Bitcoin Forum

Considering that bitcoin addresses get wasted and discarded like plastic bottles of water, is there ever a risk that we'd use up all the bitcoin addresses?

I realize the possible combinations is 36 to the power of 32, but I don't have a way to make sense of the resulting number. How many address are used in a day? How quickly are we going through these possible combinations?

Maybe in the future there will be a limit of 10 addresses per bitcoin user(or per wallet owner).
I`m familiar with this topic ,but i quess that old addresses can be re-used again,so we will never run out of combinations.

Maybe in the future there will be a limit of 10 addresses per Block bitcoin

Just take an example of the mobile numbers in this world , the most of the countries have mobile numbers digits range between 10-13 digits and they are enough for us and daily we are getting new numbers according to our needs ( new offers in sim ) , so here you can estimate that how we can complete our need with 32 character combination easily .
And in my opinion 100% possible that no one will feel the need of the lack of the bitcoin address .
Second thing is that daily new new users in the internet are coming and daily new VPN services are launching , but still we have no lack of up adress serial numbers and  we are working fine with this , so just chill by leave this problem and enjoy the bitcoin system of variable address .

The actual number of possible Bitcoin addresses is 2¹⁶⁰

This number is so large our tiny human brains cannot comprehend it.

There is no need to worry about running out.  We never will.

There are so many number combination in the address, there capital and small letter plus number, so it will be enough for all of us, and if the address is run out we can simply just add the length of the address, but it will be very long before the address run out of number

Looking at the encoding of the Bitcoin address may be fun and interesting but, like I said, the actual number of possible Bitcoins addresses is 2¹⁶⁰.

We will never run out.  Do not worry about this.

2¹⁶⁰ is about 10⁴⁸

For comparison the number of water molecules on Earth is about  5 x 10⁴⁶

So there are about 20 times more Bitcoin addresses than molecules of water on Earth.

We have enough bitcoin addressees and there is no shortage of it. What makes me feel worried is the total number of bitcoins in circulation.If everyone in the world start using Bitcoins it might get out of supply  ::)

Population growth being what it is, if bitcoin became the only worldwide currency would 2¹⁶⁰ be enough several hundreds of years down the line? According to this UN Report (https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&uact=8&ved=0ahUKEwisvM7ZhMnTAhVrw4MKHeONC48QFgg2MAM&url=http%3A%2F%2Fwww.un.org%2Fesa%2Fpopulation%2Fpublications%2Flongrange2%2FLong_range_report.pdf&usg=AFQjCNEok3R8Dcv5WQOVSoiPVf_12q8_Rg), The population of the world will be around 36.4 billion by 2300. I'm trying to understand there numbers here. Will 2¹⁶⁰ still be enough?

1.46 x 10^48, basically each person have at his disposal 1.46 x 10^39, they can't even dreaming of wasting so many address, if someone on purpose try to do it each day he/she will not have the meterial time to do it

there are only about 31.000000 second in one years and you have 10^39 to waste, which is 1000000000.000000000.000000000.000000000.000, you need something that can waste at incredible speed of 10^33 for each second of your life, not even a yotta(10^24) is enough

Not all letters and numbers are born equal!

I refer to the fact that some letters and numbers cannot be used in a Bitcoin address. This is done intentionally since a number of letters and a number of numbers can be easily confused with other letters and numbers (e.g. I and l, or O and 0). Regarding the OP's question, some folks even tried to find private keys for Bitcoin addresses which had been used on the blockchain before by generating all addresses. They don't seem to have succeeded, at least we haven't heard about that


I guess that could be safely called bullshit (or just a waste of money). It is like predicting in 1800 how many horses would be required in 2000

Yes.  There are so many Bitcoin addresses that the chance of getting the same address twice is zero for any normal purpose, which also pretty much means that the chance of running out of addresses is also zero.  Not that Bitcoin will ever be used by everyone in the world anyway.

Just write down the number 2^160 and you will realize how incredibly huge this is..

As someone said, there are more possibilities than water molecules on this planet. That is insane.

I believe there is definitely enough to go round and even the service providers suggested such to be use and its for security reasons aside that, its not compulsory to use every suggested addresses because it will even increase the amount  of transaction fees to be incurred due to aggregating the amount to be sent from various addresses.

Everything will have a possible solution. Right now everything moves in a right way. So if the bitcoin address seems a drawback then an alternate plans might been made already thinking of the future by the development team. These were minor issues that gets sought easily.

As others pointed out: not really.  

However, the possible number of addresses is not really 2^160, but rather 2^80, and in reality much smaller.  The reason for that is what is called the "birthday paradox".    If you chose 2^80 different addresses at random, out of 2^160, then you start to have a significant probability (several 10%) that two of them are equal.  Which would mean that the private key of the one, also works on the other one.  To make this probability small, one should be a huge factor below 2^80.  Say, 2^50 or so.  That's still of the order of one million billion addresses.  So it is reasonable to limit each human to a few tens of thousands of bitcoin addresses if we want bitcoin to last for a few generations.

This is in fact more limiting than one might think, if one also wants to adhere to "no address re-usage".  It would mean that each of your transactions, in your whole life, would need a new address.  Now that starts to be problematic, because if you do 10 transactions a day, you do 3000 a year, and in 3 years time, you've used up all of your address quota.

But then, we could allow for 2^60 addresses.  That would increase slightly the "collision probability", but it would still be very small (of the order of 1/2^40).  At that point, each human would be entitled to 1000 times more addresses, which would solve the issue.

That too much number digits a human can imagine. When the time comes this number all use up maybe our descendants are living in nearby planet already or this planet inhabitable already. Nice to know this numbers and analogy.

i think bitcoin address is design to fill every want and even more wallet is enough for people and i am sure that in the beginning bitcoin created, satoshi nakamoto and the team behind bitcoin is considering and thinking about this and i am sure that they are thinking that people in the world is getting increase from time to time and no matter how much people is involve in bitcoin world, the wallet address should be enough for them to cover what they need. so i am really sure that bitcoin wallet is more enough for every people.

If there are N addresses on the block chain, the probability of this happening randomly (that is, not done on purpose) is of the order of N^2/ 2^160.

This is why, when N is of the order of 2^80, chances are high that it happened.  When N is of the order of 2^60, chances are of the order of 1/2^40 that it happened.

Wow, I knew that number of possible bitcoin addresses is huge, but never thought that number is higher than water molecules on the earth. It's too big numbers for our brains.
Many people are using new adress for every transaction and also they have generated tons of addresses which hasn't been used ever and will be not used. And still, there will be enough addresses for everyone.
Someone compared it with phone numbers. I think it's wrong. We don't use new phone number for each new call or SMS.

I think the bitcoin addresses are created randomly and they are unlimited so i think there is nothing to worry about the bitcoin address because it is so easy for the bitcoin network to generate new bitcoin address everyday. I think the thing that we should worry about is the supply of bitcoin because when the massive adoption came then there will be a shortage on the supply of bitcoin.

If everyone in the world starts using Bitcoin then Bitcoin will become more valuable and you pay like BTC0.0000001 for a cup of coffee. It would mean that someone who has even BTC1 will become a millionaire. :D

Maybe in 100 years after we are long gone this could become an issue. For now there are plenty of addresses to go around.

Ha... this is not a problem for even another 1000 year... the number is so so so huge...

https://miguelmoreno.net/wp-content/uploads/2013/05/fYFBsqp.jpg

Would just figure out a quicker-expanding generation algorithm and put it into consensus.

With the development of computing technology, not only the numbers advancing, but the generation possibilities too.

there are enough bitcoin addresses and i think they are enough for us.

A silly question, it's like asking you why there are so many people in the world, but no one is the same (except the twins). All bitcoin addresses are made up of complex words, calculate its probability combinations, and you can create countless bitscoins without worrying about anything else. Furthermore, each bitcoin address is independently created, and is stored on a bitcoin basis, so it never occurs overlap. We can rest assured about it.

Not just enough, it is too much for us that everyone can have 10 of them. Bitcoin wallet is unique and so many that is why you don't need to think of these as a problem.

There are far more chances to get struck 3 times by lighting , being chased by a bear, bitten by a shark and win the loto than getting the same address somebody is using.

This will be our last problem.
I'm sure we would be unable to use all the addresses at 7tps /sec  before this galaxy will go dark.

Not only 10, everyone can have any amounts they want, just see those sites which generate a one-time address for a payment or deposits. There are so many addresses available that it needs exactly more than quintillion years to brute force an address by finding its private key randomly. Just as what people have spoken above.

James D'Angelo had a good video on the Math behind Bitcoin and he had a illustration with open post boxes.... that illustration actually made me

realize how big this number is and how impossible it would be to run out of Bitcoin addresses. It is a pity that he made all his videos private, after

he had a rage quit, because that was one of the best videos I have seen on the subject.  ;)

Technically we will run out of address combination after 250-300 years. We dont know yet that whether Bitcoin will survive that long, I dont think even Earth will survive that long if we continue to mine our Planet, So i guess no worries.

That claim has been refuted many times

And exactly according to the laws of physics (or of this Universe if you want me to put it this way). In short, the lowest theoretically possible amount of energy equals the energy of a single photon whose wavelength is approximately the size of the observable universe. You see that would be small enough to theoretically build a device that would count to 2^256 in less than half a jiffy, so "nothing more efficient possible" is a false assumption. And that has nothing to do with thermodynamics as such (as this picture suggests)

No, we will not. 300 years is roughly 100,000 days. If everyone from 10,000,000,000 people will use 100 addresses per day during the next 300 years(which will hardly happen) the number of used addresses will be still not even close to 10^48.

where all this come from do you have a source to back this up? if this was possible it was already real by now, but i don't see anything that can count to 2^256 in a short time like you said, that image simply say thay you need more energy than the universe can hold for now to run a device that can break the 2^256 key, and not even quantum computer can break that

I don't think this is an applicable example. Mobile phone numbers are not similar to bitcoin addresses.

Mobile phone numbers are 1 per phone, so usually 1 number per person...regardless of how many calls they make or how many people need to call them. The only people with exactly 1 bitcoin address are Newbies with a paper wallet that was given to them as a gift or something. If you're using Coinbase, for example, every time you seek your address to give to someone to pay you you're getting a NEW address. Bitcoin addresses are being used almost as frequently as transactions!

We're burning through bitcoin address at a crazy speed, fortunately there are enough unique bitcoin addresses to be created that there isn't a name for the number, it's so big.

Hi Burt, how does your calculation differ from the one I provided? In other words, what am I missing in the math?

I took the number of digits in the public address to the power of the number of combinations. I'm obviously not incorporating the private key.

Also, what system verifies that a new address is created (rather than a duplicate)? Are all addresses generated from blockchain.info?

Good talk here, friends, thanks!

That actually doesnt really matter how many addresses we use a day, if the current Earth population is somewhere around 9 billion people.
The reason is extremely easy, because there are just too many possibilities of a different bitcoin address, to run out of them.

In fact, there is a bigger chance that there is some guy who wins superball every single time in a year, and gets strucked with lightining at every time his heart beats.
That comparision seems insanely ridiculous, but it can show you why it is pretty much impossible to not have any free address: there are simply waaaay to many possibilities to use them all.
Also, the chance to get someones else address while generating is almost 0 too.

Yes exactly the number of combinations possible are extremely large, there is no way (practically) we would run out of bitcoin addresses even if we do, just adding one variable would increase the combinations exponentially.

Don't know what math u used there but don't use it in real life.


And even that is impossible.
Because right now we can do only 600k transactions transactions per day.
So it is impossible to actually use 10billion * 100 addresses.

I think 250 years is end of the world. 250 years is too long and as we can the bible we are last few days. So I think bitcoin addresses will survive because there are many combination of address to made. And it will continue until the developers of the bitcoin is still alive.

I suspect you should actually read what is written in small letters in the image

Apart from that, what source do you need? Did you finish school? If you didn't, then be advised to do that. If you did, you may want to visit it again. The energy of a single  (https://en.wikipedia.org/wiki/Photon_energy) photon is determined by its wavelength. The longer the wavelength of it, the lower will be its energy, as simple as that. Since the text in the picture above talks about the lowest possible energy for storing a single bit (it is not my idea after all, so ask the dude who drew that image), a photon with a wavelength equal to the size of the Universe will have such energy. And I guess you can take as many photons as you need to count in parallel. Further, there is no upper limit on energy in the Universe so even without taking the lowest possible energy to count, the claim is effectively false on its own

Don't worry too much about it. There's enough address for everyone even with our current population growth rate. And even if it comes to the point where there will not be enough, they can impose a limit on how many address a person can make. Also, addresses can be reused anyway.

What you are missing is that the encoded Bitcoin address you are looking at is not the hash of the Bitcoin public key. It is an encoded version of the hash of the Bitcoin public key.


The encoded Bitcoin address you are looking at has nothing at all to do with the private key.  The hash of the public key is a 160 bit number.  To that 160 bit number a checksum is added and then it is encoded.  That is the Bitcoin address you are looking at.  Basically it contains the checksum bits so it has more bits that the 160 bit public key hash. The checksum is added so that if you type it incorrectly it can be recognized as an invalid Bitcoin address.

Bitcoin private keys are approximately 256 bits long.  They are generated randomly.  It is just the immense address space that is used to avoid collisions.  There is no checking to see if there is a collision.  Then the public key, which is actually a point on an elliptical curve is calculated from the private key.  The public key is a point on a curve with an x and a y coordinate.  Then the public key is hashed three times and this produces the 160 bit hash of the public key.  Then the checksum is added and the whole thing is encoded and then you have a Bitcoin public address.

Note that there are approximately 2⁹⁶ public/private key pairs that map to each of the 2¹⁶⁰ Bitcoin addresses.

Good to talk to you.  It is refreshing to find someone who actually reads a thread instead of just stopping by, reading just the OP (or even just the title), and then leaving a steaming pile of their opinion in the thread just to bump their post count.

You are right, 2¹⁶⁰ is too high number for bitcoin address. I don't think that one day will reach this number of btc address even in 40 years later.
So, we don't need to worry about it, So we can use our address normally like we do now.

As for me, I will never worry about this kind of thing and I believe Bitcoin address is enough for all of us and if it is proven to be not enough, developer will make it enough.  There are lots of approaches to solve this problem and honestly, I think this is an easy to fix issue.  Just what I read on the previous post, telephone numbers or cellphone numbers uses far too short numbers of combination but everyone have enough. Bitcoin is ever evolving, that is the assurance that we will have enough Bitcoin address for everyone.

Indeed, number of address are almost infinite compared to anything we can imagine as human.  I totally agree that a possible issue is the number of bitcoin in existence.  IMO, sooner than later, we will speak in Satoshi..

What the heck are you babbling about?

Laundauer's limit defines the amount of energy needed here.  
https://en.wikipedia.org/wiki/Landauer%27s_principle

The only thing inaccurate here is that brute forcing a key doesn't require 2^256 as you only get 128 bits of security from a 256 ECDSA key.  Unused addresses have 160 bits of security.

Of course it will be more than enough. Bitcoin addresses have a combination of letters and numbers. With that in bitcoin could create billions of addresses. So you should not be afraid the bitcoin address will be exhausted lol

stop shitposting and read the thread next time before you reply. 

I think we don't need to take worry about such things because already the blockchain network made plan for such things to handle .
As an example we can estimate that we can complete our need with the fee numbers of the digits in ip adress , so you shouldn't​ worry such things .
Recently a system of up adress in the internet is going to change from iov4 to ipv6 so it may be possible if the limit of the adress in bitcoin came then they will start to any new pattern of Adress like the up adress .

Did you read my posts above and before?

I think you may really want to read them again to understand that you have chosen the wrong person to jump at. If you still fail to understand what my "babbling" is about (which I'm not surprised, anyway), I can tell you that the question is certainly not about building a real computer (as the legend makes it unambiguously clear). Nevertheless, I can point you to the relevant part which you seem to have missed entirely:


So wtf are you attacking me here? And what exactly do you disagree with?

I have encountered this kind of thread before asking if the number of bitcoin adresses is adequate for all users so this question is not new at all. As for my side, it would seem impossible (if not possible) to use all addresses. These addresses are intended to be used by everyone across the globe so its number was planned beforehand. As for the probability of usage 10^48 is so much. Let us say than the actual number of user is about 10^9 (saying that all people are using bitcoin at some point in the future), if we are to use multiple addresses, we can use about 10^39 each. By any chance that you can use them all up? To think that not all users would use so much addresses so why bother.

Yes, that was my point. Even if it was technically possible to do so many transactions per day we still wouldn't run out of addresses. So the answer to the OP's question is there are enough addresses for us all for the next billion years.

but what you refer is another thing in that image they are talking about brute forcing, not the lowest possible energy, and brute forcing isn't possible no matter how much energy you get, this was the point of that image, nitpicking and playing with semantic just to say that something is wrong is stupid

You make me laugh when I read this article, a silly question. Anyone who has graduated from high school knows this, bitcoin addresses are made up of a long and complicated sequence of characters that are encrypted and connected to a system to avoid duplication. Repeat happens, so, even though the whole world uses bitcoin, there is always enough address for everyone. Never ask such questions, it wastes everyone's time.

Yes, I agree with you time will come the combinations will be use already and reach its limit so those who kill thier accounts will be use again by others those with dead accounts that is not use for so long. But maybe this will not gonna happen anytime soon. First we need to consume all addresses and then we could have shortage, maybe after 50 years.

How is it stupid to say and prove that something is wrong?

Are you serious or what? The creator of that image bases his point on the premise that it is not even hypothetically possible to count to 2²⁵⁶ given the resources available in the Universe. So, according to you, proving that this premise as absolutely wrong is nitpicking and playing with semantics? May I ask you what semantics do you refer to here? Maybe, it is in fact you who is "playing with semantics" in this case?

If I counted right the bitcoin address has 32 marks and consist from numbers and letter. The phone numbers are much shorter and they are enough for everybody, and not used numbers with the time are coming to new users. So, I think with such wide combination of numbers and letters bitcoin wallets will be enough to every human on the Earth get his own.

BAN ALL PAID SIGNATURES

Fucking shit posting dipshits.  Read the thread, contribute to the thread or don't post at all.

We have to fix this.

Because there's no observable thing.  I believe such wavelengths are always microscopic, let alone "the size of the universe".   And even if there was, that wouldn't refute anything in that image.

There are approximately 2²⁵⁶ public private key pairs.

There are approximately 2¹⁶⁰ Bitcoin addresses.

Due to the birthday problem effect we can only use 2⁸⁰ Bitcoin addresses.

To be safe this should be reduced to at least 2⁷⁰ addresses.

There are on the order of 2³³ people on the planet.

This means each person on the planet gets 2^{70 - 33} = 2³⁷ addresses.

Put another way, the large bitcoin collider system here

https://lbc.cryptoguru.org

is capable of generating over 2⁵⁵ keys per year so they will generate 2⁷⁰ Bitcoin addresses in about

2^{70 - 55} = 2¹⁵ = 33 thousand years

Now you do not need to guess at the number just to post your fucking paid signature.

I'm not quite sure what you mean by "observable thing" (or the lack thereof)

If you mean the observable Universe (which is what I myself mean by the size of the Universe), this seems to be a pretty well established (https://en.wikipedia.org/wiki/Observable_universe) concept or notion. Regarding wavelengths, more specifically, you may want to read more about  (https://en.wikipedia.org/wiki/Electromagnetic_spectrum)electromagnetic spectrum. Radiowaves (which are the same photons, if you didn't know) have lengths starting from meters and all up to hundreds and thousands of kilometers. That's basically why they can circle around the world. These waves can penetrate seawater as well, which is why they are used for communication with submarines

Yes I think there are enough for us all because we can make accounts using bitcoin. And all are free and is accepted in this program as long as you have an internet connection in able to register on this program. Bitcoin is really enough for us all and it is really useful to be used.

^  lol... sorry Burt.  its gonna just keep happening. 



You are right that the waves can be long.  I didn't know that.

However, according to this, the longer the wavelength, the less energy it has
https://en.wikipedia.org/wiki/Photon_energy

So what happens if I alone could generate 100 million addresses and save them all with private keys if I had a powerful computer?
I want to know the CPU power, required computational power to generate 100 trillion addresses each day?
Nothing like bitcoin collision guys are doing since their job requires more computing power than just simply generating addresses.

@Burt, could you give me an estimation on the CPU power to generate at least %80 of all the possible pairs? for example the current hash power of bitcoin network if were to transform into only key generation how many years would it take to do the %80?

I don't think you described the birthday collision accurately.

There are still 2^160 Bitcoin addresses.  All of them are usable.

The Birthday collision only means that if you keep generating addresses,
you will generate the same address about once every 2^80 times. 

A bitcoin address is basically a RIPEMD-160 hash of the public key.
So, if you generated 2^80 public keys and hashed each one,
you would have about a 50/50 chance that you'd end up with
the same Bitcoin address as the output of two different hashes.

This is why there are 2^256 private keys and only 2^160 addresses.

The important thing is that any given Bitcoin address still has 160 bits of security
since you cannot use the birthday attack to crack a private key.

Oh, now you come to see my point

And after you take a photon with the longest possible wavelength (which would be equal to the diameter of the whole Universe), you will have a particle with the lowest possible energy as the picture above (or before) suggests. So, if you then accept the basic premise of that picture, i.e. the lowest possible energy level corresponding to logical 1 or 0, and look at the estimated total mass-energy of the Universe, you will see that there is nothing extraordinary in just counting 2²⁵⁶ (and that would have nothing to do with Laundauer's limit, just in case). And this is just one approach which disqualifies the "facts" presented in the "cute picture". There are a few others which involve time quantums (i.e. not linked to energy as such)

100 trillion is actually a pretty small number.  The new Antminer S9 does 14 TH/s.  That's 14 trillion hashes a second.   You need I think 4 or 5 different hashes to get an address.  
https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses

The entire bitcoin network is almost a million times more powerful.  It  generates 4.5 million TH/s,  (so lets just approximate 1 add/key = 4.5 hashes to get a round number) -- that's 10^18 pairs a second.

This is still very small compared to 2^160, which is more than 10^48... So add another 30 zeroes.  

It would take the entire bitcoin network literally more than 50 million trillion millennia to generate all the addresses....and this is assuming no collisions!, which Burt pointed out.
To actually generate all of them, worst case you need to do 2^256 like the cute picture says :)

I read about this many times in this forum, and there was a good explanation about the chance for the person to get even the same address as someone else as to happen AFTER the sun has expired. Meaning to say, even if it is possible, our planet would be destroyed first. In which case, it is not a worry:)

I read a lot of this article:

https://en.wikipedia.org/wiki/Birthday_problem

Specifically this statement:


And the table in the article titled "Probability table" which shows that at 2^N/2 the probability of a collision is about 75%, which is totally unacceptable.  Therefore, I concluded that about 2⁷⁰ addresses is all we should use before we start getting too many collisions.

2⁷⁰ is just an estimate.  If we can agree on what is an acceptable probability of a collision 10^-15? 10^-18? etc. then we could calculate a more exact acceptable number of Bitcoin addresses to be used (before we switch algorithms).

Right.  If we had 2^80 addresses in use , we would have a good chance to see a single collision.

I just didn't want people to get the wrong idea like you could crack keys by generating 2^80 addresses.

So much letter and number in the bitcoin address i guess it almost impossible to hack and with that combination i think that's enough for us but as many bitcoin user's creating wallet even one bitcoin user's almost have a 5-10 wallets.

Go to hell sig spammer.  Reported.

In fact I am going to go back and report every one of you assholes in this thread.  I hope you all get perm bans.

Considering if all of the people in the world would use bitcoin but in my opinion will not anytime soon, and your need to picture this out there are trillions and trillions of combination that the wallets have been making and it is not consist by only numbers alone but a combination of capital and small letters and numbers that is why there are so many combination a wallet can give to all users I think they can accommodate all users of bitcoin regarding there are many people using a multiple accounts on wallet!

^^ POS sig spammer reported

The amount of bitcoin addresses that can be generated is 2^160, and that, alone is incomprehensible and wouldn't be exhausted for the next 100 (or even a millenia) or so years should a billion of bitcoin users change their addresses 10 times a day. You need not to worry about losing an address, what you need to worry more is the security of your wallet and coins above anything else.

Yes, there is no doubt that we are not going to have any issues with the amount of bitcoin addresses available for particular persons.
There is no problem for every single person on earth to have even 10,000 wallets, there are still so many possibilities that there is enough of combinations to allow 9 billion people to use blockchain network with their own addresses.

Take a look what option do blockchain.info wallet services provides: obviosuly, many other wallet softwares are providing the exactly same thing, but it is just an example.
Every time you want to transfer any bitcoins on your wallet, or give an address to someone to transfer them: the programme changes the address on which you send.

That still does not make any difference, still that is enough of combinations for whole human kind.

So I'm curious, what is the definition of the birthday problem effect in this context? I assume that's the sort of weird mathematical issue where a room of 23 people has something close to a 50% chance of having two people who have the same birthday, so how does it have an impact on the amount of addresses that can be used before there is some kind of overlap? Is it the same thing where approximately only 1 in every 16 usable addresses are actually "useful" since you approach (and pass) a 50% chance of there being a copy of a public key somewhere?
I'm looking at the wikipedia page and the math they use, so is the equation for the pub addresses the same calculation, just modified to p(n)=1*(1-(n-1/2¹⁶⁰))?
I rarely do this kind of math so I'm curious. I wish I got to learn more about it but I only ever do very supplementary math or just read/watch stuff online. Either way it still surprises me that the probability curve moves in the way it does.
I apologize if this is something that I should be going and learning somewhere else.

Not sure what you are confused about.  The "room of 23 people having 50% chance to have a birthday collision" is the same exact principle, except that instead of 365 days, there's 2^160 bitcoin addresses...and instead of 23 people, its 2^80.

If the total bitcoin addresses in use worldwide reaches 2^80, there's a 50/50 chance you'd see one collision.  2^80 doesn't seem like that much (its about a trillion trillion)...this could be generated in about 2 weeks using the entire bitcoin network.  But we wouldn't grow much beyond that without taking a very large amount of time, so practically speaking, collisions aren't a problem.

there is no problem with bitcoin addresses, the number is big enough for all of us. There is almost no chance to see the same address generated.

I agree, if ever the saturation level of bitcoin address is about to be met, developers will always find another way to add more to the Bitcoin address, adding an extra number or reducing it by a number would greatly increase BTC address capability.  So definitely it is not a problem at all.

Undoubtedly. There are many other crucial problems to be solved in the bitcoin ecosystem, but this one does not seem so urgent, at least for the next ten years.

Please see my related thread here:  https://bitcointalk.org/index.php?topic=1895455.0

(no asshole signature spammers in my thread!)

not sure, a quantum computer with the Grover’s algorithm have better possibility to resolve a collision than normal computer wer have today, they might pose a threat, and they are not so far away in the future like many think

Well, I put the safety much more severe at 2^50 or 2^60, because at 2^70, there's still a chance in a million that a collision will occur.

https://bitcointalk.org/index.php?topic=1891830.msg18795938#msg18795938

That said, the conclusion is that for the moment, there's nothing to worry about, and by the time it becomes a problem, one could always increment it.

BTW, by the time it becomes worrisome, the cryptographic security of the thing becomes problematic too, because if there are 2^70 transactions on the chain (otherwise, 2^70 addresses cannot exist), and a normal spending needs nodes to look quickly through 2^70 transactions, it means that processing power is going to reduce the safety margin of a lot of things.

Most probably, bitcoin will have shut down before reaching that level.  Maybe humanity will have shut down too by then. 

I wonder what size the blockchain would be then

Apart from that, quickly looking up a transaction should not be an issue even with so many transactions provided the data is organized in a proper way and you don't have substantial delays with accessing this data. As I see it, the main headache would be adding new transactions to a search tree if you want to provide quick lookups. So to find a single transaction in a tree with 2⁷⁰ nodes would require you only around 35 iterations on average, while adding a new transaction to such a tree should get pretty expensive in terms of number of iterations

https://bitcointalk.org/index.php?topic=24268.msg304195#msg304195

There are exactly 1461501637330902918203684832716283019655932542976 addresses possible. We only have 7 billion people on earth, so I wouldn't call it a problem situation.

On another note you shouldn't worry about the brute-force attacks on private keys either:

https://miguelmoreno.net/wp-content/uploads/2013/05/fYFBsqp.jpg

but it's not wrong, the statement say that you can't bruteforce a private key of 256 bit which is true, what is wrong about this exactly? you are nitpicking a portion of the phrase and take it out of whole context just to prove something else that has nothing to do with the final principe on which that image is based

You seem to have apparent issues with logic and reasoning

If we follow the assumptions in that "cute image", it will be a wrong statement flat-out. The point of this image is that with all resources existing in the Universe (well, in the Solar system), it won't be possible to even hypothetically find all the keys. If you didn't notice, cracking all the keys is considered equal to counting to 2²⁵⁶. If you disagree with that, don't "bruteforce" me since it is not my assumption, after all. I didn't think up anything myself, I just followed the assumptions taken by the author of that image which as he thinks prove his point. In fact, you don't even need the whole Solar system to do that or energy as such

This thread has been totally trashed by signature spammers.

I have started a thread for serious discussion about the application of the birthday problem to the 160 bit hash space of Bitcoin.

Please join the signature spam free discussion here:  https://bitcointalk.org/index.php?topic=1895455.0

I may copy a few of the interesting posts from this thread over there.

Even global population wont able to accumulate all bitcoin addresses and i cant think of that we would ran out of possible combinations considering there are long combinations even having a capitalization of a certain letter would already give the difference which theres no sense to be worried about even all people would really use bitcoin and having their own wallet addresses, Dont make to stress into yourself.

Maybe you can re-summarize your point in a sentence...it seems to have gotten lost.

I don't have issues with summarizing

Here's just one sentence. Computing is an illusion. If you want a more detailed answer I can explain it to you in a greater detail (no problem with that either). What we think as computing (in practice) are no more than some physical processes going on at the lower level. It is the way we interpret them that turn them into "computing". Thereby, any claims that something cannot be "computed" with reference to some physical parameters, constants or qualities (e.g. lowest possible energy) are conceptually false, since at the lowest, physical level "computing" as such doesn't even exist. These claims are just meaningless

That is true.  However, one may very well define mathematical problems of which the computation cannot be performed in the observable universe, at least, with a given algorithm.

I would think that we start to reach some reasonable upper limit of "number of steps in a computation that the observable universe can perform" if we consider the number of Planck "volumes" in the estimated state space of the observable universe.

But they take time and energy.

I think this is not so

I see where you are getting at but I still think this is not the real limit. You basically make the same mistake as the ones who are trying to challenge my point, though at another, higher level (if that comforts you somehow). Now see how I can explain that in just one sentence again (you know why I say that). In short, in real world you may not need to take or make all the steps which your algo requires to get the result of your computation. As I understand it, this is what quantum computing is essentially about. You don't need huge amount of time, energy and effort if you can just obtain the result directly without actually having to "compute" anything (computing as a sequence of steps leading to a certain result according to the rules of some algo)


Claims require time and energy? Meaningless claims certainly do, that's why disproving meaningless claims is as meaningless. If someone starts claiming that Earth is flat and Elvis Presley still alive, are you going to prove him wrong?

computations take time and energy

Yes, your meaningless claim took time and energy.

Counting also takes time and energy.

Prove me wrong.

Proving me wrong will also take time and energy.