Boltzman Constant

http://en.wikipedia.org/wiki/Boltzmann_constant

a) Efficiency of an ideal computer: 4.4×10^-16 ergs / bit (at the average ambient temp of space)
b) Annual energy output of our star: 1.21x10^41 ergs
c) Estimated life of our star: 5 billion years
d) Estimated potential energy of our star: 6.05x10^50 ergs (b*c)
e) Estimated potential bit changes using entire energy output of our star: 1.38x10^66 (d/a)

1.38x10^66 bits ~= count from 0 to ~2^220

(note it is actually less than that because the increment of some values involve changing more than one bit so that could be considered an upper limit).

To show how far away we are from even that.  Total human energy consumption in all forms for all activities in on the order of ~132,000 TWh (4.47x10^27) annually.  If all energy consumption of the human race was diverted to power an as of yet uninvented ideal computer and that computer loaded with a program to increment a counter we could increment that counter to only ~2^146 in a year (less than one quadrillionth of one quadrillionth of a one percent of 2^256).