A math question for /sci/

I coded a calculator that does floating point math. The exponent field of this calculator's floating point representation can handle values between 99999 and -99999. What sort of problems can /sci/ propose that would cause an overflow of this field? Are there any problems in real world physics that would exceed these orders of magnitude? I mean, wouldn't the gravitational force of attraction between two protons separated by the diameter of the Milky Way fit into this range?

electron mass 10^-31
grav constant 10^-11
that's 10^-73 before distance

so you need 99926 more powers of ten
so you want these two electrons to be 10^99926/2 meters apart. I'm fairly certain that's larger than the size of the known universe.

Come on /sci/, you can do better than that. There have got to be equations in advanced physics that build up orders of magnitude faster than the basic physics I know.

Force between two electrons one Plank length apart:
charge 10 ^ -19 C
distance 10 ^ -35 m
k 10 ^ 9 N * m^2 / C^2
that would be about 10 ^ 41 N

>>3
where did you get 41? 2*-19 - 35*2 + 9 != 41

And no, we just don't deal with numbers that small or large.

Yeah, sorry to disappoint, OP. Interestingly, a couple dozen digits of PI is more than enough to calculate the circumference of the universe to the millimeter or so given its radius. We just don't need that level of exponent support. That's why even IEEE-754 128-bit floats only use 14 bits for the exponent and the other 114 bits for precision.

Also OP, you didn't say what base your exponents are in. Base 2? Base 10? For >>2, 10^-73 == 2^-245 if that's the base.

microstate counting: ideal bose/fermi gases
The distribution of microstates at any given temperature will far exceed the capacities of your new floating point standard, though the entropy (ln of the # of microstates) is within your computational capacity.
The way around, of course, is with Stirling's approx, and a craptastic use of sum -> integral