Stephens' constant

Stephens' constant expresses the density of certain subsets of the prime numbers. Let $$a$$ and $$b$$ be two multiplicatively independent integers, that is, $$a^m b^n \neq 1$$ except when both $$m$$ and $$n$$ equal zero. Consider the set $$T(a,b)$$ of prime numbers $$p$$ such that $$p$$ evenly divides $$a^k - b$$ for some power $$k$$. Assuming the validity of the generalized Riemann hypothesis, the density of the set $$T(a,b)$$ relative to the set of all primes is a rational multiple of
 * $$C_S = \prod_p \left(1 - \frac{p}{p^3-1} \right) = 0.57595996889294543964316337549249669\ldots $$

Stephens' constant is closely related to the Artin constant $$C_A$$ that arises in the study of primitive roots.
 * $$C_S= \prod_{p} \left( C_A + \left( {{1-p^2}\over{p^2(p-1)}}\right)   \right)

\left({{p}\over{(p+1+{{1}\over{p}})}} \right)$$