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[ December 23, 2016 ]
 Conjecture 
The mean merit of the borderprime gaps converges to 2.
[ Patrick De Geest ]


Here is the data I collected from my completed borderprp files.

borderprp(00000-04999).txt Sum of 4999 merits
Mean merit
10025,5455908894639596761
2,0055102202219371793
borderprp(05000-09999).txt Sum of 5000 merits
Mean merit
9975,1571466100067322068
1,9950314293220013464
borderprp(10000-14999).txt Sum of 5000 merits
Mean merit
9877,3281987156469657598
1,9754656397431293931
borderprp(15000-19999).txt Sum of 5000 merits
Mean merit
10023,0967943808295817027
2,0046193588761659162

From these four large files I noticed that the overall
mean merit wobbles around the value of 2.
Hence my conjecture based around the first 19999 consecutive
borderprime gaps that the average merit value converges to 2.

borderprp's (00000-19999) Sum of 19999 merits
Mean merit
39901,1277305959472393456
  1,9951561443370142126


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Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com