<p>No, 58^34 is greater than 2^160: <a href="http://www.wolframalpha.com/input/?i=2%2a%2a160%20%3E%2058%2a%2a34" rel="noreferrer">http://www.wolframalpha.com/input/?i=2*<em>160+%3E+58</em>*34</a></p>

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

CC BY-SA 3.0
2013-12-31T10:39:21.447Z
2013-12-31T10:39:21.447Z
jnnk
<p>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)"</p>

<p>This set is a fixed string of 34 characters.</p>

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

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

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

<blockquote>
  <p>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.</p>
</blockquote>

CC BY-SA 3.0
2013-12-31T16:33:54.563Z
As mentioned, the first character is fixed and four bytes are a "checksum" so it's more like ~58^29 ~= 2^170 >> 2^160.
dchapes
<hash><hacking><base58><ripemd160>
The bitcoin address space seems to be closer to 2^40, not 2^160
Robert Christian
# The bitcoin address space seems to be closer to 2^40, not 2^160

(Asked by: username_0 on 2013-12-31)

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.

**Tags:** hash, hacking, base58, ripemd160

> **Comments:**
> **username_1**: As mentioned, the first character is fixed and four bytes are a "checksum" so it's more like ~58^29 ~= 2^170 >> 2^160.  

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## 1 answers

### Answer by username_2 on 2013-12-31. Score: 5

No, 58^34 is greater than 2^160: [http://www.wolframalpha.com/input/?i=2\**160+%3E+58*\*34](http://www.wolframalpha.com/input/?i=2%2a%2a160%20%3E%2058%2a%2a34)

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


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