20211220, 21:52  #12  
Dec 2008
you know...around...
2^{2}×5×37 Posts 
Quote:
Well you already found 46318910903 (length 16), 103947089669 (17 and 18), and 184722051989 (19 and 20, the latter almost being of length 23), from your data in the OP at x=30. And those are probably not minimal, the columns for x=22..28 are missing  with log(184722051889) = 25.942..., x=26 would suffice here. I do expect arbitrarily long runs of gaps with merit larger than a given value. It has long been proven that the merit of a gap between two primes can become arbitrarily large, so I would expect the same to be true for a series of consecutive gaps with at least a given merit each. 

20211221, 09:39  #13 
Jun 2003
Oxford, UK
2,039 Posts 
Here is an interesting pair of graphs  they shows he median gap of a range of all gaps for primes 2 to x, with x up to 999983. The second graph ignores the results up to x=4409 so as to see the fine detail of the later ranges.
I plan to carry the range up to prime range from 2 to 1e7, although the work is relatively intensive on resources it does look as if the median gap is on the rise again at 1e6 and it is worth looking at this. Last fiddled with by robert44444uk on 20211221 at 09:42 
20211221, 09:40  #14  
Jun 2003
Oxford, UK
2,039 Posts 
Quote:


20211221, 14:46  #15  
Jun 2003
Oxford, UK
2,039 Posts 
Quote:


20211223, 18:38  #16 
May 2018
258_{10} Posts 
A gap of 102 after 10938023 would make the next prime 10938125. That is obviously not prime.

20211223, 22:43  #17  
Feb 2017
Nowhere
5·1,153 Posts 
Quote:
Code:
? precprime(109380231) %1 = 10937921 ? nextprime(10938023+1) %2 = 10938119 ? 

20211224, 08:40  #18 
Jun 2003
Oxford, UK
2,039 Posts 
I'm no programmer, Sorry for this. What is wrong therefore is the statement "Initial prime is". As the same program is used for all examples, perhaps what we could say is that the stated prime is part of a sequence with consecutive gaps of the stated size.

20220119, 23:46  #19  
May 2018
2·3·43 Posts 
Quote:


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