On Thu, May 30, 2013 at 12:16 AM, John <

mistermac39@...> wrote:

> **

> One of the points I was interested in, and perhaps you have averted to it

> but I missed it, is the corollary that there is at

>

least one prime gap equal to or less than "Zhang's Number" that has an

> infinity of occurences.

>

this is indeed true, since there is a finite number of different possible

gaps less than 71 million, and Zhang's theorem asserts that there are

infinitely many gaps of such size, so at least one of these gaps must occur

infinitely often.

>

> This probably has been proven in another way. If so, could someone please

> inform us where we can look it up, or better still give some detail on it.

>

> No, if that was proven, (that there was one gap less than Zhang's number

known to occur infinitely often), then this would have "superseeded"

Zhang's theorem.

> For some reason, the number two is the one everyone is looking forward to

> proving, if only because is the smallest candidate left.

>

why "left" ? no candidate at all has been eliminated so far...

But of course the number 2 is the ultimate challenge, it is special in

several ways, which partially may be, but aren't necessarily directly, a

consequence of the fact that its the smallest possible gap.

(For example, to name a trivial one, the pair of twin primes are

consecutive odd numbers, which is not the case for any other gap).

Maximilian

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