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It is not defined.
2
It is how 2 is defined so it is not an illusion.
Prime numbers have only 2 factors and their set is not well defined because they do not follow an orderly mathematical pattern.
Tan of pi/2 + k*pi radians, for integer k, is not defined since tan = sin/cos and the cosine of these angles is 0. Since divsiion by 0 is not defined, the tan ratio is not defined.