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 ?
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3It isn't conjectured to be an integer. – Angina Seng Jan 20 '18 at 13:02

1This is closely related to https://math.stackexchange.com/questions/13054/howtoshoweee79isnotaninteger . 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

1@JoelReyesNoche: Actually the name is Skewes, not Skewe. https://en.wikipedia.org/wiki/Stanley_Skewes – Hans Lundmark Jan 20 '18 at 18:44

@HansLundmark, thanks for the correction. – Joel Reyes Noche Jan 21 '18 at 01:00