/^1?$|^(11+?)\1+$/
I was thoroughly impressed with this regex. I'm not going to reiterate what other people have already explained. So instead I will place links to other blogs that explain this very cool regex primality test.
http://montreal.pm.org/tech/neil_kandalgaonkar.shtml
http://www.noulakaz.net/weblog/2007/03/18/a-regular-expression-to-check-for-prime-numbers/
http://zmievski.org/2010/08/the-prime-that-wasnt
Thanks to <a href="http://rantsofageek.com/">Theo</a> for sending me a link to this!