Perhaps there're some 'weights' for any nvalue:
Example:
For the range 1<k<1M I've made those days some runs.
So for n=9996 I got 136 primes and for n=9994 174!
This gives 2030 % difference (in a small range of k: consider the problem of small numbers).
Could be the same like lottery:
Since 1955 (lottery 6 from 49) the number '13' was drawn 286times (least) and '49' 397times (most) in 2844 draws!
Statistically these should be equal, but with 'only' 2844 draws there's this difference.
So for small ranges there're small difference in primes for some n.
