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When miners find a solution to a block and broadcast it, what is the incentive for the other miners to actually validate that it is correct? It seems that they might save time by just starting to work in the next block instead of validating. Do they get some kind of reward or penalty?

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what is the incentive for the other miners to actually validate that it is correct?

The incentive is to not mine a block on top of something that is invalid. If they do end up mining on top of an invalid block, then they waste effort (and thus money) on something that will never be accepted by the rest of the network.

It seems that they might save time by just starting to work in the next block instead of validating.

They do save time, and in fact, many miners actually do not validate the previous block before they start mining on it. While there is an incentive to validate blocks, no one can force anyone else to validate a block and the incentive is not high enough for miners to always validate a block before mining on it. Since invalid blocks happen rarely, many miners have found it unnecessary to validate blocks before beginning to mine on top of the block.

Many miners will still validate the block, just after they have begun mining on it. They instead will validate a block whilst they are already mining on it and only stop mining on it if it turns out to be invalid. Although they can lost money by doing this, the risk is not that great because blocks are rarely invalid but the reward is great due to the extra mining time.

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The incentive to validate blocks comes from the fact that future blocks build upon it. If a miner skips validation and just starts building a new block and it turns out that the rest of the network has rejected the previous block, any new blocks the miner creates linking to the invalid block will also be rejected, and the miner will lose any work they put into those.

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