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• ## Re: [PrimeNumbers] Known prime gaps

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• ... Prime gaps are far from smoothly distributed. Gaps divisible by 3 are more likely than ones not divisible by 3. As 30 becomes small, gaps divisible by 30
Message 1 of 11 , May 8, 2007
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--- SWagler@... wrote:
> All,
>
> Years ago I plotted a frequency distribution of prime gaps from 2 to some
> small limit and the curve always looked similar to the curve for black body
> radiation. Has anyone done this for limits large or small? Are there
> theoretical reasons to account for this?

Prime gaps are far from smoothly distributed.
Gaps divisible by 3 are more likely than ones not divisible by 3.
As 30 becomes small, gaps divisible by 30 also become more popular.
As always this can be explained by looking at small primes.

Phil

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• ... A good illustration: http://ieeta.pt/~tos/gaps.html All the best, Andrey [Non-text portions of this message have been removed]
Message 2 of 11 , May 8, 2007
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> > Years ago I plotted a frequency distribution of prime gaps from 2 to some
> > small limit and the curve always looked similar to the curve for black body
> > radiation. Has anyone done this for limits large or small? Are there
> > theoretical reasons to account for this?
>
> Prime gaps are far from smoothly distributed.
> Gaps divisible by 3 are more likely than ones not divisible by 3.
> As 30 becomes small, gaps divisible by 30 also become more popular.
> As always this can be explained by looking at small primes.

A good illustration: http://ieeta.pt/~tos/gaps.html

All the best,

Andrey

[Non-text portions of this message have been removed]
• ... Except it doesn t venture into the 30 becomes small region. I can t remember where 30 takes over on from 30 as the most likely gap. I presume that s
Message 3 of 11 , May 8, 2007
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--- Andrey Kulsha <Andrey_601@...> wrote:
> > > Years ago I plotted a frequency distribution of prime gaps from 2 to some
> > > small limit and the curve always looked similar to the curve for black
> body
> > > radiation. Has anyone done this for limits large or small? Are there
> > > theoretical reasons to account for this?
> >
> > Prime gaps are far from smoothly distributed.
> > Gaps divisible by 3 are more likely than ones not divisible by 3.
> > As 30 becomes small, gaps divisible by 30 also become more popular.
> > As always this can be explained by looking at small primes.
>
> A good illustration: http://ieeta.pt/~tos/gaps.html

Except it doesn't venture into the '30 becomes small' region. I can't remember
where 30 takes over on from 30 as the most likely gap. I presume that's touched
on somewhere on the prime pages or on mathworld, and if it isn't on both,
something should be done about that!

Phil

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• ... They are the first two hits on http://www.google.com/search?hl=en&q=%22jumping+champion%22 -- Jens Kruse Andersen
Message 4 of 11 , May 8, 2007
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Phil Carmody wrote:
>> A good illustration: http://ieeta.pt/~tos/gaps.html
>
> Except it doesn't venture into the '30 becomes small' region. I can't
> remember
> where 30 takes over on from 30 as the most likely gap. I presume that's
> touched
> on somewhere on the prime pages or on mathworld, and if it isn't on both,
> something should be done about that!

They are the first two hits on