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Old 2018-05-22, 22:43   #1
Bobby Jacobs
 
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Default Gaps between maximal prime gaps

Consider the sequence of record prime gaps.

1, 2, 4, 6, 8, 14, 18, 20, 22, 34, ...

Now, take the differences between consecutive numbers in this sequence.

1, 2, 2, 2, 6, 4, 2, 2, 12, 2, ...

These are the gaps between record prime gaps. Is there a pattern here?
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Old 2018-05-22, 23:07   #2
rudy235
 
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Quote:
Originally Posted by Bobby Jacobs View Post
Consider the sequence of record prime gaps.

1, 2, 4, 6, 8, 14, 18, 20, 22, 34, ...

Now, take the differences between consecutive numbers in this sequence.

1, 2, 2, 2, 6, 4, 2, 2, 12, 2, ...

These are the gaps between record prime gaps. Is there a pattern here?
Try this for size
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Old 2018-05-24, 14:40   #3
ldesnogu
 
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Quote:
Originally Posted by Bobby Jacobs View Post
Consider the sequence of record prime gaps.

1, 2, 4, 6, 8, 14, 18, 20, 22, 34, ...

Now, take the differences between consecutive numbers in this sequence.

1, 2, 2, 2, 6, 4, 2, 2, 12, 2, ...

These are the gaps between record prime gaps. Is there a pattern here?
http://oeis.org/A053695
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Old 2018-05-24, 16:38   #4
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Originally Posted by ldesnogu View Post
This is an interesting OEIS entry. Worded rather poorly though - "maximal gaps" was invented to describe the "record gaps"
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Old 2018-05-24, 20:03   #5
rudy235
 
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Originally Posted by robert44444uk View Post
This is an interesting OEIS entry. Worded rather poorly though - "maximal gaps" was invented to describe the "record gaps"
Maximal gaps is a clear-cut term. Irreversible.

"Record gaps" is rather vacuous. As far a I understand a "record gap" can still be reverted up to the time it becomes a CFC. And even when a "record gap" becomes definitive as a CFC, it does not, as a rule, become a 'Maximal Gap".
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Old 2018-05-25, 01:20   #6
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The biggest known number in the sequence is 208. That is the gap between the maximal gaps of sizes 924 and 1132. That is very big!
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Old 2018-05-26, 22:25   #7
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Quote:
Originally Posted by rudy235 View Post
Maximal gaps is a clear-cut term. Irreversible.

"Record gaps" is rather vacuous. As far a I understand a "record gap" can still be reverted up to the time it becomes a CFC. And even when a "record gap" becomes definitive as a CFC, it does not, as a rule, become a 'Maximal Gap".
Sorry about the confusion. I say, "record gaps" when I am talking about maximal prime gaps. I know that "record gaps" mean something different on this site. I will try to say, "maximal gaps."

Last fiddled with by Bobby Jacobs on 2018-05-26 at 22:27
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Old 2018-05-27, 00:36   #8
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Quote:
Originally Posted by Bobby Jacobs View Post
Sorry about the confusion. I say, "record gaps" when I am talking about maximal prime gaps. I know that "record gaps" mean something different on this site. I will try to say, "maximal gaps."
Don't feel like this had to do with you. It was the posting of the http://oeis.org/A053695 what made both Robert and myself make that comment.

If you think about it, all and everyone of the 1000 gaps in the Dr. Nicely 's table of gaps from 1 to 1998 are, in some way or another, "record gaps". Some are first occurrences, some are first known occurrences, and some are maximal gaps.

All maximal gaps are first ocurrences but not the other way around.
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Old 2018-07-03, 23:45   #9
Bobby Jacobs
 
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Default Record gaps between maximal prime gaps

Here are the known record gaps between maximal prime gaps.

1, 2, 6, 12, 20, 26, 30, 32, 62, 100, 208

The number 208 is more than twice the previous record of 100. In fact, 208 is only 3 terms after 100 in the sequence of gaps between maximal prime gaps. That is surprisingly large.
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Old 2018-07-04, 08:15   #10
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Quote:
Originally Posted by Bobby Jacobs View Post
Here are the known record gaps between maximal prime gaps.

1, 2, 6, 12, 20, 26, 30, 32, 62, 100, 208

The number 208 is more than twice the previous record of 100. In fact, 208 is only 3 terms after 100 in the sequence of gaps between maximal prime gaps. That is surprisingly large.
i.e. this list:

https://oeis.org/A270878
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Old 2018-07-04, 16:56   #11
rudy235
 
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Default MERITS OF MAXIMAL GAPS

1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0

In this sequence 0 represents that the merit is not the highest until this point, while 1 means that that merit is higher than all previous merits.

There are 80 data points: (gap 1 to gap 1550)
Point 75 in Red represents TOES 1476 gap and it is a 1 because there is no previous merit higher than its own)
Point 76 is Cyan and belongs to Axn gap of 1488 (it is represented by "0" because TOES gap is larger)
Point 77 is Orange and it represents Danaj gap of 1510 (it is represented by "0" because TOES gap is larger)
Point 78 is Plum and it represents Steve Coles gap of 1526 (it is represented by "0" because TOES gap is larger)
Points 79 & 80 in Black are probable gaps of 1530 and 1550 by the late Be.Nyman (they are represented by "0" because TOES gap is larger)

Last fiddled with by rudy235 on 2018-07-04 at 16:59
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