The Euler product of the Riemann zeta function at 2 restricted to primes in A002144, which is the inverse of the infinite product (1-1/5^2)*(1-1/13^2)*(1-1/17^2)*(1-1/29^2)*...

There is a complementary product_{primes == 3 mod 4} 1/(1-1/p^2) = 1.16807558541051428866969673706404040136467... such that (this constant here)*1.16807.../(1-1/2^2) = zeta(2) = A013661.