- On 26 Jul 2013, at 19:56, Jose Angel Gonzalez <josechu2004@...> wrote:

> Zhang's gap as been reduced from 70 million to 5414 in a couple of months.

Bob

> Wow.

>

> So, there is an infinite quantity of pairs of consecutive primes whose

> distance is a fixed number below 5414.

>

> Source:

>

> http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes

>

> That assumes of course that the underlying analytical maths holds up under scrutiny. Alas, the process has no hope of reaching gap 2 - for that, even more original thinking is required. But it's great to see the progress on this thorny problem, especially as the breakthrough was totally out of left field.

>

>

[Non-text portions of this message have been removed]

>

- Bob,

What is known about the fundamental lower limit of this method? I had not heard anything about a known lower bound, which your post suggests is >2. Thanks!

Roahn

----- Original Message -----

From: Bob Gilson

To: Jose Angel Gonzalez

Cc: primenumbers@yahoogroups.com

Sent: Saturday, July 27, 2013 2:55 AM

Subject: Re: [PrimeNumbers] Zhang's gap

On 26 Jul 2013, at 19:56, Jose Angel Gonzalez <josechu2004@...> wrote:

> Zhang's gap as been reduced from 70 million to 5414 in a couple of months.

> Wow.

>

> So, there is an infinite quantity of pairs of consecutive primes whose

> distance is a fixed number below 5414.

>

> Source:

>

> http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes

>

> That assumes of course that the underlying analytical maths holds up under scrutiny. Alas, the process has no hope of reaching gap 2 - for that, even more original thinking is required. But it's great to see the progress on this thorny problem, especially as the breakthrough was totally out of left field.

>

Bob

>

>

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed] - --- In primenumbers@yahoogroups.com,

"Roahn Wynar" <rwynar@...> wrote:

> What is known about the fundamental lower limit of this method?

The potential obstacle at a limit of 16 appears to come

from the (conditional!) Theorem B of the fine article

by Janos Pintz that Warren kindly advertized:

http://arxiv.org/abs/1305.6289

David