This regular expression is due to Abigail of Perl fame. Who is still very active, see http://search.cpan.org/~abigail/ for more.

However while cute, it is very slow. It tries every possible factorization as a pattern match. When it succeeds, on a string of length n that means that n times it tries to match a string of length n against a specific pattern. This is O(n^2). Try it on primes like 35509, 195341, 526049 and 1030793 and you can observe the slowdown. (Some regular expression engines may employ tricks that speed this up over the naive analysis, but none will be super speedy about it.)

Usual arithmetic is much more efficient. :-)