20180522, 22:43  #1 
May 2018
181 Posts 
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? 
20180522, 23:07  #2  
Jun 2015
Vallejo, CA/.
1110110110_{2} Posts 
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20180524, 14:40  #3  
Jan 2008
France
2×263 Posts 
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20180524, 16:38  #4  
Jun 2003
Oxford, UK
1875_{10} Posts 
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20180524, 20:03  #5  
Jun 2015
Vallejo, CA/.
2·5^{2}·19 Posts 
Quote:
"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". 

20180525, 01:20  #6 
May 2018
181 Posts 
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!

20180526, 22:25  #7  
May 2018
181 Posts 
Quote:
Last fiddled with by Bobby Jacobs on 20180526 at 22:27 

20180527, 00:36  #8  
Jun 2015
Vallejo, CA/.
1666_{8} Posts 
Quote:
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. 

20180703, 23:45  #9 
May 2018
181 Posts 
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. 
20180704, 08:15  #10  
Jun 2003
Oxford, UK
3·5^{4} Posts 
Quote:
https://oeis.org/A270878 

20180704, 16:56  #11 
Jun 2015
Vallejo, CA/.
2×5^{2}×19 Posts 
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 20180704 at 16:59 
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