Twitter has just tweeted to say the numbers they shared earlier about traffic on their system last night were INCOMPLETE.
The company now says:
Last night saw the highest sustained rate of Tweets ever. From 10:45 – 2:20am ET, there was an average of 3,000 Tweets per second. At 11p.m. ET, there were 5,106 Tweets per second. At 11:45p.m. ET, when Pres. Obama finished his remarks, there were 5,008 TPS