ON THE PRIMES WITH $P_{n+1}-P_n = 8$ AND THE SUM OF THEIR RECIPROCALS

We introduce the counting function ${\pi}^*_{2.8}(x)$ of the primes with difference 8 between consecutive primes ($p_n,\;p_{n+l}=p_n+8$) can be approximated by logarithm integral $Li^*_{2.8}$. We calculate the values of ${\pi}^*_{2.8}(x)$ and the sum $C_{2,8}(x)$ of reciprocals of primes with difference 8 between consecutive primes $p_n,\;p_{n+l}=p_n+8$ where x is counted up to $7{\times}10^{10}$. From the results of these calculations. we obtain ${\pi}^*_{2.8}(7{\times}10^{10}$)= 133295081 and $C_{2.8}(7{\times}10^{10}) = 0.3374{\pm}2.6{\times}10^{-4}$.