Topic: Limited number of bitcoin addresses (Read 5284 times)

I also learn something new every time I visit these forums.

For example, this interesting thread:  https://bitcointalksearch.org/topic/m.13097839

Nope. Not so.

Bitcoin addresses are calculated with a RIPEMD160 hash.  That's a 160 bit value.  Therefore, there are only 2¹⁶⁰ possible bitcoin addresses.

(Actually there are both P2PKH, starting with a "1", and P2SH addresses, starting with a "3", so that doubles the number of potential addresses to 2¹⁶¹)


2¹⁶¹ is approximately

2.9 X 10⁴⁸ possible addresses.

Nope.

Currently only 10⁴⁸ possible bitcoin addresses. So there are 10³² times as many atoms in the universe as possible bitcoin addresses.

It's possible that additional bitcoin address types may be introduced in the future, but its impossible to predict just how many potential bitcoin addresses those future versions may enable.

i guess it is just another reason (although low on the list) for spreading out your bitcoins across multiple addresses.

must be joking, i hope he is joking.... but sadly i do not think he is joking  

The address space is unimaginably large, address collision is extremely unlikely. I understand that ever since I first know about bitcoin. But there is still a worrying thought in my mind that this is possible and there is no protection to my coins when that happens. I have got used to using bitcoin without this insecurity because I think if a collision happened, mine won't be the first to collide. 

it'll take millions of years to have address collisions, so many possibilities

The number of base pairs in a human genome is about 3 billion base pairs.  (10^12)
The bitcoin address search space is 2^160  (10^48)

Think about the scale of that. You are not able to count to 10^48 in your lifetime, let alone generate all bitcoin addresses.
At the time when all bitcoin addresses are collected, we are long dead.

that 2^160 possible addresses is too big to fathom...but I kind of can get my head around the fact that we basically will never run out of addresses, but being truly random....it is possible for addresses to collide...although infinitesimal, yes?
and I guess the probability of that address either holding any or any significant amount of btc is even more infinitesimal?
but those possibilities exist?

The universe is estimated to be 14 billion years.  Lets say it will be there for another 50 billion years.  If you want to exhaust 2^160 addresses, you and every other person on this planet must generate 100 million addresses every picosecond (a trillionth second) until the end of the universe.  And to say what was already said in this thread in other words: once there is enough computing power on this planet to generate all bitcoin addresses, then the current bitcoin address scheme is broken and we need longer addresses.

You can't sell addresses The address is generated from a private key that you choose at random.  You don't want to use an address where someone else generated the private key and has full access to the account.

I also do not beleive that this will happen any time soon.  Once we are down to the last few hundred million addresses, I am sure they will find some way to recycle them or make it able to sell the addresses from one individual to another.  Just a thought.

This topic has nothing whatsoever to do with calculus. If you meant 'math class', say 'math class'.

While I'm at it, the distribution of particles in a gas has nothing whatsoever to do with the many-worlds interpretation of quantum mechanics, nor in fact with quantum mechanics itself. The old trope of all the gas suddenly coalescing on the left-hand side of the box is a *statistical* phenomenon, not a quantum one.

This really isn't a problem and this kind of question would only be asked by somebody who did not take a calculus course in high school. Satoshi probably had this in mind when developing the protocol and as pointed out above, it is mathematically impossible to run out of addresses. Don't worry about it. The developers already thought about it.

We have been taught since childhood that numbers don't end anywhere, they go on till infinity. So, mathematically it's impossible for numbers to get end. So, is in the case of wallet addresses.. And wallet address comprises of alphabets too , so it's currently in near future tough for them to get finished.
But, even though it happens in future, simple solution is increasing or decreasing number of digits. But, currently it's not a matter to really think upon.

An 160 bit number is a sequences of 160 binary digits, expressed as a base 2 number. The 2 comes from the fact that base 2 is the type of number system what's being used. In the mathematics of permutations and combinations, you resolve the number of combinations by taking the number of possibilities in a given position as the mantissa, and the number of positions as the exponent.

Hence, the number of possible combinations given a set of base 2 numbers with 160 positions is 2¹⁶⁰.

Nice graph at that site.

Check how impossible it is "for now".
http://www.toxigon.com/brute-forcing-bitcoin-brainwallet/

one quindecillion, four hundred sixty-one quattuordecillion, five hundred one tredecillion, six hundred thirty-seven duodecillion, three hundred thirty undecillion, nine hundred two decillion, nine hundred eighteen nonillion, two hundred three octillion, six hundred eighty-four septillion, eight hundred thirty-two sextillion, seven hundred sixteen quintillion, two hundred eighty-three quadrillion, nineteen trillion, six hundred fifty-five billion, nine hundred thirty-two million, five hundred forty-two thousand, nine hundred seventy-six

This many...

With that nubmer of addresses. My computer would give a prgram running (if it was the only program running that had a higher priority). It would take 463,439,129,036,942.83301740386628494 years running at 2Gh/s

Ah yes, good point.  I missed that.

Damn.  I'm suddenly very conscious of my breathing.  If I don't sleep well tonight I'm blaming you.

No, BurtW's analogy works fine under the conception of air as a collection of particles randomly bumping into one another, and I've used the same analogy many times.

Under the conception of air as a collection of particles bumping into one another, the molecules are effectively moving around randomly.  At any given moment in time, ANY arrangement of those molecules in a given space in has equal probability.  There are MANY such arrangements that involve enough air to be in the immediate proximity of the air holes in your face.  There are very few such arrangements that involve insufficient air to be in the immediate proximity of the air holes in your face.  Is there any thing magical about your face that forces enough air to move to that location?  Or are you simply counting on the extremely high probability that the few random arrangements that could kill you will never happen?

Finally, some people that can explain him about the problem.
I'm waiting for you guys

Thank you for this breakdown, and explanation. I was wondering, but too lazy to do the calculation!  So the number of possible bitcoin addresses is in the quindecillions?

That number really is unfathomably enormous.

Just some fun extra observations:

• In storing the addresses, each person would chew through a new terabyte drive every 20 minutes or so.
• If each address were loaded with a satoshi we would run out of satoshis (owing to the 21 million BTC limit) in less than 100th of a second.

A joke.

http://www.directory.io/faq

what is this? -> www.directory.io

As BurtW suggests, lets try some math.

7,000,000,000 people

That includes infants, elderly, and technologically inept, but for the sake of this discussion lets just pretend that for some reason EVERY single living human being on the planet are all continuously generating, storing, and tracking 40,000,000 addresses per second for no particular reason.

This means that world wide, there will be:
(7.0 X 10⁹) * (4 X 10⁷) = 280,000,000,000,000,000 addresses generated every second.

Current estimates are that the universe has existed for approximately 13,820,000,000 years.  There are approximately 31,556,900 seconds in a year.

So, there have been approximately:
(1.382 X 10¹⁰) * (3.15569 X 10⁷) = 435,800,000,000,000,000 seconds since the universe came into existence (long before stars, planets, life, or humans even existed).

So, if every currently living human had been continuously generating 40 million bitcoin addresses since the beginning of time, they would by now have generated a total of:

(4.358 X 10¹⁷) * (2.8 X 10¹⁷) = 1.22024 X 10³⁵ bitcoin addresses.

There are a total of a bit more than 1.46 X 10⁴⁸ possible addresses.

This means that after every currently living human being generates 40 million addresses every second since the begining of time, they would only have generated 0.000000000011977165% of all possible bitcoin addresses.

You do not have to doubt it as a feeling of some sort.  You can actually know it is impossible using math.

BTW 1000 keys per second is very low.  Here is one guy, just one guy, that can do 40+ million keys per second using one graphics card.

I suppose your right.


Seeing as there are about 7 billion people in the world according to google.
7000000000
VS
1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976.

But I mean it does not require alot of resources to create addresses. You could probs create like 1000 adddresses per second. Maybe?

But yeah...Highly doubt it.

Go for it.

No, we did not forget.

It is not just you.  You, me, everyone, as a human beings, cannot fathom how large this number is 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976.

Take a good look at it and try to comprehend how big it is.

what if that person then started selling those addresses, and the addresses become more valuable than bitcoin itself?
that's a sight to see

Everyone is saying we would never run out of addreses. But did you guys forget that one person can create as many as we want?


What if that one person decides to run a script to create new adddresses?

It is indeed more likely for the sun or earth to explode than running out of addresses.

 Once you master bitcoin and mathematics, you should work on your science fundamentals; specifically those regarding density.  Less dense particles would be pushed up by those of higher density... they would "float" as it were; not the other way around.  Technically that's not what BurtW was getting at anyway.

Yes true but the real point I was trying to make is that we do not have to worry about running out of Bitcoins addresses because we have 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976 of them.

Are you now satisfied as far as your original question is concerned?


I imagine BurtW was assuming the many worlds interpretation of quantum mechanics (look up "quantum tunnelling" for more).  Under this interpretation, the conception of air as a collection of particles bumping into one another is only an approximation to the truth.

Because the output of the RIPE-MD160 step in the process that calculates a Bitcoin address is a 160 bit number (hence the 160 in the name RIPE-MD160)

A 160 bit number has exactly 2¹⁶⁰ possible values.

3 - Perform RIPEMD-160 hashing on the result of SHA-256 in the following document:

https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses

I am wondering where you go tthe 2 from in that equation

It is impossible for all of the oxygen to spontaneouly move away from you in a room as there would have to be a less dense particle beneath it, to push it up and it wouldn't do so.

There seems to be some confusion since you are looking at the encoded version of the Bitcoin address.

There are exactly 2¹⁶⁰ possible addresses as long as we keep using RIPE-MD160.

2¹⁶⁰ is 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976.

We don't have to guess at this by looking at the ASCII encoded values (the human readable form you are seeing).

Do you often worry that someday all of the oxygen molecules in the room you are in will spontaneously drift away from the part of the room you are in and you would die?  After all, that could happen, right?  It is not impossible, right?

That should be a bigger worry for you than running out of Bitcoin addresses.

We should be more worried about the extinction of human race rather than the limits of Bitcoin Adresses.

Sorry; i miscounted the number of charactes in my bitcoin app as they are set into sets of 4 so I assumed there were 5.5 sets instead of the actual 8.5 sets!

the address in your signature contains 34.  If I remember correctly an address is 33-34 characters long.  There are no 22 character addresses. 

I meant if the maximum is 33 characters and the number on my address created a few days ago caontained 22 then the number of characters must increase to 23 once al of the probabilities for 22 have been used! Otherwise there is no point in setting a maximum to 33.

It's a newbie asking the question so no I don't think it is a joke.

the short answer is the addresses will not run out.

bitcoin is designed to have far far far more addresses than will every be required.  therein lies its security.

assuming the hypothetical, that there was a collision and you created an address that was already in use then you have direct access to any funds at that address (unspent outputs sent to that public key). However the probability of that happening is so low that it is impossible (see other threads for comparisons to atoms in the universe etc).  We are not talking about winning the lottery odds here, these odds are far far lower, more like winning the lottery in a trillion years type of probability.

Even if only 1% of bitcoin addresses were used up then bitcoin would be considered well and truly broken.

Unlike say, IP addresses, Bitcoin addresses cannot be exhausted.  Instead, the Bitcoin address system would become insecure should the total number of used addresses become a non-negligible fraction of the square root of the theoretical maximum.

You must be joking.  I hope you are joking.  This is a joke, right?

Does the maximum number of addresses increase as all of the previous addresses have been used?

I believe that won't be happen fast, cos the address has 33 characters max.
So it's more than enough for human being, maybe even if we're running out of addresses. It will took a long long time (CMIIW)

If there are eventually no more bitcoin addresses avaliable as all of them are in use: what will happen to the address, will it increase by a letter or will the old addresses be scrapped and new addresses brought in.
This would be unlikely as there are currently:
(22^36) throught the characters that are currently in use (letters and numbers):
2,124,303,230,726,006,271,483,826,780,841,554,627,491,524,509,696