4 Jul
2006
4 Jul
'06
3:32 p.m.
David Wilson wrote: << I would be willing to conjecture that if there are an infinitude of primes == r (mod m), then there is a prime of this form between n and n(1+e) for sufficient n.
Does "for sufficient n" mean for n >= N(r,m,e), so that possibly N(r,m,e) -> oo as e -> 0 ? (Or might it be just for n >= N(r,m) ?) * * * I would be willing to conjecture that for integers m > r > 0, GCD(r,m) = 1, then the fraction of primes == r (mod m) is asymptotically r/m. Does anyone know a counterexample to that? It seems that it might be a consequence of David's conjecture (or perhaps vice versa). --Dan