prime.\qedhere
\end{enumerate}
\end{proof}
\end{frame}
\end{document}
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