- May 30, 2013I think that this Zhang's theorem could led us very near to demonstrate the

Polignac's conjecture.

If there are infinitely many consecutive pairs of primes with some gap < 70

millions, why not all the other number bigger than 70 millions? After

all, all bigger gaps have the same or more probabilities - say, 1 - to

exist because the gaps between the primes tend to grow and the size of the

sample we can pick numbers from is infinite.

If only some number(s) below 70 million comply... Why this excepcionality?

And there are only a finite number of gaps < 70 millions. Which is an

infinitesimal part of all possble gaps (infinite).

There shouldn't exist excepcional gaps bellow 70 millions either.

If there are infinitely many gaps > 70 millions, the rest of gaps below 70

millions ought to exist too. I think.

On Thu, May 30, 2013 at 9:30 AM, Maximilian Hasler <

maximilian.hasler@...> wrote:

> **

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

>

>

> 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]

>

>

>

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