A few questions about addresses

[nimda]

1. Given the current nature of addresses, how many total addresses are possible?
2. How many addresses currently have bitcoins?
3. How many addresses with BTC will it take for it to become profitable to generate addresses at random and check their balance, then send all of its coins to another address?

For #3, assume that the addresses are being generated as fast as possible, i.e. without any regard for security. The private key might as well start at a random seed, then simply be incremented. With these provisions, I think 20 MKeys/s is a possibility.

[1715300586]

1715300586

[Pieter Wuille]

1) There are 2^160 = 1461501637330902918203684832716283019655932542976 valid normal addresses.

2) In januari, there had about 3 million addresses been used, with 123000 holding a >1BTC balance.

3) never

[Boussac]

3) never

Isn't that the short answer, the long answer being "it's far more profitable to mine than to try to hit a random funded address" ?

[Pieter Wuille]

The long answer:

Assume the entire current bitcoin hashing power switches to mining addresses. Assume it consists of all GPU's. Assume a GPU doing EC math can produce 1 address per 10 bitcoin hashes. This results in roughly 1 TAddr/s (tera address per second). This results in about 3*10^19 addresses per year.

Assume all bitcoins are mined and in circulation, and perfectly distributed and thus there are 21M addresses that each hold 1BTC. This is equivalent to saying that one in 7*10^40 addresses is interesting.

This means that each year of mining by the entire network would result in a chance of 1 in 2*10^21 for finding *at least* one interesting address. This means that after about 1.5*10^21 years (120000000000 times the age of the universe), there is a chance of around 50% of having hit one.

In other words: never.

[nimda]

Great answer, thanks!

[Vod]

Awesome answer!

[Boussac]

Thanks sipa for this thorough answer.

Incidentally, I have read somewhere that there are approximately the same number of bitcoin addresses as there are atoms on earth.
Did anyone check that ?

[Foxpup]

Thanks sipa for this thorough answer.

Incidentally, I have read somewhere that there are approximately the same number of bitcoin addresses as there are atoms on earth.
Did anyone check that ?

I guess it depends on your definition of "approximately". There are actually about 70 times as many atoms in the Earth as there are bitcoin addresses:

Number of bitcoin addresses (2^160): 1.462 quindecillion
Number of atoms in the Earth (according to Wolfram Alpha): 100 quindecillion

[Boussac]

Thanks sipa for this thorough answer.

Incidentally, I have read somewhere that there are approximately the same number of bitcoin addresses as there are atoms on earth.
Did anyone check that ?

I guess it depends on your definition of "approximately". There are actually about 70 times as many atoms in the Earth as there are bitcoin addresses:

Thanks: that's close enough