One time I was in a room where someone was reading off a 10-digit phone number. As they read it off, I added the digits in my head and made sure their cumulative sum wasn't divisible by 3 and also made sure that the last digit was a 1, 3, 7, or 9. Immediately after he said the last digit and instantly realizing it met this criteria, I blindly (but in my most confident voice I could conjure) said "that's a prime number". After a bystander pulled out a TI-89, it turned out to actually be a prime number. It was dumb luck, but I had everyone fooled into thinking I was a savant.
One time at a franchise restaurant I frequent while sitting and eating by myself (I'm a loser) I looked at my receipt and kept staring at the restaurant's phone number. After getting home, I found out that it checked out to be a prime number. I emailed this information to the CEO and they gave me a free meal (they're a very nerd-friendly franchise).
In a college physics class my professor asked for examples of matter with a specific gravity of less than one. I said, "A duck." My professor was the only one that got it, but she said it doesn't count.
Also, in calculus 2, the day before one of our breaks we decided to have a laid back "fun" math day. It consisted of two and a half hours of everybody writing as many proofs for the Pythagorean theorem as we could remember. Every student got involved (there were less than ten of us.)