How far away can you see a thunderstorm?
The top of a cumulonimbus cloud is usually about 40,000 feet and can reach heights of over 60,000 feet, which would be visible for a distance of 245 or 300 miles, respectively.  Of course, that would be the very top that would be visible at those distances, but it puts it well within the 125 mile distance from which you saw the storm.

The following formula was used:

$$\text{distance} = 3958.8 * \arccos(3958.8/(3958.8+\text{height}))$$

where $3958.8 \ \mathrm{mi}$ is the mean radius of earth.

This formula calculates the distance from an observer to the horizon, which for a six-foot tall person is close enough. If you wanted to calculate the distance an object would be visible from (given absolute atmospheric clarity) you'd have to calculate this twice (from observer to horizon and horizon to object) and add the results.