/^1?$|^(11+?)\1+$/

Don't take this regular expression too seriously, it's actually neither a regular expression (as defined in automata theory), nor a way to check if a number is a prime. It's just an awesome thing that Perl can do. See this cool article called The Prime That Wasn't by Andrei Zmievski for a discussion about how this regex fails for larger numbers because of backtracking.