I'm curious about approximating numbers as the ratio of primes.
let $p_n$ be the nth prime let $g_r(p)$ be the smallest prime greater than $r \times p$
looks like $\lim \limits_{n \to \infty} g_r(p_n)/p_n = r$
Is this true? How to prove it?
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Are you able to prove the case when $r=1$? – Crostul Aug 07 '16 at 14:04
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@Crostul: I think the prime number theorem yields a relatively easy proof for $r = 1$. – Mr. Chip Aug 07 '16 at 14:33