Answer: 5,106. According to the Montreal Gazette, "At 11 p.m. ET, there were 5,106 Tweets per second. At 11:45 p.m. ET, when President Obama finished his remarks, there were 5,008 TPS [tweets per second]" And accoding to USA Today, "Within hours, there were more than 2.2 million mentions of bin Laden on Twitter."