The following content was written by davux on November 10, 2010, 10:21:15 PM in the thread Pros and cons of using new Bitcoin addresses for each transaction?. All content is owned by the author of the bitcointalk.org post. (original)

It’s not. It’s 62^33, which is slightly over 10^59.
How did you arrive to this result?

An address has 33 significant characters, each of which has 62 possible values (10 numbers, 26 uppercase letters, 26 lowercase).
So you have 62 * 62 * … * 62 possibilities (33 times).

Actually, now that I remember, it’s 58 (uppercase i and lowercase L are not included because they look too similar, same for zero and uppercase o).

So there are 58^33 possibles values, which is slightly more than 10^58. Still high, but not quite as high as 10^92.

The following content was written by theymos on November 10, 2010, 10:40:57 PM in the thread Pros and cons of using new Bitcoin addresses for each transaction?. All content is owned by the author of the bitcointalk.org post. (original)

An address has 33 significant characters, each of which has 62 possible values (10 numbers, 26 uppercase letters, 26 lowercase).
So you have 62 * 62 * … * 62 possibilities (33 times).

Actually, now that I remember, it’s 58 (uppercase i and lowercase L are not included because they look too similar, same for zero and uppercase o).

So there are 58^33 possibles values, which is slightly more than 10^58. Still high, but not quite as high as 10^92.

As ByteCoin already explained earlier in the topic, an address contains a non-data check code and version number. There are actually “only” 160 bits of randomness in each address: 2^160, or 1.46×10^48 possible addresses.

Addresses can also be 25-34 characters in length, depending on how numerically large the hash160+check code is (the larger it is, the more base58 characters required).