Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.2

Twin Prime Statistics


Harvey Dubner
85 Long Hill Road
Oakland, NJ 07436
USA

Abstract:

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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(Concerned with sequences A001097 A001359 and A006512 .)

Received May 3 2005; revised version received August 25 2005. Published in Journal of Integer Sequences August 29 2005.

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