1) The regex works because of backtracking. Perl's regular expressions *want* to match, and they keep trying until they've exhausted every possibility that will let them match.

Once you understand that, you'll understand why it "doesn't" match the whole string in $_. I say "doesn't" because you're right, in a sense--the pattern *does* match the entire string. But then it moves on to the next part of the regex (the \1+) and sees that, if the first part matches the entire string, there's nothing left for the \1+ to match. So the regex wouldn't match.

So the matcher moves back one x in the string, and tries to match again; and it keeps moving backwards (backtracking) through the string until it finds a match. If it doesn't find a match, the match fails, and you have a prime--because there is no pattern such that the pattern repeated a certain number of times matches the string; and since the string is x repeated N number of times, this means that there is no number such that the number times another number equals the original number. That sounded confusing--I suppose that's why symbolic notation was invented. :)

For more on backtracking, look in perlre.

2) \1 is used because \1 is used "inside" of a pattern (on the left-hand side of a substitution operator, or inside a matching operator); you use $1 "outside" of a pattern (on the right-hand side of a substitution operator, or outside a matching operator). More in perlre.