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A little item for anyone who wants to test their new exaflop machine. Given some $\operatorname{prime}(n)/\log\operatorname{prime}(n)={}$as near as possible to a prime $q,$ for both log base $10$ and base $e,$ what is $\operatorname{prime}(n)$? Near as possible means the minimum difference from either above or below $q;$ thus $126.9999$ or $127.00001$ would be considered to be very close to prime $127.$

Michael Hardy
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J. M. Bergot
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  • So $prime(n)$ is the $n$'th prime number ? – Zubzub May 03 '18 at 19:29
  • Yes, p(n) is the nth prime. – J. M. Bergot May 03 '18 at 20:04
  • Using Wolfram Alpha over the Internet (which is quite likely nowhere near exaflop) I get 1, 3, 5, 9, 16, 23, 28, 29, ... Select[Range[1000], PrimeQ[Round[Prime[#]/Log[Prime[#]]]] && PrimeQ[Round[Prime[#]/Log[10, Prime[#]]]] &] – Mr. Brooks May 03 '18 at 22:12
  • The point is to find the particular prime(n) which produces AS CLOSE AS possible that prime q and print what q is. It is NOT the same as simply rounding q. – J. M. Bergot May 04 '18 at 18:09
  • Prime(29)=109, divided by log base 10 gives 53.49877, which is not very close to pure 53; divided by log base e gives 23.234, which is also not very close to pure 23. Very close means a few thousandths or less. – J. M. Bergot May 05 '18 at 17:54

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