--- dasimov@earthlink.net wrote: ...
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
In Harvey Cohn, "Advanced Number Theory" a proof is given that the primes in arithmetic progression are equidistributed among residue classes in the sense that, for gcd(a,m) = 1, sum(1/p^s, p == a mod m) 1 ------------------------ ==> ------ as s ==> 1. sum(1/p^s, all primes p) phi(m) Cohn states without proof, and without citation, that as x ==> infinity, Number of primes < x that are == a mod m 1 ---------------------------------------- ==> ------ Number of primes < x phi(m) is difficult but true. Gene __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com