In the answer to this [question][1], engelbret mentions "a conjecture of H. L. Montgomery (not the one on pair correlations, another one), which implies both the GRH and the Elliott-Halberstam conjecture.". My question is : what does this conjecture says, and where is it stated ? I am also interested in any references that would discuss that conjecture. [1]:https://mathoverflow.net/questions/834/arithmetic-progressions-without-small-primes/1498#comment364029_1498