Here is a famous quote from theymos from that time:
I generated 5 blocks today on my Pentium processor. Two of them were within 3 minutes of each other.
Since this was before the first halving, the block rewards were of course 50 BTC, so 5 blocks would yield 250 BTC. But, theymos also mentioned that his computer is turned off while sleeping...
This is exactly where the "250 BTC/day" mentioned in my original post, was sourced. Which is why I am confused. If odolvlobo is correct, his number was calculated at 3000 BTC/day being mined. Again, a very large variation in results, which is what I am trying to figure out. How can one result be 250 and the other 3,000? Even if theymos ran it only 16 hours per day (while awake,) under the formula by odolvlobo, it should have produced 2,000 BTC/day. 250 BTC would be produced with only 2 hours of time in that formula, assuming a has rate of 3 and difficulty of 1.