20200104, 01:33  #12 
Jun 2015
Vallejo, CA/.
2^{2}×239 Posts 

20200104, 13:35  #13  
Dec 2008
you know...around...
3^{2}×61 Posts 
Quote:
Code:
gap/30 mod 7 number of open residues 2, 5 0 (as you already noticed) 1, 6 1 3, 4 2 0 3 

20200104, 14:26  #14  
Jun 2003
Oxford, UK
3·5^{4} Posts 
Quote:
Has anyone got a perl or an exe file that can take the results from Thomas11's program and make a list of first instances? I'll take this to 1e13 Last fiddled with by robert44444uk on 20200104 at 14:26 

20200105, 04:30  #15  
Jun 2015
Vallejo, CA/.
2^{2}·239 Posts 
Quote:
Because this search is being done exhaustively they should not be any C?C, just gaps not yet discovered like:25964 and 26074 

20200105, 08:20  #16 
Jun 2003
Oxford, UK
11101010011_{2} Posts 
At 2e13 the earliest I could find without a value appears to be 42981
The largest was 129489 16837633318811 These results should be considered provisional until I get a program to handle the results. 
20200106, 08:34  #17  
Feb 2003
11×173 Posts 
Quote:
Both assume that your master gap list is stored in the file "gaplist.txt" (an example file with gaps up to 1e12 is included). Usage is as follows: Code:
perl update_gaplist.pl logfile.txt Code:
perl check_gaplist.pl The screen output of the latter will look as the following: Code:
21764 (1)  unknown 22700 (6)  unknown 22807 (1)  unknown 23143 (1)  unknown 24100 (6)  unknown Last fiddled with by Thomas11 on 20200106 at 08:37 

20200106, 09:55  #18  
Jun 2003
Oxford, UK
3×5^{4} Posts 
Quote:
I'll post the results when I get to 1e14  at the moment I am at 3e13 with 52048 as the smallest unknown. The largest gaps to 3e13 are: 111504 29595233745191 112105 26248083591881 113152 28184538475271 113467 25801593675041 114083 8547351574961 115224 15114108020021 118307 18317170605491 125692 18888105484811 129489 16837633318811 

20200106, 19:52  #19  
Dec 2008
you know...around...
3^{2}·61 Posts 
Quote:
You might have a look at similar data from prime gaps (check successive maximal values of p in increasing gaps g and how many are g mod 3 = 1 or 2) or twin prime gaps (how many g/6 mod 5 = 1 or 4). I'd guess the bias for quad prime gaps should be even stronger. 

20200107, 04:45  #20  
Jun 2015
Vallejo, CA/.
2^{2}×239 Posts 
Quote:


20200107, 17:09  #21  
Jun 2003
Oxford, UK
3×5^{4} Posts 
Quote:
Code:
140945 30709975578251 143014 68802225596051 143374 73374129557621 148435 48935654916221 151264 43785651890171 153447 47998980412211 159414 74498625237131 162830 55341128536691 Last fiddled with by robert44444uk on 20200107 at 17:09 

20200107, 18:37  #22  
Dec 2008
you know...around...
3^{2}·61 Posts 
Quote:
For ordinary prime gaps, this is A100180 

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