Date: May 17, 2013 9:34 AM
Author: Pubkeybreaker
Subject: Re: First Proof That Infinitely Many Prime Numbers Come in Pairs

On May 17, 6:42 am, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote:
> In article <4c7758a5-2b88-4756-91f1-d59d43bcd...@d6g2000yqi.googlegroups.com>,
>
> Pubkeybreaker  <pubkeybrea...@aol.com> wrote:

> >This is a gross misstatement of the proof. It did NOT prove that there
> >were infinitely many prime pairs.  What it did prove was that the gap
> >between primes is FINITELY BOUNDED infinitely often.  The bound is 70
> >x 10^6.

>
> I agree that the article (quoted from Scientific American) is unclear,
> but it appears to be using "prime pairs" to mean "successive primes",
> and "twin primes" to mean "prime pairs where the difference is 2".
>
> That makes the headline misleading because we already knew there were
> infinitely many pairs of successive primes.


Not with a finitely bounded gap between them we didn't.