Can we proove "Bertrand postulate" for primes a(mod q), namely: there is always a prime number   
p=a(mod q) betwen nq and nq^2 for every n>0 and (a,q)=1. (This would mean that betwen nq and nq^2 there is alwajs at least phi(q) primes, each belong to different residuum clas mod q.)