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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
$10^{600}$.

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