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

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