--- In

primenumbers@yahoogroups.com, Jud McCranie <j.mccranie@a...> wrote:

> This is true, isn't it?

>

> For every epsilon > 0, let x = 1+epsilon. There is always a prime

between

> x^n and x^(n+1) for all n>m, where m depends on epsilon.

Yes it's true. More standard short interval prime results show

existence of primes in intervals [x,x^(1-epsilon)], for small epsilon

and all sufficiently large x.

Taking epsilon the same in both statements, yours is true provided that

n>(log(1/epsilon))/(epsilon^2),

which is pretty huge, at least for small epsilon.

Andy