I'm confused that why exactly and what is the reason to conjecture that $e^{e^{^e{^{79}}}}$ is not integer , why not for example with $n=87$ or any other prime $p$ ?Is this number special ? or is there any non trivial characterization to choose $n=79$ ?
2026-03-27 00:57:17.1774573037
Why it were conjectured that $e^{e^{^e{^{79}}}}$ is not an integer only for $n=79$ ? any non trivial characterization?
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It is very unlikely that $e^{e^{e^n}}$ is an integer, or for that matter algebraic, for any integer $n$. There is certainly nothing special about $79$, except that $e^{e^{e^{79}}}$ happens to arise in a certain estimate.