Good, good, we needed one of these...

Actually 69 does not really have any special number-theoretic properties (sum-of-powers, primality, etc.) and almost all of the "special" numbers encountered in analysis are transcendental.
Here are some of the more common special numbers:
http://pauillac.inria.fr/algo/bsolve/constant/constant.htmlOut of those, the ones I most frequently encounter and use are the following. All have some really amazing propeties.

Archimedes' Constant (
p)
Natural Logarithm Base (e)
Euler-Mascheroni Constant
Gamma Function Constants
Exponential Integral Constants
Stieltjes Constants
Khinchin's Constant
Omega Constant
I will post some nice special function proofs in a little while.
