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Old 2019-06-10, 06:08   #10
robert44444uk's Avatar
Jun 2003
Oxford, UK

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Originally Posted by VBCurtis View Post
Would it be valuable to compare these upticks to the size of gap after a prime n given n+2 is known to be not-prime?
I wonder how much is a sort of 'magical' clearing out of primes around twins, versus the simple explanation that removing a possible gap of 2 from the distribution of next-prime-gap alters the averages/medians in this way.
I'm not certain there is any "twin" effect at play here, but I am nervous about that statement. The reduction in the average percentage uptick for larger n suggests that this uptick is caused by a localised effect involving the count of small gaps and hence the n+2 prohibition is likely to be the main culprit.

As well as n+2 out, it possible to take out all 2mod6 - I'm sure we can explain away most (if not all) of the uptick. I'm not sure how to do this, other than by looking at the basic distribution of prime gaps and removing some of these from the distribution. gaps of length 0mod(x#) where # represents a primorial are greater in number. Removing the 2mod6 gaps is above my pay grade.
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