Summary: Hardy and Littlewood conjectured that the the number of twin primes less than $x$ is asymptotic to $2C_2\int_{2}^{x}\frac{dt}{(\log t)^{2}}$ where $C_2$ is the twin prime constant. This has been shown to give excellent results for $x$ up to about $10^{16}$. This article presents statistics supporting the accuracy of the conjecture up to $10^{600}$.

11B05, 11A41

prime gaps, twin primes, twin prime constant