user-1: Nextcoin seems to convert 256-bit Curve25519 256-bit public keys into "account numbers" that have only arabic numbers and seem to only have a length of 20.
How is that done?
Examples
In the Nextcoin forum, users leave their account numbers.

user14985: Public keys are 256 bits. Account numbers (for brevity) are 64-bits. However, the person who sends first outgoing transaction with that account, controls the account with 256-bit public key. 
You cannot take over an account by collision as it's protected by 256-bit public key. 

user11761: According to these lines an accountId seems to be...
int(sha256(publicKey(sha256(passphrase)))[7:0], 256)

...which translates to 256^8 accounts or roughly 2 * 10^19, which fits the idea of around 20 arabic numerals.
Given there are only 2^64 unique accountId and the birthday paradox, you can check this collision probability table (the 16 bytes/64 bits row). If each person in the world had a single Nextcoin account, the collision probability is greater than 75%! I'm sure this is the least of their problems.
This looks really amateurish. Really amateurish. Really, REALLY, REALLY amateurish. Stay away from this coin!

-1: <p>Nextcoin seems to convert 256-bit Curve25519 256-bit public keys into "account numbers" that have only arabic numbers and seem to only have a length of 20.</p>

<p>How is that done?</p>

<p><strong>Examples</strong></p>

<p>In the <a href="https://nextcoin.org/index.php?topic=1411.0">Nextcoin forum</a>, users leave their account numbers.</p>
 14985: <p>Public keys are 256 bits. Account numbers (for brevity) are 64-bits. However, the person who sends first outgoing transaction with that account, controls the account with 256-bit public key. </p>

<p>You cannot take over an account by collision as it's protected by 256-bit public key. </p>
 11761: <p>According to <a href="https://bitbucket.org/JeanLucPicard/nxt-public/src/4073c21098076d3469b3f74d49e73ffabe3a2001/Nxt.java?at=master#cl-4972">these lines</a> an accountId seems to be...</p>

<pre><code>int(sha256(publicKey(sha256(passphrase)))[7:0], 256)
</code></pre>

<p>...which translates to 256^8 accounts or roughly 2 * 10^19, which fits the idea of around 20 arabic numerals.</p>

<p>Given there are only 2^64 unique accountId and the <a href="https://en.wikipedia.org/wiki/Birthday_paradox#Probability_table">birthday paradox</a>, you can check this <a href="https://en.wikipedia.org/wiki/Birthday_paradox#Probability_table">collision probability table</a> (the 16 bytes/64 bits row). <strong>If each person in the world had a single Nextcoin account, the collision probability is greater than 75%!</strong> I'm sure this is the least of their problems.</p>

<p>This looks really amateurish. <strong>Really</strong> amateurish. Really, REALLY, <strong>REALLY</strong> amateurish. Stay away from this coin!</p>
