<p>No, it is not a threat, because the number of possible private keys is about 2^256. Even if every atom on earth was a Petabyte hard drive, you would still not have nearly enough storage for a record of all keys.</p>

<p>(More interesting is the finite number of Bitcoin addresses, but that is still enormously large.)</p>

CC BY-SA 3.0
2014-05-01T12:11:37.457Z
2014-05-01T13:55:20.497Z
2014-05-01T13:55:20.497Z
Meni Rosenfeld
<p>There's around 2^256 possible private keys. However, there's only 2^160 valid wallet addresses. To store each key-address pair we need 160+256 bits = 25 bytes, so the searchable record will take <a href="http://www.wolframalpha.com/input/?i=(2%5E160+*+25+bytes)+%2F+(4+TiB)+*+(0.6+kg)" rel="nofollow">several million mass of solar system if stored on 4TiB harddrives</a>.</p>

<p>But first we need to create this database. If we equip each PC on Earth (around 2 billion) with 4 GPUs (each generating around <a href="https://en.bitcoin.it/wiki/Vanitygen_keysearch_rate" rel="nofollow">20Mkey/s</a>), we will need <a href="http://www.wolframalpha.com/input/?i=2%5E160+%2F+%28%2820e6+1%2Fs%29+*+%284*2e9%29%29" rel="nofollow">much more time than the age of the universe</a>. By the way, we most likely will also hit the hard drive write performance limit if we write each pair to disk.</p>

CC BY-SA 3.0
2014-05-01T12:21:23.307Z
2014-09-12T07:25:41.830Z
2014-09-12T07:25:41.830Z
aland
<p>Since the set of all private keys is denumerable, it is at least possible to create a searcheable record of all keypairs. Which, when finished, is a killer for the whole idea. Am I right or do I miss some essential part?</p>

CC BY-SA 3.0
2014-05-01T11:35:02.907Z
You're meaning something like [this](http://directory.io/)?
aland
CC BY-SA 3.0
2014-05-01T17:13:22.247Z
@aland Clever! I think I just found the smallest vanity address: 19's compressed address starts with [`1Amy`](https://blockchain.info/address/1AmybvuPDrDpsqsgSzqbwALGcW1t6Yn9uN)
Tim S.
CC BY-SA 3.0
2014-09-12T06:25:15.690Z
It's pretty hard to represent non-denumerable sets on a finite state digital computer.
Nate Eldredge
CC BY-SA 3.0
2014-09-12T13:24:27.490Z
OP - It's not denumerable, it's finite. "Denumerable" in standard mathematical terminology means countably infinite.
Meni Rosenfeld
<security>
Is the denumerability of private keys a threat?
Isabaellchen
# Is the denumerability of private keys a threat?

(Asked by: username_0 on 2014-05-01)

Since the set of all private keys is denumerable, it is at least possible to create a searcheable record of all keypairs. Which, when finished, is a killer for the whole idea. Am I right or do I miss some essential part?

**Tags:** security

> **Comments:**
> **username_1**: You're meaning something like [this](http://directory.io/)?  
> **username_2**: @username_1 Clever! I think I just found the smallest vanity address: 19's compressed address starts with [`1Amy`](https://blockchain.info/address/1AmybvuPDrDpsqsgSzqbwALGcW1t6Yn9uN)  
> **username_3**: It's pretty hard to represent non-denumerable sets on a finite state digital computer.  
> **username_4**: OP - It's not denumerable, it's finite. "Denumerable" in standard mathematical terminology means countably infinite.  

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## 2 answers

### Answer by username_1 on 2014-05-01. Score: 6 | Accepted answer

There's around 2^256 possible private keys. However, there's only 2^160 valid wallet addresses. To store each key-address pair we need 160+256 bits = 25 bytes, so the searchable record will take [several million mass of solar system if stored on 4TiB harddrives](http://www.wolframalpha.com/input/?i=(2%5E160+*+25+bytes)+%2F+(4+TiB)+*+(0.6+kg)).

But first we need to create this database. If we equip each PC on Earth (around 2 billion) with 4 GPUs (each generating around [20Mkey/s](https://en.bitcoin.it/wiki/Vanitygen_keysearch_rate)), we will need [much more time than the age of the universe](http://www.wolframalpha.com/input/?i=2%5E160+%2F+%28%2820e6+1%2Fs%29+*+%284*2e9%29%29). By the way, we most likely will also hit the hard drive write performance limit if we write each pair to disk.


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### Answer by username_4 on 2014-05-01. Score: 3

No, it is not a threat, because the number of possible private keys is about 2^256. Even if every atom on earth was a Petabyte hard drive, you would still not have nearly enough storage for a record of all keys.

(More interesting is the finite number of Bitcoin addresses, but that is still enormously large.)


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