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The question is not about how bitcoin mining works, but rather how bitcoin system adapts to progress in ability to tackle proof-of-work problems.

Suppose that proof-of-work problems used for bitcoin mining become very easy to solve. (eg. P=NP with very fast practical polynomial-time solver, though of course unlikely, but let me play a hypothetical game.) Then it seems that bitcoin system would collapse - 32-bit nonce may be insufficient to counter how fast proof-of-work can be done, in case that this becomes reality.

Is there any part in the current bitcoin implementation that would protect the bitcoin ecosystem from this type of collapse? Is the "difficulty target" system enough to resolve the hypothetical issue?

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    A sidenote: The 32-bit nonce (i.e. ~4 GHashes) has been far from sufficient for a long time. – Daniel R Nov 24 '17 at 11:36
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They already did find a faster way. Bitcoin mining now is run on specialized ASIC chips but it wasn't always that way. In early days it was CPU or GPU.

So nothing happens really, difficulty will adjust so that new blocks are found every 10 minutes on avg.

If this new mining tech is only in the hands of one entity though, then they could potentially do bad things, but your question was "What happens if everyone...".

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The difficulty adapts dynamically to the increasing capability of miners to solve the proof of work, in order to maintain a 10mins block time. If some new tech (like quantum computing) would make the current POW trivial then Bitcoin would have to switch to another POW or any other working consensus mechanism. This would require a hard fork.

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A typical miner runs through all possible nonces in a fraction of a second. Fewer than one in a trillion times will it find a nonce that works. It then tries all the possible nonces for a different block and repeats this process over and over.

The 32-bit nonce doesn't have to be "sufficient" for anything special.

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