Euler Constants of Euler Products

It is well-known that the Euler constant γ is considered as the constant term of the Laurent expansion at s=1 of the Riemann zeta function ζ(s). In this paper, we define the Euler constant γ_p as the constant term of the Laurent expansion of the zeta function ζ_p(s) given by the Euler product over elements of a prime set P, and establish the expression of γ_p as the sum over elements of P, which is similar to the one obtained by de la Vallee-Poussin [9].