# Why is this number : $e^{e^{e^{79}}}$ conjectured to be an integer number which is a skew number? [duplicate]

skew number is defined as : $e^{e^{e^{79}}}$ , I seek for the mathematical reasons which let $e^{e^{e^{79}}}$ conjectured to be an integer ?
• This is closely related to math.stackexchange.com/questions/13054/… . The main point is that $e^{e^{e^{79}}}$ is too large to compute digits to see if it is an integer, and the current knowledge of transcendental number theory is not able to prove that the number is not an integer. This is interesting because many people feel that the number should "obviously" not be an integer, although they can't prove it. – Carl Mummert Jan 20 '18 at 13:03