Is Skewes' number e^e^e^79 an integer?

Importance: Medium ✭✭
Recomm. for undergrads: no
Posted by: VladimirReshetnikov
on: December 13th, 2011

\begin{conjecture} % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. Skewes' number $e^{e^{e^{79}}}$ is not an integer. \end{conjecture}

% You may use many features of TeX, such as % arbitrary math (between $...$ and $$...$$) % \begin{theorem}...\end{theorem} environment, also works for question, problem, conjecture, ... % % Our special features: % Links to wikipedia: \Def {mathematics} or \Def[coloring]{Graph_coloring} % General web links: \href [The On-Line Encyclopedia of Integer Sequences]{}


Skewes, S. (1933), "On the difference $\pi(x) − Li(x)$", Journal of the London Mathematical Society 8: 277–283

* indicates original appearance(s) of problem.

Schanuel's conjecture

Assuming \Def[Schanuel's conjecture]{Schanuel's conjecture}, one can show that e^e^e^79 is transcendental.

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