A paper appeared in arXiv.org, physics/0511145.
The compression factor can be quite large.
--- In email@example.com
> Here is a comment about the utility of your
> prime factorizations.
> First what is the probability of a random sequence
> being prime.
> Second what is the probability of a subsequence of those
> digits being prime.
> The probability grows to unity, the longer the sequence
> is. So, after finding a subsequence and after
> labeling the prime numbers with the integers, you will
> find a compression factor on that information contained
> in that sequence, which grows without bound.