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Is there a limit to the number of Bitcoin addresses? And if so, what stops someone from making all these addresses and holding the private keys for them so no one else can make a new public key?

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Is there a limit to the number of Bitcoin addresses?

If I understand it correctly, there can never be more than 1461501637330902918203684832716283019655932542976 of the current type of addresses. 2160.

what stops someone from making all these addresses and holding the private keys for them ...

Probably:

There aren't enough atoms in the universe to make a big enough computer.

There isn't enough time left in the universe before those atoms cease to exist.

..so no one else can make a new public key?

Other than the improbability of it occurring, there's nothing in the Bitcoin protocols or concensus rules that would prevent two or more people independently generating the same addresses. Any of those people could then spend any money sent to that address.

Which is to say, your bad-actor can't prevent anyone from generating an private-key a public-key or an address.

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  • It may be worth mentioning that holding the private key to an address does not prohibit another user from generating the same address.
    – Murch ♦
    Dec 28, 2018 at 16:47
  • @Murch: Good point, answer amended accordingly.
    – RedGrittyBrick
    Dec 28, 2018 at 16:55
  • Physics nitpick: "There isn't enough time left in the universe before those atoms cease to exist", the most-accepted physical theories postulate a heat-death of the universe, which does not include a deconstruction of atomic matter. Heat-death instead describes the universe reaching a state of thermodynamic equilibrium, which implies no further work may be performed by exploiting entropic differences between different localities of matter. But in either case, your conclusion is right, we won't be able to calculate all possible addresses before that time comes :)
    – chytrik
    Dec 28, 2018 at 21:42
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One would have to flip a coin 160 times. Get the same 1 or zero 160 times IN ORDER to succeed. To get the same address. Is this close?

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  • This does not answer the question. Brute forcing all possible HASH160s will still not allow you to take over the address, since you require a private key, which is 256 bits.
    – Raghav Sood
    Dec 30, 2018 at 8:58

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