Wow, what an idea...
If I remember correctly, there are about 2000 systems in the Imperium. The Zhodani Consulate has ???? systems, and I've never heard how many systems the Solomani, Aslan, Vargr, Hivers, K'Kree, Luriani, Sydite or other races control.
Now, the only information on the number of species on Earth that I found is from Redlist.org which tracks endangered species. They claim that there are approximately 52000 species of vertebrates on Earth now.
Using their numbers as an average for other worlds (unscientific, but this is just an exercise) that would give a figure of about 104,000,000 entries for the Imperium alone. If you assume that the Imperium controls 50% of known space that would be approximately 208,000,000 entries for vertebrates.
That's a lot of work.....
