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:

$2, 8, 35, 205, 1224, 8169, 58 \, 980, 440 \, 312, 3 \, 424 \, 506, 27 \, 412 \, 679, \ldots$

This sequence is A007508 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Sources

• 1976: Tables Concerning Irregularities in the Distribution of Primes and Twin Primes to $10^{11}$

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $8169$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3,424,506$