# Issues

Issue #96 resolved

# Documentation: Bug in Euclid's proof

Sebastian Korten
created an issue

There is a problem with euclids proof in the tutorial at the beginning of the beamerguide --- it is wrong.\

By the stated proof (13! + 1) should be prime, which it is not (it's 83 * 75024347).\ [Furthermore: (17!+1) = 538105034941 * 661 and (19! +1) = 1713311273363831 * 71)]\

It it true that (19!+1) is not divisible by any integer <= 19, but that is definitely not enough to prove that it is prime.\

You will find euclids proof explained here:\ http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html\

The reason why I report this as a bug is that I read the beamer documentation some years ago and up until two days ago I thought the proof was valid ;o)

I hope you understand that this 'bugs' me ;o)

Btw, I love beamer. Thank you so much for your effort!

1. reporter

This would be a possible fix:

\begin{proof}
\begin{enumerate}
\item<1-> Suppose $P$ is a set containing all known prime numbers
\item<2-> $q = (\prod\limits_{x\in P}{x}) + 1$
\item<3-> $q$ is not divisible by any number in $P$
\item<4-> \alert{Either} $q$ is prime and $q \not\in P$
\item<5-> \alert{or} $q$ is not prime, but has at least two prime factors $a, b \not\in P$
\item<6-> $\Rightarrow$ there are more prime numbers than those in $P$\qedhere
\end{enumerate}
\end{proof}

2. reporter
• removed assignee

Fix to my fix ;o) There are not necessarily "two" prime factors \not\in N if $q$ is not prime, just one