I think a much better example is of the style of the highest rated answer in the thread. If you look at the wiki page [0] you see that the constant has a non-tr

I think a much better example is of the style of the highest rated answer in the thread. If you look at the wiki page [0] you see that the constant has a non-trivial relationship with a major mathematical question ("what is the behavior of the prime numbers?") and, as you compute estimations of it within your computational ability it waves above and below its true value. For things like e^i you almost cannot define the idea of complex powers without knowing the right concepts. The sqrt(2) example clearly converges toward 2 as you stack the tower. Binet's formula was arrived at via derivation from the Fibonacci recursion formula... so anyone who had it would obviously know its significance. So, to be clear, the only reason why those examples would look strange is if someone showed it to you (armed with only high school mathematics) without explanation. Or if you don't know how to estimate the solution to f^n(1), f(x) = sqrt(2)^x for n, say, in [1,10]. "Legendre's Constant" has none of those features. That said, with today's computational power deriving a sufficiently strong estimate that it "might be 1" isn't so hard. One can imagine that other slower to converge examples exist today [0] http://en.wikipedia.org/wiki/Legendre%27s_constant http://en.wikipedia.org/wiki/Legendre%27s_constant