Interesting idea, but factoring a number does not compress it - the number of digits (binary or otherwise) will stay roughly the same. You can see this using lo

Interesting idea, but factoring a number does not compress it - the number of digits (binary or otherwise) will stay roughly the same. You can see this using logarithms: a x b = c implies ln a + ln b = ln c. But ln x is proportional to the number of digits of x, so a and b have roughly the same length together as c.