The Green-Tao is true for any subset of the primes of positive relative density; the primes in a fixed arithmetic progression to modulus $d$ have relative density $1/\phi(d)$.
@KoundinyaVajjha, I think that another reason to love MO is the exactly 256 upvotes (each) that Ben Green and Terry Tao got. — LSpiceNov 23 '16 at 17:15
The Green-Tao is true for any subset of the primes of positive relative density; the primes in a fixed arithmetic progression to modulus $d$ have relative density $1/\phi(d)$.
