20210902, 04:40  #45 
"Curtis"
Feb 2005
Riverside, CA
3·1,667 Posts 

20210902, 15:47  #46 
Mar 2021
110101_{2} Posts 
If a gap has a low Jacobs value then the gap is lower than expected. This means the next maximal gap is also likely to have a gap that is lower than expected. Similarly, if the Jacobs value is high then either the next maximal gap will also have a high Jacobs value or the starting value will be much higher.
Take the 1550 gap for example. The value predicted by your metric is about 1630. It's about 7x harder to find a gap of 1630 than a gap of 1552 so it isn't surprising to have a long sequence of low values. There are 8 consecutive negative values from 288 to 394 and 13 consecutive negative values from 468 to 602. It's possible there is a missing gap above 1600 but how many 1600+ gaps would you expect from 2^{64} to 2^{64} + 13*10^{16}? I would expect 0 (I would also expect 0 above 1550). How many would you expect from 2^{64} to 2^{65}? I would expect about 2. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prime gaps  Terence Schraut  Miscellaneous Math  10  20200901 23:49 
Gaps between maximal prime gaps  Bobby Jacobs  Prime Gap Searches  52  20200822 15:20 
The new record prime gaps  Bobby Jacobs  Prime Gap Searches  6  20181207 23:39 
Prime gaps above 2^64  Bobby Jacobs  Prime Gap Searches  11  20180702 00:28 
Prime gaps and storage  HellGauss  Computer Science & Computational Number Theory  18  20151116 14:21 