If you replace 163 by 67 in the second identity, you get 67 / log(67) ≈ 15.93. I had heard the explanation for e^(pi sqrt(x)) in terms of the j-function, but I

If you replace 163 by 67 in the second identity, you get 67 / log(67) ≈ 15.93. I had heard the explanation for e^(pi sqrt(x)) in terms of the j-function, but I don't know where this x / log(x) thing is coming from...