[necovek]

You mean like those guaranteed-always-compresses-by-at-least-one-bit algorithm patents gzip page made fun of?

In your case, doing prime factoring is where the cost would be, wouldn't it?

[avmich]

Yes, but the point is to look for different representations, not necessarily use this specific one.

[necovek]

Yes, but the point is that getting to a different representation from a natural one (eg. binary one with computers or a decimal one for human use) is going to have some "external" overhead which is likely to negate the savings.

Yes, sometimes a neat trick like the one in the article of replacing one multiplication with substraction appears, but that is not as universal.