The bitcoin address space seems to be closer to 2^40, not 2^160 The Base58 Encoding of a public key hash outputs:  "A set of 58 alphanumeric symbols consisting of easily distinguished uppercase and lowercase letters (0OIl are not used)"

This set is a fixed string of 34 characters.

That is to say, "A bit coin wallet's address is 34 characters, each character being one from a possible set of 58"

So the total possible addresses is 58^34 which is just slightly less than 2^40.

I understand that the hash space is 2^160, but the final result is much smaller at 2^40.  What am I missing?


  Edit:  I made a simple math mistake reducing 58^34 to a power of two
  by adding not multiplying the exponents...  The bitcoin address is
  sufficient to contain the 2^160 possible hashes:  58^34 is 904
  octodecillion (60 decimal digits), and 2^160 is 1 quindecillion (49
  decimal digits)... the larger number accounts for the version byte and
  checksum.
No, 58^34 is greater than 2^160: http://www.wolframalpha.com/input/?i=2*160+%3E+58*34

Note, that the address also contains a checksum and a network id not carrying additional information. That's why the numbers are not equal.