Number of Twin Primes less than Powers of 10

Sequence
For each $n \in \N$, the number of pairs of twin primes below $10^n$ is given by the following sequence:
 * $2, 8, 35, 205, 1224, 8169, 58 \, 980, 440 \, 312, 3 \, 424 \, 506, 27 \, 412 \, 679, \ldots$