Date: May 23, 2013 5:54 AM
Author: Phil Carmody
Subject: Re: First Proof That Infinitely Many Prime Numbers Come in Pairs

Pubkeybreaker <> writes:

> On May 17, 6:42 am, (Richard Tobin) wrote:
> > In article <>,
> >
> > Pubkeybreaker  <> 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.

I interpreted the headline (having already heard the story via other routes)
as meaning that there is a finite gap such that there are infinitely many
consecutive primes with that gap. At no point did I interpret "prime pairs"
to mean "twin primes" rather than "consecutive primes a fixed, but unspecified,
distance apart".

"In a world of magnets and miracles"
-- Insane Clown Posse, Miracles, 2009. Much derided.
"Magnets, how do they work"
-- Pink Floyd, High Hopes, 1994. Lauded as lyrical geniuses.