This is fishing, not caching!!!
The search for divisors, however, can be greatly optimized with the upper bound of sqrt(number) + 1

This could run much faster if you replace starting point of a by: n/sqrt(2). Easily provable.

Note: {1,} is the same as +

Cool. I'd just modify the pattern to (\d{1,})(\D*) so you don't need to filter out the last element.