Topic: There are more private keys than addresses ? - page 2. (Read 636 times)

The first address starting with "12345" is 12345111111111111111111111114o2pK8, which corresponds to a pubkey hash of 0B5B8501474371E179BFBE6E08AEA6DAC6D84557.

The last address starting with "12345" is 12345zzzzzzzzzzzzzzzzzzzzzzzq2Caed, which corresponds to a pubkey hash of 0B5B88B07F4F1265E590BF6672462DAFDD698ED7.

Converting those two pubkey hashes in to decimal, and calculating the difference, gives the following answer:

I would like to generate a number between 1 and 11003746553177333670973076095724981362930873955835419598865333617435674804223

only after several searches I can’t find anything here is a piece of my code : in golang

This is a legacy address before we encode it with base58:      ^{(thanks to o_e_l_e_o btw)}

Knowing 12345 means that you know the first 8 hex characters of the above. I made that conclusion from this site. This means that you reduce the 16⁵⁰ to 16⁴² which is still a very large number.

It's 2⁴⁴² which is equal with 2¹⁶⁸ different addresses regardless the checksum.

Edit: I just found out that base58 was invented by Satoshi Nakamoto. Wow.

how to calculate the number of addresses starting with 12345 knowing that you don't have to count the checksum

There's a little more to it than that. To turn a RIPEMD160 result in to an address, you first need to add a prefix byte (00 for P2PKH addresses, 05 for P2SH addresses), hash that number using SHA256 twice, add the first four bytes of the result to the end of the previous number, and then encode that number in Base58.

If you take all the WIF private keys which start with 5H, and convert them to hexadecimal, they are between the following two numbers:
and

This is approximately 2^252.6 private keys (and around 9.5% of all possible private keys). So theoretically yes, there will a private key in there which would give every legacy address, of which there are "only" 2¹⁶⁰.

It's called BITcoin because the raw private key is a string of 256 bits so that is 256 ones or zeroes.
A private key which starts with 5 or K or L already contains more information then just the 256 Bits or raw binary key.
It can contain compression type information and also a checksum or a version byte.
You can also look at the number of public points and the addresses that can be spawned off of those.
It's always as small as the smallest possible unit.
So if the space of hash160 is smaller then the private/public key space then the hash160 space will be the limiting factor.
One private key can generate a maximum of 255 type 1 addresses compressed and 255 uncompressed because every bit or one can be translated into an address.
But it can also generate a maximum of 255 type 3 addresses.
And also a maximum of 255 type bc addresses.
So this is already at least 1020 potential addresses for one private key in that respect there are more addresses then private key's.
This is because one private key can visit many public points and those public points can have many types of addresses.
Of course the addresses that exist in the lower bit range are not as secure as the ones that live in the higher ranges.
But those also count as valid and possible addresses.
You could also say that one private key can have many addresses, or that many addresses can have the same (raw) private key.

This is not how you should see it. Private keys that start with 5H, 5J, 5K are WIF. A private key that your computer firstly generates is in hexadecimal. For example:

Then it encodes it to WIF which has a checksum. If you want to calculate how many addresses can be generated by knowing the first character of a private key, then you should do it for the hexadecimal.

For example, knowing the first character of a hexadecimal private key reduces all possible combinations of a private key to 2²⁵². If I'm not mistaken, addresses' combinations remain. The hash of the address is 160 bits which means 2¹⁶⁰.

each private key starts with 5H, 5J, 5K
if I take all private keys beginning with 5H all bitcoin addresses would be there?

Yes. There are more private keys than addresses if you take all possible combinations. Actually a bitcoin address doesn't differ that much from a RIPEMD 160 result. It's just encoded with base58. Hence, all addresses can be 2¹⁶⁰, all private keys are slightly lower than 2²⁵⁶. Hence, every address most likely has an enormous number of valid private keys.

Specifically every address has 2⁹⁶ different private keys on average.

Edit, hosseinimr93 is faster.

ok thanks for info

1 bitcoin address can be generated by 79228162514264337593543950336 private keys

There are 2²⁵⁶ valid private keys and 2¹⁶⁰ valid addresses.

Yes, every bitcoin address can be generated by 2⁹⁶ private keys, on average.

number of privatekeys = 2^256
number of hash160 = 2^160
number bitcoin address = 2^96

1 address can therefore have several private keys ?