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:

$\pi^e \approx 22 \cdotp 45915 \, 77183 \, 61045 \, 47342 \, 7152 \ldots$

This sequence is A059850 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Progress

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

Sources

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): Table $1.1$. Mathematical Constants
• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 1$: Special Constants: $1.11$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $22 \cdotp 459 \, 157 \, 718 \, 361 \, 045 \, 473 \, 427 \, 152 \ldots$
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.29$: Liouville ($\text {1809}$ – $\text {1882}$)
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.18$: Algebraic and Transcendental Numbers. $e$ is Transcendental
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $22 \cdotp 45915 \, 77183 \, 61045 \, 47342 \, 7152 \ldots$