From: Fred W. Helenius <fredh@ix.netcom.com>
Subject: Re: 8n+5
Date: Mon, 05 Jun 2000 13:13:24 -0400
Newsgroups: sci.math
Summary: [missing]

"Calla" <vdwestch@mweb.co.za> wrote:

>Could someone please repost the proof on why there are infinite many primes
>of the form 8n+5

Not a repost, but here goes:

Let p1, p2, ... , pn be any finite collection of primes of the form
8n+5.  Consider the number (2*p1*p2*...*pn)^2 + 1.  It cannot be
divisible:
   by 2, because it's odd;
   by any 4n+3 prime, because -1 is a quadratic residue;
   solely by 8n+1 primes, because it's of the form 8n+5.
Therefore it has a prime factor of the form 8n+5, and this factor
cannot be in the original collection.

-- 
Fred W. Helenius	<fredh@ix.netcom.com>