Is Pi to the power of Euler's Number Rational?

Open Question
It is not known whether $\pi$(pi) to the power of Euler's number $e$:
 * $\pi^e$

is rational or irrational.

Its decimal expansion gives its value to be approximately:
 * $\pi^e \approx 22 \cdotp 45915 \, 77183 \, 61045 \, 47342 \, 7152 \ldots$

Progress
See Schanuel's Conjecture Implies Transcendence of Pi to the power of Euler's Number.