Let $a_n:= $ number of primes of the form $6k-1$ and $\le n$
and $b_n:= $ number of primes of the form $6k+1$ and $\le n$.
I was playing with my computer and noticed that $a_n\ge b_n$ for all $n\le 10^8$. Can this be extrapolated for larger integers? Also it was evident that $a_n-b_n$ grows. Is this unbounded?