# Gelfond-Schneider constant

The $2^{\sqrt{2}}$ was one of the first numbers to be proven to be transcendental by appying Gelfond’s theorem. However, naming the constant after Gelfond and Schneider comes from Eric Weisstein, with many people preferring to refer to it simply as 2 to the power of square root of 2.

Its value in base 10 is approximately 2.66514414269022518865029724987313984827421131371. Its continued fraction representation is neither terminating nor periodic, and begins

 $2+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{72+\,\cdots}}}}$
Title Gelfond-Schneider constant GelfondSchneiderConstant 2013-03-22 18:54:36 2013-03-22 18:54:36 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11J81