Twin-prime constant ($C_2={\prod }_{p>2}(1-(p-1{)}^{-2})$)

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