Google Groups

Ratios of primes

Chris Long Apr 18, 1990 11:02 PM
Posted in group: sci.math
In article <1990Apr19.0...@Neon.Stanford.EDU>, Ilan Vardi writes:

> The answer is yes, p_i/p_j is dense in R+. I think that this is
> a special case of the following lemma with f(x) = x log x:

Another way of looking at it is to note that p(x) ~ x*ln(x),
and so lim p([rx])/p(x) = r.  If I'm not mistaken, the more general
result you mention can be found in Kuipers et. al. _Uniform
Distribution of Sequences_.