Twin-prime constant
= Twin-prime constant
{title2=$C_2=\prod_{p>2}(1-(p-1)^{-2})$}
This positive convergent product corrects for the dependence of primality of $n$ and $n+2$ at each odd prime. The associated singular series is $2C_2$: the factor at two is two, and at an odd prime the local correction is $(1-2/p)/(1-1/p)^2$. It appears in the <Hardy–Littlewood twin-prime asymptotic conjecture> and in upper bounds from the <Selberg sieve>.
// Target: analytic-number-theory.bigb