No way to measure record prime gaps - Page 5

VBCurtis · 2021-09-02, 04:40

Quote:

Originally Posted by Bobby Jacobs

Here are the Jacobs values of...

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CraigLo · 2021-09-02, 15:47

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.

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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.