2 to the power of 256 - 1 in my Excel yields 1.16e+77 and yes it does look like some arbitrary number...
Excel doesn't have bignum support. Python does.
>>> 2**256-1
115792089237316195423570985008687907853269984665640564039457584007913129639935L
>>> hex(_)
'0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffL'
Which has nothing to do with the question or answer

The aim on a normal pool is to get around 18 shares per minute, to ensure variance isn't too high, and of course you aren't submitting too many shares.
Back in the dark ages when we mined with GPUs or FPGAs it would take around 20 or more seconds to find a 1 diff share, but as mining got faster, finding 1 diff shares got faster, of course.
At some point most pools realised that you had to mine higher difficulty shares, otherwise you were sending way too many share, too quickly, to the pool.
So if we say 18 shares per minute, then 3.33.. seconds per share, then you can work out how to convert a hash rate to 18 shares per minute as so:
A 1 diff share averages 2^32 hashes per share (and 2^32 is roughly 4.3 billion)
Thus a 4.3GHs miner gets approximately 1 share per second at 1 diff
Thus a 1.3GHs miner gets approximately 1 share per 3.33.. seconds at 1 diff
So to get one share per 3.33.. seconds with an XHs miner, you need to divide it's hash rate by 2^32*0.3 (i.e. 1.3GHs) = multiply it by 7.76*10^-10 to get the difficulty it should mine at.
e.g. a 13THs miner = 13*10^12 * 7.76*10^-10 = ~10,089 Diff
So ... I guess that number is some vague relation to 7.76*10^-10 ... you'd have to check the code, I hate python so I'm not gonna work that part out
