
Re: First Proof That Infinitely Many Prime Numbers Come in Pairs
Posted:
May 23, 2013 5:54 AM


Pubkeybreaker <pubkeybreaker@aol.com> writes:
> On May 17, 6:42 am, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote: > > In article <4c7758a52b88475691f1d59d43bcd...@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.
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".
Phil  "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.

