How big are the keys? - digression

As of 2005 the largest asymmetric key factored by conventional methods was 663 bits, 2^663 is 200 decimal digits. 1024 bits is 309 decimal digits, 2048 bits is 617 decimal digits.
Every time you add a bit, the search space doubles in size.
Numbers on this scale have little relevance outside mathematics, e.g. the number of atoms in the visible universe can be expressed as about 10^81.

As of 2005 the largest asymmetric key factored by conventional methods was 663 bits, 2^663 is 200 decimal digits. 1024 bits is 309 decimal digits, 2048 bits is 617 decimal digits.