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Message from discussion A proof that there are infinitely many primes
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Norman Megill  
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 More options May 8 2005, 8:57 am
Newsgroups: sci.math, sci.logic
From: Norman Megill <n...@see.signature>
Date: Sun, 08 May 2005 08:57:31 -0400
Local: Sun, May 8 2005 8:57 am
Subject: A proof that there are infinitely many primes
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While Euclid's classic proof that there are infinitely many primes is
easy to understand intuitively, I found the following proof simpler to
formalize for an automated proof verifier.  (Specifically, this proof
avoids the product of a hypothetical finite set of all primes, which I
found cumbersome to work with.)

Here is the proof:

   For any natural number n, the smallest divisor (greater than 1) of n!+1
   is a prime greater than n.  Hence there is no largest prime.

As simple as it is, I was unable to find a published reference for this
proof.  Is it a known proof?

--
Norm Megill http://public.xdi.org/=nm


 
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