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Re: This is true, isn't it?

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  • Andrew Swallow
    ... between ... 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
    Message 1 of 2 , Dec 6, 2004
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      --- 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
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