>>792686756000*4/(365*3+366)
The thing is, not all of these 6000 people participate in chat. If I had to guess, I'd say around 10 % of people, a bit less, actually write something. Perhaps it's as low as 200 to 300 people. Then again, there's quite some fluctuation of people coming in and out...
You also have to think about the fact that birthdays are not spread out equally over 365,25 days.
All in all, the number of birthday havers today is extremely high. This was a very easy calculation that doesn't consider those certain factors.