mersenneforum.org No way to measure record prime gaps
 Register FAQ Search Today's Posts Mark Forums Read

2021-09-02, 04:40   #45
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

3×1,789 Posts

Quote:
 Originally Posted by Bobby Jacobs Here are the Jacobs values of...
Naming something after yourself is the most reliable way I know of to ensure nobody else ever uses your name to describe it.

 2021-09-02, 15:47 #46 CraigLo   Mar 2021 59 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 264 to 264 + 13*1016? I would expect 0 (I would also expect 0 above 1550). How many would you expect from 264 to 265? I would expect about 2.

 Similar Threads Thread Thread Starter Forum Replies Last Post Terence Schraut Miscellaneous Math 10 2020-09-01 23:49 Bobby Jacobs Prime Gap Searches 52 2020-08-22 15:20 Bobby Jacobs Prime Gap Searches 6 2018-12-07 23:39 Bobby Jacobs Prime Gap Searches 11 2018-07-02 00:28 HellGauss Computer Science & Computational Number Theory 18 2015-11-16 14:21

All times are UTC. The time now is 04:18.

Wed Aug 10 04:18:54 UTC 2022 up 33 days, 23:06, 1 user, load averages: 1.75, 1.65, 1.45