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Feb 14, 2011 at 16:36 comment added Fedor Petrov I would be happy with non-elementary methods (with $L$-functions probably) aswell, if they give results of such type.
Feb 14, 2011 at 8:59 comment added Felipe Voloch It is not known how to make these kinds of elementary arguments work with $c$ arbitrarily close to $1$. I don't know how to get it better than $c=2$ but it might be possible.
Feb 14, 2011 at 8:50 comment added Fedor Petrov Thank you! Though this seem to work for intervals $[n,2n]$ and I do not see how to change arguments for $[n,cn]$ with $c$ sufficiently close to 1.
Feb 14, 2011 at 0:38 history answered Felipe Voloch CC BY-SA 2.5