Is 2 to the power of Euler's Number Rational?
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Open Question
It is not known whether $2$ to the power of Euler's number $e$:
- $2^e$
is rational or irrational.
Progress
See Schanuel's Conjecture Implies Transcendence of 2 to the power of Euler's Number.
Sources
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.18$: Algebraic and Transcendental Numbers. $e$ is Transcendental