# Is there a proof that $\pi \times e$ is irrational?

It is known that either $\pi + e$ or $\pi \times e$ is transcendental (or possibly both), but no proof is known that one of those two numbers in particular is transcendental.

If we just want irrationality rather than transcendence, is a proof known?

Can we prove $\pi+e$ is irrational? Can we prove $\pi \times e$ is irrational?

It is not known whether $\pi + e$ is irrational, nor whether $\pi \times e$ is irrational. See $\# 22$ here.

• I typeset your answer to change * to $\times$ and to add the webpage as a link. Hope you don't mind.
– user17762
Mar 21 '11 at 4:51
• @Sivaram: Not at all, thanks for cleaning it up. Mar 21 '11 at 4:53
• The link does not work anymore. Here is the version from Google cache. Jun 17 '12 at 6:56