A bitcoin address is an identifier that represents a possible destination of bitcoin payments.It is recommended that user should use unique address for every transaction over bitcoin network.Whenever a user generate a private key bitcoin core protocol allocates a random 256 bit digit number to user as a private key
Since Bitcoin addresses are basically random numbers, it is possible, although extremely unlikely, for two people to independently generate the same address. This is called a collision. If this happens, then both the original owner of the address and the colliding owner could spend money sent to that address. It would not be possible for the colliding person to spend the original owner's entire wallet (or vice versa). If you were to intentionally try to make a collision, it would currently take 2^107 times longer to generate a colliding Bitcoin address than to generate a block. As long as the signing and hashing algorithms remain cryptographically strong, it will likely always be more profitable to collect generations and transaction fees than to try to create collisions.
This arises the question that is it possible that bitcoin will run out of addresses.In short the answer is theoretically it is possible but practically it is impossible.
Let us see why it is theoretically possible ,ah it is not very tough to imagine that out of different 256 bit number two address can get same address at same time.
But imagination is not practical always, so let us see the practical aspect of this:
Chances of Getting same private keys by two users are same as chances of getting same sample space if two person tosses a coin 256 times.On every trial both of them must have same outcome .
Let us think it mathematically : so we have 256 bits number and each bit can have 2 values one or zero,Total number of combinations one can generate with 256 bits are 2^256.
2^256=1.15 * 10^77,which is huge
Total number of bitcoins to be generated till 2140 are 21 * 10^6 bitcoins.
Number of satoshis 21 * 10^6 * 10^8= 2.1 * 10^15 satoshis.
So if we divide number of satoshis with number of possible address (2.1*10^15)/(2^256) what we get is a very very small number which is 1.8 * 10^(-62).
It means that if we store every satoshi to be generated ever in unique address .The number of addresses left are more than enough .
So we reach at conclusion that it is practically no possible that bitcoin will run out of addresses and
