I'm running your script and watching the memory usage (top), and it's minimal and also not growing, I don't think that memory is your problem. Instead, I think it's just that the code you've implemented is relatively slow, so you probably want to look into optimizing it. A couple of recommendations there: you could, for example

• research faster algorithms for determining whether a number is prime, as well as faster algorithms for determining the factors of an integer,
• investigate where your code is spending the most time by profiling it with something like Devel::NYTProf,
• set up caching for a speed/memory tradeoff for your sub is_prime by using Memoize to cache its return values (or even cache its results to disk using that module or one of the methods I mention below), and
• think about how you might conceptually improve your algorithm. For example, you're looking for the largest prime factor, so why don't you iterate through the (potential) factors from largest to smallest, stopping when you've found the first prime one?

Alternatively, for the task you're doing I can recommend Math::Prime::Util, it has lots of really helpful mathematical routines and it can deal with huge numbers (you should install Math::Prime::Util::GMP for speed). However, if this is homework, that might be considered cheating ;-)

use Math::Prime::Util qw/factor/;
use List::Util qw/max/;
print max(factor(20)), "\n";
print max(factor(13195)), "\n";
print max(factor("600851475143")), "\n";
__END__
5
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[download]

As for your original question, note that once you put things on disk, you'll have disk I/O as a potential bottleneck. But if you still want to look into that, there are a few Perl modules that make storing things on disk fairly transparent, such as AnyDBM_File for tying a hash to a DBM file, or Tie::File for tying an array to a flat text file. Also, this thread might be an interesting read: Is there any cache mechanism for running perl script, where the replies show how to cache data structures using Storable, JSON, or Path::Class (the latter only for simple arrays).